Controlling the inlet valve of an oil-injected screw compressor

Transcription

1 FACULTEIT INDUSTRIELE INGENIEURSWETENSCHAPPEN CAMPUS Groep T Controlling the inlet valve of an oil-injected screw compressor Matlab based modelling and preliminary mechanical design based on present-day valve technology Jeroen AFSLAG Laurien MICHOTTE Promotor: Prof. Dr. Ir. Peter Slaets Co-promotoren: Ir. Joris Mertens Masterproef ingediend tot het behalen van de graad van master of Science in de industriële wetenschappen: Elektromechanica Prof. Dr. Ir. Maarten Vanierschot Academiejaar

2 Copyright KU Leuven Without written permission of the supervisor(s) and the author(s) it is forbidden to reproduce or adapt in any form or by any means any part of this publication. Requests for obtaining the right to reproduce or utilize parts of this publication should be addressed to KU Leuven, Campus Groep T Leuven, Andreas Vesaliusstraat 13, B Leuven, or via fet.groept@kuleuven.be. A written permission of the supervisor(s) is also required to use the methods, products, schematics and programs described in this work for industrial or commercial use, and for submitting this publication in scientific contests.

3 FOREWORD This thesis is written as completion to the master of Science in Engineering Technology, at the Catholic University of Leuven. Our master program focuses on electromechanical engineering with option intelligent mechanics, which relates to designing, developing and optimizing automated mechanical machines. The subject of this thesis, controlling an inlet valve of an oil-injected screw compressor, falls within the scope of this masters field because simulating the system, as we will explain later, plays an important role in the automation of the valve. The subject is selected in co-operation with Atlas Copco and since October 2016, we have been conducting research on this topic. We experienced this period as very thoughtprovoking and instructive. At the beginning, our knowledge about compressors was restricted. The research was difficult, however, extensive investigation allowed us to achieve a result with which we are very satisfied. Several persons have contributed to this project and we would like to take the opportunity to thank them. First of all, we would like to thank Atlas Copco for the chance they gave us to investigate this topic. In particular our supervisor, Joris Mertens, who guided and supported us in all circumstances during this project. We also wish to thank another colleague, Jose Baltazar, who helped us with the CFD analysis of the valve. This thesis would of course never be possible without the help of our supervisor Peter Slaets and co-supervisor Maarten Vanierschot. We would like to thank them for their time, valuable input and support throughout the entire master period. Their critical view and comments were a source of inspiration for the theoretical development and end result of this thesis. Last but not least, we would like to thank our parents for their constant support during our studies. If we ever lost interest, they kept us motivated. Thank you for everything. Laurien and Jeroen 16 th of May, Leuven i

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5 ABSTRACT A recent study proves that increasing the turndown ratio of a variable-speed drive compressor ensures higher efficiency. Atlas Copco wants to avoid the shut down of this compressor type, when an operator decides to decrease his demand for compressed air. A valve, which throttles the inlet of this machine, allows further reduction of the current percentage of the turndown ratio. This thesis focuses on the selection of an appropriate valve and combines this with modelling the system using a Matlab based simulation. The selection of the valve is based on different criteria such as operation pressure and temperature, but more importantly, the throttle characteristic. Taking the sealing of the valve into account, this literature study selects three valves, which provide the optimal control at the inlet of the compressor. The next part focuses on modelling the system by comparing a theoretical approximation with a more practical derivation of the system models. The latter results in a second order system for the compressor, which is in contradiction to the zero order model of the first approach. To determine a model for the valve that is based on thermodynamics, a mechanical implementation is necessary. Without this, it is impossible to determine the valve-sizing coefficient that allows to estimate the pressure drop across the valve. A secondary, experimental approach examines these models by applying a step response to the inlet of the compressor. By sampling the pressure at the in- and outlet over time, a transfer function is estimated by the use of a Matlab toolbox, namely System Identification Toolbox. The best fit for the compressor itself is of second order. After identification of the entire control loop, a controller is designed and selected in accordance with the requirements of the customer. Investigating both a PID-controller and a lead-lag controller, allows to identify an estimate of the optimal result with a minimal overshoot and relatively fast settling time. A combination of these two types of controllers seems the best fit for the system requirements. A further investigation of the differences between the systems is necessary, on top of a detailed mechanical design of the valve. Keywords: Variable-speed drive compressor, PID-controller, lead-lag controller, oilinjected screw compressor, valve modelling iii

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7 EXTENDED ABSTRACT Atlas Copco is momenteel marktleider op vlak van de turndown ratio van variable-speed drive compressoren. Deze eigenschap geeft de verhouding weer tussen het maximale en minimale inlaat debiet dat net geen overbelasting van de compressor veroorzaakt. Om de concurrentie voorop te blijven, leek het hen noodzakelijk om deze eigenschap van de huidige 20% naar een nog lagere verhouding te kunnen brengen. Verschillende soorten kleppen laten toe om de inlaat van een compressor te smoren en zo het ingaand debiet te verminderen. Dit heeft als gevolg dat men een uitschakeling van de compressor vermijdt. Sommige van Altas Copco s klanten verminderen hun vraag naar gecomprimeerde lucht, wat leidt tot inefficiëntie. De implementatie van een inlaatklep maakt het mogelijk de levensduur van de machine te vergroten. De modellering van dergelijke toepassingen maakt in dit geval gebruik van een klant die vier bar vraagt aan de uitlaat van de compressor. Op een bepaald ogenblik besluit deze klant de vraag naar gecomprimeerde lucht te verminderen. Een staprespons, waarbij de uitlaatdruk plots stijgt met een bar, stelt deze verstoring voor in de simulatie. De selectie van de geschikte klep gebruikt verschillende criteria waaraan het ontwerp moet voldoen. Een van deze beperkingen is de smoorkarakteristiek. Als de klep in staat is om het ingaand debiet te controleren, moet deze bovendien ook bestand zijn tegen de aanwezige temperatuur en druk. Na het maken van deze analyse blijven slechts drie kleppen over die geschikt zijn voor deze toepassing: een iris, pinch en vlinder klep. Deze laatste heeft als nadeel dat ze meerdere seals vereist om afdichting te garanderen. Zo is er een seal meer nodig, in vergelijking met de iris en pinch klep, om te vermijden dat er gecomprimeerde lucht verloren gaat. Dit verhoogt met andere woorden de kans op een verlies aan gecomprimeerde lucht. De klant wil een systeem dat zo efficiënt mogelijk is en net hierom besluit men om enkel de werking van een iris en pinch klep verder te onderzoeken. Nadien volgt de modellering van het systeem door een vergelijking op te stellen tussen een theoretische benadering en een meer praktische afleiding van de verschillende modellen. De controle lus zelf bestaat uit vijf onderdelen: de controller, de actuator, de klep, de compressor en tot slot de digitale druksensor. De modellen van de inlaatklep en de compressor zijn gebaseerd op de wetten van de thermodynamica, waarvoor enkele aannames noodzakelijk zijn. Zo is het fluïdum, dat in dit geval gecomprimeerde lucht is, benaderd als een ideaal gas. Om de wiskundige complexiteit te vereenvoudigen, wordt een isentrope compressie aangenomen. Dit resulteert in een wiskundig model van orde nul, dat elke invloed van inertie in dit systeem negeert. Anderzijds maakt de transferfunctie van de klep gebruik van een valve-sizing vergelijking die de vorm van de klep in rekening brengt. Om deze vergelijking te kunnen gebruiken, bouwt men de klep in om vervolgens de drukval erover te meten en de coëfficiënt experimenteel te benaderen. v

8 Een tweede, experimentele benadering gaat deze modellen na door een staprespons aan te leggen aan de inlaat van de compressor. Door het samplen van de druk aan de in- en uitlaat, wordt een transferfunctie geschat met behulp van een Matlab toolbox, namelijk System Identification Toolbox. Deze toolbox geeft aan dat de beste fit voor de compressor van tweede orde is. Matlab bepaalt dit op basis van een percentage dat aangeeft hoe nauw het model aansluit bij de meetresultaten. Dit betekent dat het vooraf bepaalde, theoretische model inaccuraat is. Het experimentele systeem heeft bovendien een controller nodig om de gewenste vier bar te kunnen bereiken. Bij het aanleggen van een stap naar vier bar aan de inlaat van de compressor, zal het model bij een lagere druk settelen, indien er geen controller aanwezig is. Om een controller te ontwerpen moeten verschillende criteria mee in rekening gebracht worden. Naast het feit dat het systeem zo snel mogelijk moet reageren, is er een beperking in overshoot nodig. Het is voor de compressor onmogelijk om meer dan vier bar te leveren, indien de referentie op deze waarde is ingesteld. Daarom laat men geen enkele vorm van overshoot toe. Dit punt komt overeen met een net niet, marginaal stabiel systeem. Het nagaan van zowel een PID-regelaar als een lead-lag controller, resulteert in de conclusie dat een combinatie van beiden het optimale resultaat geeft. De PI-controller verhoogt de reactietijd tot het punt waarop het systeem bijna start met oscilleren, terwijl de lead-lag controller deze oscillatie net vermijdt. Een verbetering van het theoretisch systeem is noodzakelijk. Omwille van de complexiteit van de verandering in intern volume binnenin het schroefelement, vormt de wiskundige representatie een probleem. Een Computational Fluid Dynamics model kan dit probleem oplossen. Het combineren van voorgaande informatie in het mechanisch ontwerp van een iris klep resulteert in een 3D-model dat geoptimaliseerd is naar de doorlaatoppervlakte van de klep. Door deze verder te verkleinen, vergroot het effect van het smoren. Aangezien Atlas Copco momenteel marktleider is in dit onderzoeksgebied en er bovendien niet echt vraag is naar verbetering op het vlak van turndown ratio, zal deze technologie enkel leiden tot een hogere verkoopprijs. In overleg met het departement aankoop binnen Atlas Copco, is besloten dat deze investering momenteel nog niet rendabel is om te implementeren. vi

9 FOREWORD ABSTRACT TABLE OF CONTENT... I... III EXTENDED ABSTRACT... V TABLE OF CONTENT... VII LIST OF FIGURES... IX LIST OF SYMBOLS... XI LIST OF TABLES... XV INTRODUCTION LITERATURE STUDY Selection criteria Different kind of valves Suited valve Modelling THEORETICAL MODELS System identification Model of the iris valve Model of the friction losses in pipes Model of the compressor PRACTICAL MODELS Measurements System identification COMPARISON OF THE THEORETICAL MODELS AND THE EXPERIMENTAL APPROXIMATIONS Differences between the systems Selection procedure for the controller Influence of a PID-controller Influence of a lead-lag controller Correction of the theoretical system CONCLUSION REFERENCES APPENDICES vii

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11 LIST OF FIGURES Figure 2-1: Control loop... 9 Figure 3-1: Experimental setup Figure 3-2: Flow - orifice diameter characteristic Figure 3-3: Pressure drop across the valve in function of the changing diameter Figure 3-4: Influence of throttling the inlet over time Figure 3-5: Simulation of the outlet pressure with or without a controller Figure 4-1: General control loop of Simulink model Figure 4-2: Comparison between theoretical and experimental model of section Figure 4-3: Bode plot comparing the theoretical system with the experimental system Figure 4-4: Root locus of the original open loop (left) and the simplified open loop with three poles (right) Figure 4-5: P-controller for both the theoretical and experimental system Figure 4-6: Influence of an I-action on an experimental compressor system Figure 4-7: Influence of a PI-controller on an experimental compressor system Figure 4-8: Comparison of automatically tuned PI-controller with manually tuned response Figure 4-9: Adding a lead-lag compensator to the previous controller Figure 4-10: Comparison between PI-controller and additional lead-lag controller Figure 4-11: Control loop of the implemented system Figure 4-12: Communication between pressure sensor and valve actuator [22] Figure 4-13: Flowchart implementation of PID and lead-lag Controller Figure 4-14: Setup of implemented controllers Figure Appendices-1: Setup experiment [24]... A.1 Figure Appendices-2: Moody Diagram... F.1 Figure Appendices-3: Comparison of the theoretical control loop and the experimental control loop by the use of Simulink software... G.1 Figure Appendices-4: Page 1 of the appendix of the digital pressure sensor at the outlet H.1 Figure Appendices-5: Page 2 of the appendix of the digital pressure sensor at the outlet H.2 Figure Appendices-6: Page 3 of the appendix of the digital pressure sensor at the outlet H.3 ix

12 Figure Appendices-7: Page 1 of the appendix of the digital volume flow rate sensor at the outlet... I.1 Figure Appendices-8: Page 1 of the appendix of the digital temperature sensor at the inlet... J.1 Figure Appendices-9: 3D drawing of an iris valve mechanism... K.1 Figure Appendices-10: Datasheet of the current actuator of Atlas Copco... M.1 Figure Appendices-11: Datasheet of Egger actuator... N.1 x

13 LIST OF SYMBOLS dp Differential pressure [bar] dp f Differential pressure friction losses [bar] e(t) Error in time / f Friction factor / s Laplace variable / v Velocity of air [m/s] A Cross section [m 2 ] C v Valve coefficient / D Diameter [m] G Specific gravity / K Minor losses coefficient / K p Proportional action PID-controller / L Length [m] P Pressure [bar] P 0 Inlet pressure [bar] Q scfh Gas flow rate [cu ft/h] Re Reynolds number / T Temperature [ C] T d Derivative action PID-controller / T i Integral action PID-controller /!! Constant that determines the border frequency / ρ Density [kg/m 3 ]!! Constant that determines the border frequency / ν Kinematic viscosity [m/s 2 ]! Gas flow rate [m 3 /s] xi

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15 ABBREVIATION LIST CAD CFD MIMO MPC ipm PID SISO VSD Computer-aided design Computational fluid dynamics Multiple input Multiple output Model predictive control In-house permanent magnet Proportional integral derivative Single input Single output Variable-speed drive xiii

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17 LIST OF TABLES Table 1-1: Summary of different valve types and their (dis)advantages... 4 Table 1-2: Decision matrix... 7 Table 3-1: Components of experimental setup Table 3-2: Overview of the different system components Table 4-1: Common signal conditioning of pressure sensor Table Appendices-1: Components of experimental setup... A.1 Table Appendices-2: Sensor specifications... B.1 Table Appendices-3: List of friction factors... D.2 Table Appendices-4: Static measurements... L.1 xv

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19 INTRODUCTION A common problem for many industrial manufacturers was the varying air demand of a customer. The fixed speed compressor has a lower efficiency when the demand for air is lower, since the consistent frequency and voltage of the compressor was not being used at its fullest capabilities. Therefore, large electrical cost savings can be achieved by installing a variable-speed drive compressor, wherein a minimum drop time is guaranteed, even in the most severe conditions. This VSD automatically adjusts its motor speed, which results in a varying air flow delivery. The current minimum flow rate that can be achieved by a VSD compressor of Atlas Copco is 20% of its total flow range. The total flow range of each compressor is dependent on the installed power. If a significant lower amount of air is requested by the customer, the compressor will shut down until the air consumption is rising again. The Atlas Copco Group has currently the largest control range of all compressor manufacturers and they are constantly looking for innovation to stay one of the world s leading suppliers in compressor equipment. This thesis is based on a research project of Atlas Copco to investigate if it is possible to develop an inlet valve, which enlarges the control range of the VSD compressor. The first part of this project consists of making a literature review to investigate all existing valve types. A comparison matrix investigates if one of these working principles is more appropriate for this project. The valve must be able to throttle the inlet of the compressor, whereby the air flow rate at the inlet and the pressure in the container decreases if the customer is not demanding compressed air. The last part of this literature study covers the preliminary design of the selected valve, taking into account the main design criteria such that the minimum and maximum opening diameter of the valve are optimized. Another requirement is adjusting the model to the chosen actuation principle. The next research section describes the simulation of the influence of the valve on the inlet flow of the compressor and designing a suited controller for the actuator. To simulate this situation, it is necessary to predict a theoretical model based on some thermodynamic assumptions. If the total system setup is described by a theoretical model, the behaviour of the dynamic system is analysed by using time domain models, made with the software package Matlab. These models are determined experimentally on an existing setup in a lab of the KU Leuven. The paragraph also covers a discussion of the comparison between the theoretical and practical approximations. The differences between the two models determine if the theoretical systems should be improved or not. The last part of this section covers the implementation of the PI-controller, combined with a lead-lag controller. The combination of the automation and mechanical design of the valve eventually lead to a conclusion of this research project, which contains proposals for improvements in future research. 1

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21 1 LITERATURE STUDY This section describes the selection process, used for choosing a suitable valve for the desired application. It describes various criteria, which are the basis of the categorization of current inlet valves. This results in a summarizing table that makes it possible to continue this study with one flow control device. 1.1 Selection criteria To understand the basic principles of a control valve, all different possibilities have to be divided into subsections. A first approach is to distinguish the mechanisms or operating principles of the valve, which results in four possible groups: closing down-, sliding-, rotaryand flex body valves. Another aspect determining the selection is the intended use. The valve can operate as a start/stop or as a throttling device. Other applications might be to divert the flow of a piping system or to control the flow of fluids containing solid particles. There are several criteria on which the type of valve, suited for this application, is selected [4]: A. Can be used for throttling applications B. Ability to resist corrosion/erosion and temperature influences C. Fluid is a liquid or a gas D. Fluid pressure E. Advantages and disadvantages F. Working principle is not too complex G. General design H. Possibility for automatic control I. Degree of leak tightness J. Maximum pressure drop that can be tolerated through the valve All these criteria need to be taken into consideration, whereby it is necessary to do a decision matrix analysis. This technique is a very useful tool if there are a number of good alternatives to choose from and many different factors to take into account. A weighted score is therefore assigned to each criterion to work out the importance of that specific feature. The next paragraph covers the different valve types that are currently available on the market. 1.2 Different kind of valves Many different types of manual valves are used in industrial applications worldwide. This paragraph covers the general mechanism and function of different valve types, including the most important advantages and disadvantages. Table 1-1 gives a short overview. [6] [8] 3

22 Table 1-1: Summary of different valve types and their (dis)advantages Valve type Advantage Disadvantage Suitable for flow regulation Gate valve - Linear motion valve - Inexpensive - Small mounting space - Low friction loss - Slow open and close time - Airtight seal impossible Typically not used for regulating the flow (unless specifically designed), designed for on/off services Globe valve - Linear motion valve - Excellent, precise throttling characteristic for high-pressure systems - Liquid and gas systems - Low-flow coefficients - Longer operating time - Higher pressure drop than other valve types Recommended for flow regulation and throttling Ball valve - Pressure drop across the ball is relatively low - Relatively expensive - Reliable, bubble-tight sealing - Low purchase and maintenance cost - Constant wearing on the seats - Cause erosion to the seat - Poor throttling characteristic Not ideal for throttling applications (but can be used if a low level of accuracy is required) Plug valve - Suited for liquids, gases and non-abrasive slurries - Simple design - Cheaper and lighter than other valves - Fast response - Relatively little internal disturbance - Several design variations - Requires greater force to actuate, due to high friction - Plug valves may cost more than ball valves Suited for on/off services and also throttling services if eccentric or V- plug designs are used 4

23 Diaphragm valve - Operating parts are isolated from the flow - Have the ability to be installed in any position - Extremely clean and tight shut-off - Easy maintenance and reduced leakage to the environment - Cannot be used in multi-turn operations (shortened lifespan) - Temperature limit (-51 to 232 ºC) Recommended for flow regulation and throttling Needle valve - Relatively small - Suited for precise adjustment of the flow - Bi-directional - High operating pressure and temperature - Wide range of applications - Relatively low, calibrated flow rates - More expensive - Limited connection diameter Suited for both on/off and throttling services Butterfly valve - Fast response time - Little resistance to flow (thin disc) - Lower in cost to other valve designs - Lighter in weight - Allow small mounting space - Allow a high coefficient of flow - Difficult to clean Recommended for flow regulation and throttling limited to low differential pressure Iris valve - Precise control of the flow rate - Self-cleaning if they slide over each other - Higher cost than other valves Recommended for flow regulation and throttling Pinch valve - Linear motion valves - 100% tight shut-off - Can be used for liquid, solid and slurry applications - Fast-acting - Not suited for transport media at a high temperature (max. ± 120 C) Recommended for flow regulation and throttling 5

24 Poppet valve - High operating pressure and temperature - Optimized flow area and less pressure drop - Low wear - Not recommended for use with vacuum - High operating force (depends on the pressure times the valve area) Not ideal for throttling applications Spool valve - Less force required to actuate - Can lock pressure downstream - Seals are exposed to wear (shortening the life span) - Open crossover (leakage) - Lower flow rate than poppet valves Not ideal for throttling applications 1.3 Suited valve Since the working principles, advantages and disadvantages of all the different valves are known, an appropriate valve for controlling the inlet of an oil-injected screw compressor can be chosen. First of all, the most important feature of the valve that is necessary for this application, is criterion A. If a valve type is not suited for flow regulation, this one is neglected for the research. From table 1-1, it is clear that the poppet and spool valve are not ideal for throttling services. All the other possibilities are recommended or require a more specific design, whereby carefully weighing the advantages and disadvantages is necessary. The decision matrix helps choosing the best alternative by weighing up the different criteria mentioned in section 1.1. The relative importance of these weights is determined by a score ranging from 0 to 5, where 0 means that the criterion is absolutely unimportant and 5 means that it is very important. It is acceptable to have criteria with the same importance. Scoring each alternative for each criteria and adding up these scores gives an overall score for each option. The alternative that scores the highest, is the best suited valve for throttling the inlet of a compressor. Table 1-2 gives an overview of the possible valve types and the weighted criteria. 6

25 Table 1-2: Decision matrix Weighing criteria Criteria A B C D E F G H I J Total score Possible valve types Scores (0 = does not meet the requirement at all, 10 = perfectly meets the requirement) 1 Gate valve Globe valve Ball valve Plug valve Diaphragm valve Needle valve Butterfly valve Iris valve Pinch valve Table 1-2 shows that there are four valve types which are more suited for this application (see total scores in bold). The working principle of the diaphragm valve is similar to that of a pinch valve. They both have a flexible elastomer body that can be pinched close to obstruct the flow. Since the pinch valve has a higher score in the matrix, the diaphragm valve is neglected for further investigation. The three plausible valves are therefore the butterfly valve, the iris valve and the pinch valve. According to table 1-2, the iris valve is the best option. An extra point of interest of the advantages and disadvantages of the different valve types is the sealing. The butterfly valve seems to have a less tight seal than the other alternatives, making it less suitable for the application. [12] Moreover, since the design of the iris valve is the simplest and cheapest, it s easier to eventually use this valve type. The common iris mechanism is a simple device that opens and closes a circular hole towards the center. [15] Examples of the working principle are camera shutters and the irises in our eyes, which both control the entrance of light. As one can see on Figure Appendices-9 of Appendix K, the preliminary design of the iris valve consists of a metal casing, called the valve body, enclosing a concentric ring to actuate the opening diameter of the valve. The inner control disk is able to rotate and shift the blue blades at the same time. These are hinged at one end and sweep simultaneously, providing an accurate aperture. The advantage of these blades is the uniform design, what entails a simple and compact model. The different number of components needed for the construction of the valve is therefore limited, which minimizes the production cost. The strength of the material of the blades can be lower, since the pressure at the inlet of the compressor stays restricted and the valve is not subjected to high stresses. Another advantage of designing the blades in this way is the diameter of the opening, which can be reached. The minimum diameter that can be reached using these design criteria is 2.5 mm. The maximum diameter is equal to the diameter of the pipe and thus corresponds to a fully open pipe. 7

26 There exist several possibilities for operating the valve: hand-wheels, levers, gears, and actuators. [11] The actuators can be divided into manual, electrical, pneumatic or hydraulic actuators. The focus for this research is an automated actuator that reacts fast and accurate. The electrical actuator, namely a stepper motor, meets these criteria, but requires an adjustment to the design of the valve. Figure Appendices-9 in Appendix K shows that the concentric ring is provided with some teeth at the outer side, where an additional gear rotates the control disk. This gear serves as transmission between the motor and the blades. The total gear transmission does not take the required torque into account, but a standard stepper motor can be connected to the end of the worm gear. The biggest advantage of this motor type is that it is able to precisely control the opening of the valve and therefore the flow at the inlet of the compressor. 1.4 Modelling Since an appropriate valve is chosen on the basis of standard requirements, the next step will be simulating the influence of the valve on the inlet flow of the compressor and designing a suited controller for the actuator. The situation that needs to be simulated is as follows: The 7 GA VSD+ compressor of Atlas Copco, with a pressure setpoint of 4 bar, is running at 100% flow rate. [2] [3] The customer suddenly stops demanding compressed air and as a result, the pressure in the container will rise. Because the compressor is already running at the lowest possible speed to reduce energy consumption, the motor will shut down to keep the pressure in the tank under the limit of 5 bar. The valve should ensure that it is not necessary to stop the motor and will consequently decrease the inlet flow of the compressor to keep the pressure in the tank under control. This control valve is in other words designed to enlarge the control range of the compressor. To simulate this situation, it is necessary to predict a theoretical model based on some thermodynamic assumptions and eventually compare this model to a practical model. The following paragraph covers these simulations. 8

27 2 THEORETICAL MODELS Designing a controller begins with the identification of the control loop and the different subsystems. Appendix A shows that the system consists of three subsystems: the compressor itself, the piping losses between the in- and outlet and the inlet valve. The following section focuses on a theoretical approximation for the models of these components. 2.1 System identification The control valve is part of the compressor system and is the most important element of the loop that is controlled by using a PID controller. To investigate the theoretical model, one first needs to identify the input and output and how their behaviour is modified by feedback. As explained in section 1.4, the output of the compressor is set to 4 bar and the pressure in the tank rises if the compressor doesn t need to supply compressed air, which is simulated by a disturbance. This means that the output of the system is the output pressure of the compressor, dependent on a desired control signal, called the reference pressure. To do this, a controller is designed, which will actuate the iris valve to bring the actual output closer to the reference value. The block diagram presented in Figure 2-1 defines the system. Figure 2-1: Control loop To elaborate a mathematical model of the total control loop, a model for all the different elements is developed: a model of the control valve, a model of the piping losses and eventually a model of the compressor. If these models are known, different type of controllers can be investigated and simulated. 9

28 2.2 Model of the iris valve The changing orifice of the valve, actuated by a controller, has a certain influence on the flow rate and therefore changes the inlet pressure of the compressor, which in turn changes the outlet pressure of the system. The airflow through the iris valve can be modelled by using the following basic sizing equation (2.1) [5]:!" 520!!"#$ = 59.64!!!!!!!" (2.1) Where:!" = Pressure differential [bar]!! = Atmospheric pressure [bar]! = Specific gas constant [bar]!! = Valve-sizing coefficient [/]! = Temperature [K]!!"#! = Air flow rate [cu ft/h] à! = 0.028!!"#! = Volume flow rate [m 3 /h] The entire calculation, as shown in Appendix C, is based on C v, which is the valve-sizing coefficient. This parameter is determined experimentally and gives a relationship between the volume flow rate through the valve and the pressure drop across it. [7] Rewriting equation (2.1) to the pressure drop, which instantaneously changes over time, gives the following result:!!!!" = 59.64!!!!!! 520 (2.2) By filling in all the different parameters with constant values, which are measured at the inlet, transfer function (2.3) is derived: Where:! = Volume [m 3 ]!!!"!#! =!"! = 2 10!!!!! (2.3) To study the relationship of C v, a prototype model of the designed valve should be made. This analysis therefore only investigates the differences between the theoretical and practical model of the compressor. The calculation of the valve-sizing coefficient would only be possible after implementing the mechanical design. 10

29 2.3 Model of the friction losses in pipes The friction losses are function of the system geometry, the fluid properties and the flow rate in the system. This overall head loss consists of major and minor losses, which can be calculated by general equation (2.4): [9] [17]!! = 4!!!!! 2 +!!! 2 (2.4) Where:! = Length [m]! = Diameter [m]! = Velocity [m/s]! = Friction factor [/]! = Minor losses coefficient [/]! = Pressure drop friction losses [bar] Equation (2.4) is only valid for circular and relatively straight pipes with a constant diameter. The density of the fluid at the inlet of the compressor is not constant, but because it varies 20% at most, this variation is neglected. Taking the maximum value of the pressure into account, results in a maximum friction loss. Since the pipes before and after the compressor have different diameters, the system is split up into two parts. The piping diameter before the compressor is 7 cm, whereas the diameter afterwards is 2.5 cm. The first part of equation (2.5) gives the major losses before the compressor, while the part after the summation describes the losses after the compressor.!!!!"! = (2.5) ( )! ( )! Equation (2.6) describes the minor losses for both the in- and outlet of the compressor.!!!!"! = ! ! (2.6) 2 ( )! Where:! =! 1000! [m/s] A = surface area [m 2 ] Appendix D contains the entire calculation, with as result:!!!!"! = 2.39!!! !!! (2.7) 11

30 One can identify the output dp! as an instantaneous pressure change and the input V as the flow rate at both the inlet and outlet of the system. Since the developed model is nonlinear, a Taylor series will be used to approximate the nonlinear process with a linear one. The linearization around a working point of 4 bar is only necessary if the influence of the friction losses is sufficiently large. To see if these friction losses are negligible, equation (2.8) shows a maximum value:!"! = [!"#] (2.8) The linearization is not necessary, concluding that this pressure drop is relatively low in comparison with the output pressure of four bar. 2.4 Model of the compressor Previous research describes this complex subsystem on two different ways. A first approximation uses the geometric shape of the compressor element, which in this case is a double helical screw. The model for the change in pressure is either based on the inertia of the element or on energy-efficiency formulas. This has as limit that the volume flow rate is not directly taken into account. The simulation of a reduction in flow rate represents the consumption of less compressed air. The reason for this simulation is that the operator wants to avoid a shut down when closing down the outlet valve. A second way to control this system appeals to physics and more specifically, the thermodynamics of a compressor system. [9] [14] The system identification uses the first law of thermodynamics for open systems and assumes that the air used, is an ideal gas. The simplification of the compressor system results in equation (2.9):!" = (1 +!!! )!!"!/! (2.9) Where:! = Specific gas constant [J/kg K]! = Mass [kg]! = Pressure [bar]!! = Flow coefficient [/] This equation is only valid for an isentropic compression and is also non-linear. The requested pressure difference over the compressor is as close as possible to three bar. This property and the first noticeable point of the experimentally, applied step response selects a working point for the linearization of the system. Chapter three provides the complete measurement for the linearization. Linearizing around the following operation point:!! = 283 [!"! ]!! = 718 [!!"! ] 12

31 !! = bar inlet pressure!" = 3.03 bar pressure differential!!!! =!!! = [!" ] Using the above values results in the linearized system of equation (2.10).!!!"#! =!" 3.183! 7.25 =!! (2.10) Equation (2.10) is valid for an analysis at 16mm and bar at the inlet. This gives a transfer function with as output the differential pressure and as input the volume going into the system. To be able to compare the theoretical system with the practical system, they need to have the same in- and output. As shown later on in this paper, the experiment models the setup using the outlet pressure as the output of the transfer function and the inlet pressure as the input. Rewriting the original model of equation (2.9) to similar in- and output, results in equation (2.11):!! =!! + 1 +!!!!!!!!!!!!!!!! + 1 +!!!!!!!!!!!!!! (2.11) Differentiating the ideal gas law forms the basis for this conversion to the pressure at the inlet and outlet. Equation (2.12) shows the relationship between the volume flow rate and the differential pressure.!!!!!(! )!!!"!!!!"! = =!!!!"!!!"!!!!" (2.12) Rewriting this to the fraction, p2 over p1 gives equation (2.13).!"!"#! =!! 3.597! =!!! (2.13) Appendix E provides the complete derivation of this approximation. The zero of the transfer function has a coefficient smaller then four, which results in undershoot because of the maximal pressure at the inlet of the system. The air entering the setup is in this case limited to one bar. The next chapter describes the comparison between the two control loops. 13

32 14

33 3 PRACTICAL MODELS The calculated models are based on theoretical assumptions, such as the hypothesis of an isentropic compression. Consequently, these approaches result in a deviation of the actual system. To identify this irregularity, it is necessary to perform an experiment to investigate the influence of a step response to the compressor system. 3.1 Measurements Figure 3-1 shows the experimental setup, based on the oil-injected screw compressor and the adjustments that were made to the system, including the additional sensors, to perform the measurements.[3] The different components are listed in Appendix A. Figure 3-1: Experimental setup 15

34 Table 3-1: Components of experimental setup 1 Inlet filter 8 Safety valve 15 Outlet digital pressure sensor 2 Sentinel valve 9 Oil separator 16 Outlet temperature sensor 3 Screw element 10 Minimum pressure 17 Condensate prevention cycle valve 4 ipm 11 Solenoid valve 18 Outlet digital volume flow rate sensor 5 Air/oil vessel + 12 After-cooler 19 Inlet vacuum manometer separator 6 Thermostatic 13 Fan 20 Inlet digital temperature sensor bypass valve 7 Oil filter 14 Oil-cooler 21 Inlet valve (simulated iris valve) By manually throttling the inlet of an oil-injected screw compressor, using rubbers with each a different orifice diameter, it is possible to simulate the operation of an iris valve at the inlet of the compressor. By measuring the differential pressure and the flow rate at the outlet of the system, it is possible to identify a transfer function for the simulated throttling valve and the compressor. This transfer function models the pressure of the system as an output to the volume flow rate as input of the system. Figure 3-2 shows the relationship between the change in orifice diameter and the volume flow rate at the output of either the compressor or the valve. Reducing the inlet diameter causes a smaller flow rate through the system, which is related to the pressure drop across the simulated valve, shown in Figure 3-3. Assuming a constant mass flow rate throughout the system, gives the flow at the inlet of the compressor. The difference emanates from the variation of the density. Output flow rate [Nl/s] Diameter of the orifice D [mm] Compressor Valve Figure 3-2: Flow - orifice diameter characteristic 16

35 Input pressure of the compressor [bar] 1,2 1 0,8 0,6 0,4 0, Diameter of the orifice D [mm] Figure 3-3: Pressure drop across the valve in function of the changing diameter The determination of the system control loop relies on Matlab software to identify the different systems. Matlab provides a fitting percentage, which shows how closely the transfer function approximates the measurements. The results of the experiment can be found in Appendix L. This experiment is only a static measurement that cannot be used to derive a transfer function. To do so, one needs to check the influence of applying a step response to the inlet of the compressor over time. Figure 3-4 gives an overview of the change in outlet pressure over time. During this experiment, the operator applies a step response to the inlet using a rubber with a different orifice diameter. Meanwhile, he samples the pressure level at certain points throughout the system. The following procedure describes the exact process to clarify the different steps: 1. Turn on the compressor and let the output reach four bar. The pressure vessel is also at four bar to guaranty the same volume flow going in and out this component. 2. Writing down different values of atmospheric, inlet and outlet pressure and temperature as baseline measurements. 3. Throttle the inlet by using a rubber with a specific orifice diameter. There will be a certain transition phase, because it is impossible to perfectly close it at once. This will influence the result of the experiment. 4. Sample the earlier mentioned parameters over time and look at the output pressure. When this parameter stabilizes, remove the rubber from the inlet. 17

36 Outlet pressure compressor [bar] 4,5 4 3,5 3 2,5 2 1,5 1 0,5 0 Pout-Eme Time [s] 2mm orifice 4mm orifice 8mm orifice Figure 3-4: Influence of throttling the inlet over time Figure 3-4 consists of measurements that have a sampling rate of two seconds. This is inconclusive to determine the order of the system, because both first order and second order systems have a fitting percentage of over ninety per cent. On top of that, a first order model with one zero is also plausible. Increasing the sampling time to one second reduces the fitting percentage that Matlab provides. This leads to the conclusion that the system is not of first order. A system with one pole and one zero gives a zero order model. This is uncommon for a purely mechanical component like a screw compressor, because of the steady state error. A second order system is the appropriate choice here, taking into account that the inertia of the screw element plays a role in the acceleration of the air particles. Section 3.2 explains the simulation of the experimentally determined control loop. 18

37 3.2 System identification The entire control loop uses the following four transfer functions: Table 3-2: Overview of the different system components Component Transfer function theoretical model Transfer function experimental model Nr. Compressor 3.597! ! ! !! ! (3.1) Iris valve 2 10!! 1!!! 3! ! (3.2) Digital pressure sensor outlet / ! + 1 (3.3) Actuator / 1 3! + 1 (3.4) Some limitations are taken into account by the use of a saturation limit in Simulink. The limit at the inlet can be interpreted as a maximum input of atmospheric pressure. The disturbance on the other hand, is defined as a pressure rise of one bar so that the output goes from four to five bar. Appendix G shows the complete control loop, including a PIcontroller. Notice that there are some similarities between the theoretical model for the compressor and the one determined experimentally. The two transfer functions, used to simulate the iris valve, have a different order because of the flow discharge coefficient. This component represents the opening of the iris valve, using a constant that depends on the position of the valve. The position is in turn related to the flow rate and the pressure drop. [5] That is also the reason why the manufacturer determines this coefficient experimentally by measuring the pressure drop. The theoretical transfer function does not take the actuation into account. For this reason the actuator, used in practice, is multiplied with this equation. The transfer function of the actuator is based on the fact that it permits up to 1200 operations per hour. [27] The obtained equation is of first order and thus comparable to the experimental model. The next paragraph will compare the two control loops more in detail. 19

38 Step response to 4 bar Outlet pressure compressor [bar] Initial model without controller Model + I-controller: I-action = time [s] Figure 3-5: Simulation of the outlet pressure with or without a controller A plot of the output makes clear that the system itself needs amplification to reach the requested four bar. Figure 3-5 displays the difference between a system without any type of controller and a system with an I-action, which removes the steady state error. At a random timestamp, in this case four hundred, the operator closes the discharge valve, which results in a disturbance. A step response simulates this as a sudden increase in pressure. Section 4 explains the selection procedure of the controller and how to optimize the response to this disturbance. 20

39 4 COMPARISON OF THE THEORETICAL MODELS AND THE EXPERIMENTAL APPROXIMATIONS 4.1 Differences between the systems The compressor equations of Table 3-1 have a different number of poles and zeros, but the gain factor on the other hand is similar. The iris valve is a purely mechanical component, which is comparable to a motor. A first order model closely approximates the behaviour of this component. This is in contradiction with the theoretical approach, because of the earlier mentioned valve-sizing coefficient. Figure 4-2 displays the differences in output between the theoretical and experimental approach, while applying a step of four bar to the control loop. The transfer function of this latter is determined by manually applying a step to the inlet of the compressor as explained in section 3.1. An I-action that lies between 0.01 and 0.03, is necessary, to guarantee that the output reaches the requested four bar without overshoot. Equation (4.1) gives the transfer function of the I-controller, wherein K i is changed to this value.!(!) =!!! (4.1) The difference between a first and second order is still inconclusive, whereby an analysis in the frequency domain is necessary. The equations below give the open loop transfer functions for the control loops of Figure 4-1 for both the theoretical models (4.2), as for the experimental models (4.3). The open loop starts at the reference value and ends directly after the digital pressure sensor. Appendix G provides the entire Simulink model ! !"!",!! = 0.012!! !! + 129!! !! ! (4.2) 4.22! !"!",!" = 0.012!! !! !! !! !! ! (4.3) Figure 4-1: General control loop of Simulink model 21

40 Theoretical model vs. experimental model Outlet pressure compressor [bar] Experimental model: manually applied step to GA7-37 VSD+ Theoretical model Time [s] Figure 4-2: Comparison between theoretical and experimental model of section 3.2 The open loop analysis allows to draw a conclusion about the correctness of either one of the systems. The bode plot of Figure 4-3 shows both the compressor model and the entire open loop. The theoretical model of the compressor (see equation 2.13) has a pole in and a zero in This means that the system increases with 20dB at the latter frequency, but directly afterwards decreases with -20dB. This results in a horizontal line after rad/s. The output of the theoretical model keeps following the reference point of four bar. This output is independent from the frequency of the input, which cannot be correct for a system that has a sampling rate of one second. After this frequency, the system should at least stop following the reference input, like the behaviour of the experimental model of equation (3.1). Figure 4-3: Bode plot comparing the theoretical system with the experimental system 22

41 Because of the influence of inertia, the controller is designed for the second order system that is calculated by the use of Matlab software. Looking at the output of the control loop of Appendix G, one may notice that the disturbance is active after a random point in time, when the output is already at four bar. In case of this simulation, that point is four hundred seconds (see Figure 4-2). The outlet pressure may not exceed five bar, otherwise the pressure ratio over the screw element exceeds twenty. This means that the system will become sensitive to wear and cavitation, which will damage the element. 4.2 Selection procedure for the controller Before determining the controller type, an investigation of the kind of control system is necessary. The pressure is a variable that changes over time and does not respond infinitely fast to an input. This means that the system is dynamic and not static. This application is of the type SISO, which means single input, single output. A MIMO system, multiple input, multiple output, needs more than one controller to separately control the different outputs of the states. There are different possibilities to represent the compressor model, for example an ordinary differential equation, a state space model or a transfer function. The latter is an appropriate choice, but it is necessary to linearize the theoretical model. Modelling the system using transfer functions, simplifies the design of the controller in the frequency domain, but does not allow MIMO systems. A state space model generally uses more than one input and output. There are two remaining options; either designing the controller in the continuous time domain or in the discrete (Z-)domain. The latter is typically a better choice when one of the components is relatively slow compared to all the others. The feedback sensor has the fastest reaction in contradiction to the compressor, which is the main component of the control loop. Looking at the previous plots, the simulation shows a rise time between forty and fifty seconds for a step input to the experimental model, from zero to four bar. Taking into account that a compressor has a certain lead-time to reach the requested output, a continuous controller suffices. In reality a digital controller is an appropriate choice, but this conclusion can only be confirmed after the analysis. Starting from previously mentioned criteria, a selection between a PID-controller and a lead-lag controller is necessary. This section analyses both types to see which gives the optimal result. Besides the fact that a PID-controller is the most common type of process control in all sorts of areas, it is also preferred in this application, because they are relatively cheap and flexible as explained in section 4.6. [26] A lead compensator increases the stability or speed of the response of a system; a lag compensator reduces, but not eliminates the steady-state error. Depending on the desired effect, a lead, a lag or a combination of both compensators is possible. Other more advanced process control techniques, like multivariable MPC, are disregarded because of their complexity. Multivariable MPC also requires a linear model in contradiction to nonlinear MPC. These models are suited to control multiple variables simultaneously and are in this case an appropriate choice to control the outlet pressure of the compressor. 23

42 4.3 Influence of a PID-controller When there is no active controller, the transfer function of the open-loop system is of fifth order. This implies that a simplification of the system is necessary to design a PID controller. The transfer function below allows to exclude two poles, namely -250 and , because they are relatively faster than all the other poles. 4.22! !"!"!"#!!"#!"#$%"&&'% = 0.012!! !! !! !! ! (4.4) Poles: [ ; ; -1,17; -1/3; ] This gives a system that is one order too high for designing a PID controller. Ziegler- Nichols might give an approximation, but because of the high order of the system, this gives only an estimate, which still differs from practice. Another reason for not using Ziegler-Nichols is, that this approach works well, when the system is linear and has a transfer function of the form of equation (4.5). [25] For mechanical systems like a compressor, Ziegler-Nichols also needs to take into account that no overshoot is allowed.!" =!!!!" (! +!) (4.5) The remainder of this section focuses on tuning the PID controller and the search for other, more suitable controllers. The derivative action of a PID controller acts quickly on every type of change, for example noise. The amount of expected noise is uncertain and when applying this action to a Simulink model, the system becomes unstable. For those reasons, the derivative action is not applicable. The goal is to examine the influence of a P-controller and a I-controller separately, in such a way that the best combination of these two actions gives the desired outcome. Figure 4-4: Root locus of the original open loop (left) and the simplified open loop with three poles (right) 24

43 The root locus plots of Figure 4-4 help to identify the possible proportional controllers. Dependent on different types of constraints, like allowed overshoot or damping ratio, the P- controller has different values. Since the customer requests four bar and he wants to avoid any sort of pressure rise, no overshoot is allowed. Figure 4-5 simulates different values for the P-action to show the influence of this type of controller. outlet pressure [bar] P-controller for experimental system time [s] 5 P-controller for theoretical system outlet pressure [bar] P-action = 1 P-action = 2 P-action = 5 P-action = 10 P-action = 20 P-action = 0.1 P-action = time [s] Figure 4-5: P-controller for both the theoretical and experimental system Figure 4-5 shows that a P-controller with a value smaller than one, increases the undershoot of the system. The difference between a P-factor of ten and twenty is barely visible. Both of them make the output of the step response oscillate. Increasing this action would result in an even more unstable output. The theoretical model has no overshoot when applying a small proportional controller, which is not the case for the experimental system. This type of controller is not the appropriate choice for the application. A further investigation of an I- action is still necessary to make a conclusion. When the theoretical model displays overshoot, the reaction of the outlet pressure on the applied step of section 4.1, is so fast that there is no oscillation. In reality this in impossible and that is also the reason why the remainder of the modelling is based on the experimental system. Because the compressor system does not allow an outlet pressure higher than five bar, which actually corresponds to the overshoot of the system, the limit of the I-action is similar to that of the P-controller. On top of that, the client requests an exact outlet pressure of four bar, but he consumes less compressed air. That means no steady state error is allowed and the settling time needs to be as small as possible. 25

44 An I-controller might help to reduce the steady state error to the smallest value possible, but Figure 4-6 proves that this reduces the reaction time. Raising the effect of the I-action mainly minimizes the error, but also increases the rise time. Taking the disturbance into account, one can notice that the appropriate I-action lies between 0.05 and When the controller tends more to a value of 0.01, the response to the disturbance becomes slower and slower. Values of an I-action, which are even smaller then the once of Figure 4-6, make the system insufficiently fast. Larger values on the other hand, make the output oscillate even more. I-controller experimental system 5 4 Outlet pressure [bar] I-action = 0.1 I-action = 0.05 I-action = 0.02 I-action = Time [s] Figure 4-6: Influence of an I-action on an experimental compressor system Before selecting the most suitable I-controller, an investigation of the combination of both the P-action and the I-action is necessary. This might solve the problem of either slowing down the system or creating an overshoot that is not allowed. The reason for combing both an I- and P-action is to create the perfect balance between amplifying the signal and reducing the steady state error. Figure 4-7 provides an overview of different combinations, which makes it clear that the necessary proportional gain depends on the integration factor. The operator wants the influence of the I-action as small as possible to make sure that the delay on the output does not become noticeable. Equation (4.6) proves that increasing this value, reduces the influence.!! =!! (!! + 1!!!!"!! +!!!"(!)!" (4.6) 26

45 Where: e(t) = Error in time k! = Proportional action PID-controller T! = Iterative action PID-controller!! = Derivative action PID-controller All the different scenarios of Figure 4-7 are an estimate, which should be tested in reality. The output displays overshoot when the operator raises the integral part of the PI-controller above a certain limit. This maximal value is in this case The proportional component has as goal to relate the output as close as possible to marginally stable. This corresponds to the fastest reaction possible without any apparent overshoot. Matlab also provides a way of optimizing the output, taking into account the closed-loop stability, adequate performance and adequate robustness. Figure 4-7 compares this result, obtained by the use of the PID Tuner toolbox, with the optimal combination so far. PI-controller experimental system Outlet pressure [bar] P-action = 1; I-action = P-action = 0.1; I-action = P-action = 0.1; I-action = 0.1 P-action = 0.5; I-action = 0.1 P-action = 0.5; I-action = Time [s] Figure 4-7: Influence of a PI-controller on an experimental compressor system The main design criterion of this controller is the ability to control any sudden change in output. For this reason, the input disturbance rejection of Matlab plays an important role in modelling the compressor system. The Matlab tool rejects the necessary constraints concerning overshoot. This results in Figure 4-8, comparing both the automatically generated, and the manually tuned controller, after applying a disturbance at the output of the compressor model. The disturbance, simulated by a step of one bar, is active after a random point in time. One can notice that the difference between the responses to the disturbance is minimal. If the operator wants to reduce the demand of compressed air, the pressure drops below four bars when using the configuration of the PID Tuner. 27

46 Comparison of automatically generated PI-controller vs manually tuned 5 Automatically generated PI-controller using Matlab toolbox: P = 0.599; I = Experimental model of section 3.2: P = 0.49; I = Outlet compressor [bar] Time [s] Figure 4-8: Comparison of automatically tuned PI-controller with manually tuned response 4.4 Influence of a lead-lag controller Since the open loop of the system has a higher order transfer function, the standard equations and rules of thumb for determining overshoot or rise time are not valid. Using Sisotool in Matlab is therefore necessary to design and implement a lead-lag controller, which meets certain requirements. The standard equation for a continuous time lead-lag compensator in the frequency response is:!! =! 1 +!!!!! 1 +!!! 1 +!!!!! 1 +!!!!h!"!!! > 1,!! < 1 (4.7) Where:!!,!! = constants that determine the border frequencies of the compensator K = compensator gain Sisotool allows to design the compensator in an interactive way, using the root locus and bode diagram techniques. The architecture is automatically set to a unit feedback system, but the sensor used during the experiment has a certain time delay, which is dependent on the sampling time of the sensor. Equation (3.2) in Table 3.1 shows the transfer function, which is implemented in the architecture design of Sisotool. The reference value is also a standard step size of one, which is changed to four bar to simulate the required output pressure of the compressor. 28

47 While our system does not have the form of a standard second order system, it is still possible to use the standard relationships between time and frequency response as a starting point in the design. The pressure setpoint is four bar and the compressor is not allowed to exceed this target. This means that the maximum overshoot of the system is equal to 0%. An overshoot of 0% theoretically corresponds to ζ = 1, but this critically damped case is not feasible in practice. A very small overshoot of maximum 0.1% is therefore allowed in the compensated system. Since the overshoot needs to be less than this maximum, the damping ratio! needs to be larger than 0.9. The lead controller increases the speed of response of the system by adjusting the bandwidth. Figure 4-8 shows that the current 2% settling time of the system with tuned PIcontroller is equal to 11.2 seconds. The compensated system should react faster and therefore has a higher bandwidth than the current bandwidth of Hz. Making the system response faster causes an increase in overshoot. Therefore, the overshoot must be reduced in conjunction with making the system faster. This can be accomplished by adding the lead-lag compensator to reshape the bode plot of the open loop system and increasing the gain crossover frequency. The additional positive phase added by the lead compensator increases the phase margin, thus increasing the damping, which is one of the requirements. Since the system is already of type one, namely a plant with integrator, the steady state error for the step input of four will be zero for any value of the gain K of the compensator. Tuning a compensator, which meets all of the above requirements, is done manually through trial and error. Sisotool allows to adjust the locations of the poles and zeros of the compensator and shows directly the effect on the response of the closed loop system. These poles and zeros are moved until the desired transient and steady state response are achieved. After tuning the compensator in this way, the frequency response of the system looks like Figure Step Response of the closed loop system with PI- controller and Lead/lag compensator Amplitude Time (seconds) Figure 4-9: Adding a lead-lag compensator to the previous controller 29

48 Examination of Figure 4-9 demonstrates that the lead-lag compensator increased the system response time. The settling time of the compensated system is 8.21 seconds and the transfer function of the lead-lag controller is as follows:!! = (! ) (! ) (! ) (! ) (4.8) Identifying this function with the standard transfer function gives!! = 4.81,!! = 1.13,!! = 2.19,!! = 0.01 and! = with the first part the lead controller, followed by the lag compensator. These parameters meet the limits, given above in equation (4.7). An important remark here is that the disturbance is not taken into account, because adding the disturbance cannot be simulated in the Matlab code. A possible solution to test if the lead-lag compensator has a positive influence on the system, is adding the transfer function of the compensator before the PI-controller in the control loop of Appendix G. Figure 4-10 shows the result. 5.5 Comparing the response of the system Outlet pressure compressor [bar] PI controller with: P-action = 0.49 and I-action = 0.13 Pi-controller and leag-lag compensator Time [s] Figure 4-10: Comparison between PI-controller and additional lead-lag controller Adding the lead-lag compensator has a positive influence on the system. At start-up and right after the disturbance, the oscillations disappear and the pressure moves gradually to it s steady state value of four bar. This response is preferred above the response of the system with only the PI-controller. 30

49 4.5 Correction of the theoretical system The beginning of this chapter describes the comparison between the theoretically and experimentally determined systems. This section focuses on the reasons why the theoretical model is one order lower and why there is a difference in gain factor. This leads to a conclusion about how to solve these problems and why the theoretical model is considered insufficiently accurate. Avoiding the limitations of the theoretical calculations, like taking into account the acceleration of the change in pressure, is a challenge that should be tackled in another research project. The first problem is the lack of inertia of the zero order compressor model. This means that the use of thermodynamic formulas neglects the existence of any type of acceleration at the outlet of the compressor. This is incorrect when you think about the screw element that has a certain inertia value. A possible explanation is, that the internal volume of the screw element causes this second order component. This is impossible to integrate into the current derivation, because both points lie outside of the compressor. To solve this problem, a representation of the volume or pressure at a specific point inside the compressor is necessary. Current research on this issue is scarce and complex. A CFD analysis makes these dependencies clear and provides a visualisation of the volume flow rate and acceleration. The second concern is the difference in gain factor. The experimental model has as gain factor of 2.24 in contrast to the 2.04 of the manually linearized model. Besides the selected point for the linearization, there are other causes that change the ratio of the constant terms. Adding the previously calculated piping losses to the transfer function of the compressor, raises the constant in the nominator and consequently the gain factor of the transfer function. A higher sampling rate changes the transfer function significantly as explained in the experimental approach. The main reason for the limit of one second is that an analogue manometer measures the inlet pressure of the compressor, after the throttled atmospheric pressure. Changing the sensor to a digital pressure sensor optimizes the output values of the applied step. The transfer function, used in this research, is based on measured values coming from an applied step. A second way to derive this equation is to apply a pulsating signal, which has a certain frequency. Next to the CFD-analysis, this is another way of checking the result of this research. 4.6 Implementation of both PID-controller and Lead-lag controller It is possible to implement a controller by using analog components or by using a more flexible solution, namely a microcontroller. The suggested control loop combines two controller types, which uses a digital pressure sensor as feedback. The flexibility of using digital control includes the possibility for an adaptive PID controller, but also the possibility to use MIMO systems. The latter becomes of importance when the customer wants to control more parameters than only the outlet pressure of the system. An adaptive PID controller means that the costumer can control the plant offline. It is also a possibility to perform a careful, automatic search for the different parameters of the PID controller. 31

50 The control loop of Figure 4-11 shows the necessary components to complete the automatic control of the inlet valve. The three main parts are the actuator, the sensor and the microcontroller. To measure the output signal, a digital pressure sensor with an appropriate sampling time is necessary. A rule of thumb for the sampling rate is that it lies between one tenth and one hundredth of the settling time. If it is larger, the variance in delta T increases, which means a higher deviation of the sampling time. In case it is smaller, the lag time becomes larger. [18] Figure 4-11: Control loop of the implemented system Paragraph 4.4 shows a settling time of 8.21 seconds for a simulation using both a PIDcontroller and a lead-lag compensator. However, this is only a simulation, which still differs from practice. Regardless of this, the current pressure sensor samples at 3ms. (Appendix H) The range around this settling time is faster than the earlier mentioned rule of thumb, which leads to a variance in delta T. The output signal of the pressure sensor is analog. Data acquisition converts these pressure samples into digital numeric values that can be processed by a computer. The analog to digital convertor of Figure 4-11 is a component of the DAQ. There are five questions you need to take into account when selecting DAQ hardware. [19] 1. What type of signals measures the sensor? The different functions of a DAQ device are: Analog inputs measure analog signals Analog outputs generate analog signals Digital inputs/outputs measure and generate digital signals Counter/timers count digital events or generate digital pulses/signals In case of the setup of Appendix A, only the first two functions are applicable. A multifunction DAQ device is more appropriate, when taking into account that this setup might change. This combines analog and digital inputs/outputs with counters but increases the cost with a factor ten. [20] 2. Is signal conditioning necessary? Table 4-1 gives an overview of common signal conditioning for pressure sensors. This can be done by using external signal conditioning or with build-in signal conditioning. [19] 32

51 Table 4-1: Common signal conditioning of pressure sensor Type of sensor Amplification Attenuation Isolation Filtering Excitation Linearization CJC Bridge Completion Load, pressure, torque (mv/v, 4-20mA) x x x x 3. What is the necessary sample rate? This parameter depends on the maximum frequency of the pressure signal. Sampling two to ten times faster than this frequency, allows to accurately reconstruct the measured signal. The measurements of the experiment have a sample rate of one second, which is insufficient to accurately control the system. Taking into account the rule of thumb, related to the settling time, leads to an appropriate sampling rate between fifty milliseconds and one second. This is the case if the settling time lies between five and ten seconds. 4. What is the necessary resolution? This refers to the amount of binary numbers, used to represent a signal in an analog to digital convertor. Because the sensor has an output signal of 0V to 10V, it is similar for DAQ. To detect a change of 0.1 bar, which corresponds to 1.25mV, the DAQ system needs to have a 14 bit resolution. Comparing this to the price of a 12 bit resolution shows that it doubles the price. [21] 5. What is the necessary accuracy? This term represents how reliable the measured value of the signal is. It can never be better than the resolution, but it is not related to this term. A general way to express this, is by using the absolute accuracy. Equation (4.9) shows how to calculate this.!"#$%&'(!""#$%"& = ([!"#$%&'!"#$!""#"] + [!"#$%&'!"#$%!""#$%!""#"] +!"#$%!"#$%&'("&)) (4.9) Because both the noise uncertainty and the gain error are unknown, these selection criteria are disregarded for the moment. The next component of interest is the microcontroller. Figure 4-12 shows how this component fits between the implementation of the actuator and the sensor. This figure lacks a VSD compressor between the sensor and the control valve, but shows the communication between them. 33

52 Figure 4-12: Communication between pressure sensor and valve actuator [22] The program used for the experiment, uses LabView as a control design and simulation Toolbox. Using the same software to program both controllers, simplifies the current setup. Figure 4-13 explains the implementation of both controllers by using a flowchart representation. Writing the program using LabView, means that the computer of the current setup becomes part of the control system. 34

53 Figure 4-13: Flowchart implementation of PID and lead-lag Controller The final component is the actuator. Because compressed air is already available, a pneumatic actuator is the obvious choice. The air available is at four bar, which is too high to actuate the valve. This means that a pressure regulator is necessary, which on his turn increases the cost and the complexity of the control loop. An electric actuator does not encounter this problem and is suited for multi-turn operations, in contradiction to a pneumatic actuator. Atlas Copco generally works with an actuator of the ESBE ARA600 series. Appendix M gives the datasheet of this component. The design of the current valve needs to change in order to use this actuator. The schematic of Figure 4-14 represents the new setup with the different components. This is only an example, based on the current setup and the components that were already available. [22] 35

54 Figure 4-14: Setup of implemented controllers 36

55 CONCLUSION Atlas Copco examines different possibilities to throttle the inlet of an oil-injected screw compressor to avoid the shut down of this machine, when the demand of air at the outlet is reduced. This thesis focuses on the selection of the necessary technology and how to model this application, based on Matlab simulated results. Present-day valve technology is applicable to all sorts of applications, but after a literature study on the advantages and disadvantages of all these possibilities, only three remain. For previously explained reasons, the iris valve is most suited, because of its throttling characteristics. This all results in a preliminary mechanical model that optimizes the design to the available orifice area. Taking into account the seals is the next step in the mechanical design to guarantee the minimal losses of the client. Modelling a valve is dependent on more than two variables, which leads to the simplification of the theoretical models. Checking the variation of the output parameter over time results in a secondary model that contradicts the previous one. Based on the working principle of the compressor, the experimental approach is considered to be correct. The lack of inertia in the theoretical derivation is in reality impossible, because the screw element itself realizes an acceleration of the air particles that are going through the compressor. As a consequence, additional research is necessary to determine where this inertia comes from. The secondary aspect of simulating a compressor system using Matlab simulations is selecting the appropriate controller. Designing in the continuous domain suggests that a combination of both a PID-controller and a lead-lag controller gives the desired outcome. The system reacts as fast as possible to the applied input, without causing prominent overshoot. The rise time of the system is reduced to 8.21 seconds, which is realisable in reality when taking into account that the output of the system is measured after the compressor and not after the pressure vessel. The sampling ratio is of importance for the determination of the system models. The experimental setup used for modelling, is not optimal because of the slow response of the analogue, vacuum manometer at the inlet and the pressure container at the outlet. They both slow down the response of the system, which influences the obtained result. The main unreliability lies in the outlet valve that not guarantees an equal pressure going in and out of the pressure container. Changing this valve to a more suitable throttling valve, resolves some uncertainties of this thesis. To make sure the designed controller and the preliminary mechanical design obtain the requested result, a mechanical implementation of both components is necessary. 37

56 38

57 REFERENCES [1] AKO. (sd). Pinch Valve Advantages & Disadvantages. Consulted on 30 March 2017 through [2] Atlas Copco. (2015). Compressed Air Manual. (8th edition) Wilrijk: Atlas Copco. [3] Atlas Copco. (2012). Oil-injected rotary screw compressors. (1st edition) Wilrijk: Atlas Copco. [4] Emerson Process Management. (2005). Control Valve Handbook. (4th edition) U.S.A: Fisher. [5] Emerson. (sd). Valve Sizing Calculations. Consulted on 30 March 2017 through ce/d351798x012_11.pdf [6] Garlock. (sd). Butterfly Valve Performance. Consulted on 30 March 2017 through [7] Honeywell. (sd). Valve Selection and Sizing. Consulted on 30 March 2017 through alveselectionsizing.pdf [8] Parr, A. (2011). Control Valves. In A. Parr, Hydraulics and Pneumatics : A Technician's and Engineer's Guide (Vol. IV, pp ). Butterworth-Heinemann. [9] Pipe Flow Calculations. (sd). Flow in pipe - diameter, velocity, Reynolds number, Bernoulli equation, friction factor. Consulted on 5 May 2017 through [10] Prakash, R., & Singh, R. (1974). Mathematical Modeling and Simulation of Refrigerating Compressors. Thesis, University of Roorkee & Purdue University, School of Mechanical Engineering. [11] Smith, P., & Zappe, R. (2004). Valve Selection Handbook. (5th edition) USA: Elsevier. [12] Spirax Sarco. (sd). Control Valve Actuators and Positioners. Consulted on 30 March 2017 through Engineering-Tutorials/control-hardware-el-pn-actuation/control-valve-actuatorsand-positioners.aspx [13] Spirax Sarco. (sd). Control Valve Characteristics. Consulted on 30 March 2017 through Tutorials/control-hardware-el-pn-actuation/control-valve-characteristics.aspx [14] Stosic, N., Smith, I., & Kovacevic, A. (2005). Screw Compressor. In Mathematical Modelling and Performance Calculation. The Netherlands: Springer. [15] Van der Borght, M., & Veulemans, J. (2016). Optimalisatie studie van een olië geïnjecteerde cchroefcompressor met variabele snelheid aan de hand van inlaatklep en olieregeling. Thesis, Campus Group T, Faculty of Engineering. 39

58 [16] Werner, S., & Young, T. (2007). Iris Valves: How they work and how to apply them. Vortex Valves. North-America: CSC Publishing. [17] Walters, T. (2000, January). Gas-Flow Calculations: Don't Choke. Chemical Engineering. [18] University Of Washington. (sd). Lecture 9 Implementing PID Controllers. Consulted on 14 May 2017 through [19] National Instruments. (2016). How to Choose the Right DAQ Hardware for Your Measurement System. Consulted on 14 May 2017 through [20] National Instruments. (sd). Simple Solutions to Complex Challenges. Consulted on 14 May 2017 through [21] National Instruments. (sd). USB Consulted on 14 May 2017 through [22] IBS Batch Control. (sd). Exi Batch controller Batching Master 110i/210i. Consulted on 14 May 2017 through [23] Shaival, S., Agraj, S., & Anuj, S. (2011). Modernisation Of Pressure Control System Using LabView. Consulted on 14 May 2017 through PRESSURE-CONTROL-SYSTEM-USING-LabVIEW/ta-p/ [24] Atlas Copco. (2015). Oliegeïnjecteerde schroefcompressoren. Consulted on 14 May 2017 through tch_tcm pdf [25] Aström, K. (2002). PID Control. Consulted on 14 May 2017 through [26] Microstar Laboratories. (sd). Ziegler-Nichols Tuning Rules for PID. Consulted on 14 May 2017 through [27] Egger. (sd). IRIS Diaphragm Control Valve. Consulted on 14 May 2017 through 40

59 APPENDICES APPENDIX A SCHEMATIC REPRESENTATION OF THE COMPRESSOR... A.1 APPENDIX B INFORMATION SENSORS... B.1 APPENDIX C TRANSFER FUNCTION DERIVATION FOR THE IRIS VALVE... C.1 APPENDIX D TRANSFER FUNCTION DERIVATION FOR THE FRICTION LOSSES IN PIPES... D.1 APPENDIX E TRANSFER FUNCTION DERIVATION FOR THE COMPRESSOR... E.1 APPENDIX F MOODY DIAGRAM... F.1 APPENDIX G CONTROL LOOP EXPERIMENTAL SYSTEM... G.1 APPENDIX H DIGITAL PRESSURE SENSOR OUTLET... H.1 APPENDIX I DIGITAL VOLUME FLOW RATE SENSOR OUTLET... I.1 APPENDIX J DIGITAL TEMPERATURE SENSOR INLET... J.1 APPENDIX K 3D DRAWING IRIS VALVE... K.1 APPENDIX L STATIC MEASUREMENTS... L.1 APPENDIX M CURRENT ACTUATOR ATLAS COPCO... M.1 APPENDIX N IRIS VALVE ACTUATOR EGGER... N.1 APPENDIX O MEASUREMENTS USED FOR SYSTEM IDENTIFICATION... O.1 41

60 Appendix A SCHEMATIC REPRESENTATION OF THE COMPRESSOR Figure Appendices-1: Setup experiment [24] Table Appendices-1: Components of experimental setup 1 Inlet filter 8 Safety valve 15 Outlet digital pressure sensor 2 Sentinel valve 9 Oil separator 16 Outlet temperature sensor 3 Screw element 10 Minimum pressure 17 Condensate prevention cycle valve 4 ipm 11 Solenoid valve 18 Outlet digital volume flow rate sensor 5 Air/oil vessel + 12 After-cooler 19 Inlet vacuum manometer separator 6 Thermostatic 13 Fan 20 Inlet digital temperature sensor bypass valve 7 Oil filter 14 Oil-cooler 21 Inlet valve (simulated iris valve) A.1

61 Appendix B INFORMATION SENSORS Table Appendices-2: Sensor specifications Sensor Number Symbol Type Error 15 Wiki Model S-10 +/- 0.25% 16 Thermocouple type J +/- 2.2 C or +/-.75% 18 RVG-ST G25 DN25 +/- 1% 19 Mecman +/ bar 20 Hygrasgard AFTF /- 0.8 C B.1

62 Appendix C TRANSFER FUNCTION DERIVATION FOR THE IRIS VALVE dp = Q scfh G T c2 v p with G = 1; T = 25 o C = R; p 0 =1bar; Q scfh =0.028m 3 /h; (1) dp dp V = c 2 v 520 (2) V = c v 2 dp V = c v 2 [cuf t/h] (3) [m 3 /h] (4) C.1

63 Appendix D TRANSFER FUNCTION DERIVATION FOR THE FRICTION LOSSES IN PIPES 1. Major Losses with f = 16/Re; Re = v D/ dp 0 =4 f L v2 D 2 (1) 1 =2.34 [kg/m 3 ](see tabela 25C); 2 =5.72 [kg/m 3 ](see tabela 4bar) A 1 = m 2 ; A 2 = m 2 ; v 1 = Q A = m =6.155 [m/s] (2) v 1 = m = [m/s] (3) Kinematic viscosity : = (@ 298K); = (@ 308K) Determining reynoldsnumber : Using Moody Diagram to Calculate f f 1 =0.028; f 2 =0.032 Before the compressor : Re 1 = = (4) Re 2 = = (5) dp 0 f,1 = V ( ) 2 = V 1 2 (6) After the compressor : dp 0 f, = V 2 = ( ) V 2 2 (7) 2. Minor Losses Before the compressor : dp 00 f = X K v2 2 (8) dp 00 f,1 =1.7 V 2 1 = ( ) V 1 2 (9) D.1

64 After the compressor : dp 00 f,2 =5.15 V 2 2 = ( ) V 2 2 (10) 3. Total Losses: all these coe cients are multiplied with the density and then they are converted to a pressure drop in bars dp f = dp 0 f,1 + dp00 f,2 + dp00 f,1 + dp00 f,2 = V V 2 (11) 4. Determining a maximal value for the friction losses to see if they are not negligible: dp = =0.234[bar] (12) This is a maximal value that is relatively small compared to the 4 bar at the outlet. Point 5 will give an introduction in case that this approximation is not su cient. 5. How to linearize this approximation: A complex di erential equation based on the ideal gas law, rewrites this model to pressure variables similar to the experimental model: V = m R T p (13) dv = ṁ R T p m R T p 2 2 dp dt (14) With as friction factors for minor losses Table Appendices-3: List of friction factors Flow Obstacle Friction Factor Elbow, Threaded Regular 1.1 (90 ) Elbow, Flanged Regular 0.6 (90 ) Ball Valve, 2/3 closed 2.75 D.2

65 Appendix E TRANSFER FUNCTION DERIVATION FOR THE COMPRESSOR 1 Approximation using first law of thermodynamics with : dq =0(isentropic compression); ideal gas law : p V = m R T ; Internal energy : du = m c v dt ; du = dq p dv (1) c v R (p dv + V dp) = p dv (2) dp = (1 + R c v ) p dv V/m 2 Linearization around 4 bar and 16mm openingwith: R = 283 [J/kg K] c v = 718 [J/kg K] p 0 =0.975 [bar] (inlet pressure) dp =3.03 [bar] V/m = 1 =0.427[m 3 /kg] dp = (1 + c R v ) p dv V/m! v = (3) dp = (p p 0 ) (v v 0 ) 7.25 ( v v 0 ) (4) Transferfunction : dp V = 3.183s 7.25 s (5) 3 Rewriting the model to the variables used in the experimental approximation Making futher use of the ideal gas law and deriving this equation to both p 1 and p 2, the following simplifications can be made : V m = R T p d(v/m) dt = R T p 2 dp 1 1 dt R T p 2 dp 2 2 dt with as result : p 2 p 1 = (1 + R c v ) p1 2 dv RT (6) p 2 = p 1 +(1+ R ) p1 2 RT c v RT p 1 2 p 1 +(1+ R ) p1 2 p 2 c v p 2 2 (7) p 2 = 2.39 p ( p 1 p 2 ) 2 (8) E.1

66 4 Linearization around settling pressure of the experiment using 2mm inlet diameter with: p 2 =1[bar] p 1 = [bar] p 1 = [bar/s] p 2 = [bar/s] p 2 = ( p 1 Transferfunction : p 1,0 ) (p ( ) 2 1 p 1,0 ) (p ( ) 2 2 p 2,0 ) 0 p 2 (s) = 3.597s p 1 (s) (9) (10) E.2

67 Appendix F MOODY DIAGRAM Figure Appendices-2: Moody Diagram F.1

68 Appendix G CONTROL LOOP EXPERIMENTAL SYSTEM experimental system Step error PI(s) PID Controller 1 3s+1 output actuator Actuator Saturation s Iris Valve s+1 Electrical pressure sensor Theoretical system Step1 P(s) PID Controller1 1 3s+1 Actuator1 Saturation s Iris Valve1 error output output actuator klep s+1 Electrical pressure sensor1 disturbance 4.862s s s Experimental compressor system distubances s s Theoretical compressor system Matlab: P-action = 0.49; I-action = 0.13 Experimental system Theoretical system Bode Plot Combination Figure Appendices-3: Comparison of the theoretical control loop and the experimental control loop by the use of Simulink software G.1

69 Appendix H DIGITAL PRESSURE SENSOR OUTLET Figure Appendices-4: Page 1 of the appendix of the digital pressure sensor at the outlet H.1

70 Output signal Available output signals Signal type Current (2-wire) Voltage (3-wire) Ratiometric (3-wire) Other output signals on request. Permissible load in Ω Signal Current output (2-wire) (power supply V) / A ma ma DC V DC V DC V DC V DC V DC V DC V with optional settling time of 1 ms: (power supply V) / A Voltage output (3-wire) > maximum output voltage / 1 ma Ratiometric output (3-wire): > 4.5k Signal limiting (option) ma: Zero point: 3.6 ma 4) / 3.8 ma / 4.0 ma Full scale: 20 ma / 21.5 ma / 23 ma DC V: Full scale: DC 10 V / DC 11.5 V 4) Not possible in combination with zero point adjustment by the customer Voltage supply Power supply Maximum power supply for culus approval: DC 35 V (DC 32 V with heavy-duty connector) Current output (2-wire) ma: DC V (DC V with optional settling time of 1 ms) ma: DC V Voltage output (3-wire) DC V: DC V DC V: DC V DC V: DC V DC V: DC V DC V: DC V DC V: DC V Ratiometric output (3-wire): DC V: DC 5 V ±10 % Dissipation loss Current output (2-wire) 828 mw (22 mw/k derating of the dissipation loss with ambient temperatures 100 C (212 F)) Voltage output (3-wire) 432 mw Current supply Current output (2-wire): Current signal, max. 25 ma Voltage output (3-wire): max. 12 ma Time response Signal type Settling time per IEC Signal damping Standard 5) Option 1 6) 7) Option 2 Current (2-wire) 3 ms 1 ms 10 / 50 / 100 / 500 / 1,000 / 5,000 ms Voltage (3-wire) 2 ms 1 ms 10 / 50 / 100 / 500 / 1,000 / 5,000 ms Ratiometric (3-wire) 2 ms 1 ms 10 / 50 / 100 / 500 / 1,000 / 5,000 ms 5) 3 db limit frequency: 500 Hz 6) 3 db limit frequency: 1,000 Hz 7) Alternative specifications for ma output signal: Load: (power supply V) / A Power supply: DC V Switch-on time 150 ms Switch-on drift 5 s (60 s with optional zero point adjustment 0.1 %) WIKA data sheet PE /2014 Page 3 of 13 Figure Appendices-5: Page 2 of the appendix of the digital pressure sensor at the outlet H.2

71 Accuracy data Non-linearity (per IEC ) BFSL Terminal method Standard ±0.25 % of span ±0.5 % of span ±0.5 % of span Option 1 ±0.5 % of span ±1.0 % of span ±1.0 % of span Option 2 ±0.125 % of span 8) ±0.25 % of span 8) ±0.25 % of span 8) 8) Restrictions for the non-linearity of % BFSL or 0.25 % with terminal method: Available output signals: ma and DC V Available measuring ranges: All measuring ranges specified in the data sheet For further output signals or measuring ranges, please ask the manufacturer Calibration temperature Standard C ( F) Option 1 4 C ±5 C (39.2 F ±41 F) Option 2 40 C ±5 C (104 F ±41 F) Option 3 60 C ±5 C (140 F ±41 F) Option 4 80 C ±5 C (176 F ±41 F) Accuracy at calibration temperature Zero point adjustment Standard ±0.2 % of span, factory setting Option 1 ±0.1 % of span, factory setting 9) Option 2 ±10 % of span, customer setting 10) (stepwise 0.05 %) 9) Restrictions for the zero point adjustment of 0.1% (factory setting): Available output signals: ma and DC V Available measuring ranges: All relative pressure measuring ranges specified in the data sheet Not available in combination with optional calibration temperatures. 10) The customer zero point adjustment is not available for all variants of electrical connection, see Electrical connections. Relationship to the mounting position For measuring ranges < 1 bar (15 psi), an additional zero offset of up to 0.15 % applies Non-repeatability ±0.1 % of span Temperature hysteresis 0.1 % of span at > 80 C (176 F) Long-term drift (per IEC ) ±0.1 % of span ±0.2 % of span (with special measuring ranges and measuring ranges < 1 bar (15 psi)) Temperature error (for calibration temperature C ( F)) For measuring ranges < 1 bar (15 psi), special measuring ranges and instruments with an increased overpressure limit the respective temperature error increases by 0.5 % of span Temperature error [%] Medium temperature [ C] Page 4 of 13 WIKA data sheet PE /2014 Figure Appendices-6: Page 3 of the appendix of the digital pressure sensor at the outlet H.3

72 pr p Z hlwerk addiert pr p pr p Z hlwerkaddiert pr p Appendix I DIGITAL VOLUME FLOW RATE SENSOR OUTLET RVG: Rotary Gas Meters / fl ange connection Technical data RVG Gas temperature -20 to +60 C Ambient temperature -20 to +70 C Operating pressure Max. 20 bar Protection class IP67 (suitable for outdoor installation) Housing Aluminium or cast iron GGG-40; pistons made of aluminium Metrological approval PTB ATEX approval Ex-zone 1 Media Natural gas, town gas, inert gases, further gases on request Max. error ± 1 % for Q t - Q max ± 2 % for Q min - Q t Q t = 0.2 Q max, for measuring range 1:20 Q t = 0.15 Q max, for measuring range > 1:30 Q t = 0.1 Q max, for measuring range = 1:50 Q t = 0.05 Q max, for measuring range > 1:50 Reproducibility < 0.1% Applicable standards EN 12480, DIN EN and -5, EN 50020:2002 Index variants S1 (standard), Double direction index S1D, Absolute-ENCODER S1D (option) Retrofi table LF-Pulser IN-Sxx (Reed switch) Outputs Retrofi table LF-Pulser IN-W11 (Wiegand sensor, option) HF-pulser A1K (option) Pressure/temperature tapping 2 pressure tappings ¼ NPT, 2 thermowells applicable Measuring ranges: according EEC type approval D Size Measuring chamber [dm³] Start-up fl ow rate [m³/h] Q min [m³/h] national 1:160 Q min [m³/h] National 1:100 Q min [m³/h] National 1:65 Q min [m³/h] EU-Norm 1:20 Q max [m³/h] 2xNF [imp/m³] HF * [imp/m³] (Option) G 16 DN ~ G 25 DN ~ G 40 DN ~ G 65 DN ~ G 100 DN ~ 7528 G 160 DN ~ 3882 G 250 DN ~ 3178 G 400 DN ~ 2191 G 400 DN ~ 2191 * statet HF pulse values nominal, Specifi c values can deviate Double direction index S1D (option) p r p r p RVG with S1D and IN S11 Flow direction according to arrow on cover plate here left rght Flow direction according to arrow on cover plate, here top bottom p Upper index covered, lower free When fl ow direction bottom top cover is turned round, upper index is free, lower index covered pr-offtake always at inlet Horizontal fl ow: Reading from top Vertical fl ow: Reading from the front Absolute-ENCODER S1D Electronically readable mechanical double index PTB and ATEX approval For detailed information please see data sheet Absolute-ENCODER S1 2 Figure Appendices-7: Page 1 of the appendix of the digital volume flow rate sensor at the outlet I.1

73 Appendix J DIGITAL TEMPERATURE SENSOR INLET G HYGRASGARD KFF KFTF, AFF AFTF, AFF - LC AFTF - LC Quality product for HVAC sector, accuracy 3 % r.h. The calibrateable duct humidity outdoor humidity temperature sensors HYGRASGARD KFF KFTF, AFF AFTF, AFF - LC AFTF - LC measure the relative humidity and or temperature of air. They convert the measurands into standard signals of 0-10 V or ma and are optional available with or without display. Terminal box enclosure made of impact-resistant plastic with enclosure cover with quick-locking screws. They have four switchable temperature ranges and are applied in non-aggressive dust-free ambiences in refrigeration, air conditioning, ventilation and clean room technology. Relative humidity (in % r. H.) is the quotient of water vapour partial pressure divided by the saturation vapour pressure at the respective gas temperature. These measuring transducers are designed for exact detection of humidity. A digital long-term stable sensor is used as measuring element for humidity measurement. Fine adjustment by the user is possible. TECHNICAL DATA: Power supply: V AC (± 20 %) and V DC (± 10 %) for U variant V DC (± 10 %) for I variant (depending on working resistance) Power consumption:... < 1.1 VA 24 V DC ; < 2.2 VA 24 V AC Sensors:... digital humidity sensor with integrated temperature sensor, dew-proof, small hysteresis, high long-term stability Sensor protection:... membrane filter, plastic, exchangeable HUMIDITY: Measuring range, humidity: % r. H. (output corresponding to 0-10 V or 4 20 ma) Operating range, humidity: % r. H. (without formation of dew) Deviation, humidity: ± 3 % r. H. (20 80 %) at +20 C, otherwise ± 5 % r. H. Output, humidity: V at U variant 4 20 ma at I variant, working resistance < 800 Ω, see load resistance diagram TEMPERATURE: Measuring range, temperature:... multi-range switching (see table) C; C; C; C (output corresponding to 0-10 V or 4 20 ma) Operating range, temperature: C Deviation, temperature:... ± 0.8 K at 20 C Output, temperature: V or 4 20 ma or Ohm value Ambient temperature:... storage C, operation C Electrical connection:... 2-, 3-, or 4-wire connection (see connecting diagram), mm², via terminal screws on circuit board Enclosure:... plastic, material polyamide, 30 % glass-globe-reinforced, with quick-locking screws (slotted Phillips head combination), colour pure white (similar RAL 9010) KFF KFTF, AFF - LC AFTF - LC: enclosure cover for display is transparent! 72 x 64 x 37.8 mm (Thor III without display) 72 x 64 x 43.3 mm (Thor III with display) AFF AFTF: 108 x 70 x 73.5 mm (Thor II) Cable gland: M 16 x 1.5, including strain relief, exchangeable, max. inner diameter 10.4 mm Protective tube:... stainless steel, Ø 16 mm KFF KFTF : nominal length NL = 230 mm (optional 400 mm, 500 mm) AFF AFTF, AFF - LC AFTF - LC : NL = 45 mm Process connection:... KFF KFTF : by mounting flange, plastic (included in the scope of delivery, galvanised steel optional) Long-term stability:... ± 1 % per year AFF AFTF, AFF - LC AFTF - LC : by screws Protection class:... III (according to EN ) Protection type:... IP 65 (according to EN ) Standards:... CE conformity, according to EMC directive EC, according to EN : 2006, according to EN : 2006 Optional:... two-line display with illumination, cutout ca. 36 x15 mm (W x H), for displaying ACTUAL temperature and or ACTUAL humidity 10 Figure Appendices-8: Page 1 of the appendix of the digital temperature sensor at the inlet J.1

74 Appendix K 3D DRAWING IRIS VALVE Figure Appendices-9: 3D drawing of an iris valve mechanism K.1

75 APPENDIX L STATIC MEASUREMENTS Tabel Appendices-1: Static measurements Diameter [mm] Atmospheric pressure [bar] Pressure output [bar] 4 bar Pressure Output flow after valve compressor [bar] [l/s] Temperature Inlet [ C] Temperat ure vat [ C] Electric power [W] Relative humidity [%] Calculation: Pressure Difference dp compressor dp valve [bar] [bar] 70 1,00 4,03 1,00 8,15 23,10 35, ,14 31,00 3,030 0, ,00 4,04 1,00 7,69 22,90 35, ,96 31,00 3,040 0, ,00 4,00 0,98 6,76 22,90 35, ,14 32,00 3,025-0, ,00 4,01 0,98 5,44 22,40 34, ,16 33,00 3,035-0, ,00 3,98 0,95 4,48 22,40 33, ,90 32,00 3,030-0, ,00 3,93 0,75 3,37 22,50 34, ,80 33,00 3,180-0, ,00 3,93 0,60 2,79 22,50 33, ,30 34,00 3,330-0,400 Calculation Normal Flow Rate Using Formula Lab Session/Isentropic Compression Calculation using Constant Mass Flow Rate [Nl/s] Calculation using Ideal Gas Law [Nl/s] Output flow compressor [l/s] Input flow compressor [Nl/s] Input flow valve [l/s] Output flow compressor [Nl/s] Output mass flow compressor [kg/s] Input flow valve [Nl/s] Output flow compressor [Nl/s] Input flow compressor [Nl/s] Input flow valve [Nl/s] 28, ,312 78,312 28,94 165,52 70,74 29,07 78,66 78,66 27, ,142 74,142 27,35 156,43 66,85 27,47 74,47 74,47 23, ,192 64,024 23,78 136,05 58,14 23,89 65,49 64,32 19, ,929 51,981 19,28 110,26 47,12 19,37 53,18 52,23 15, ,004 42,421 15,82 90,47 38,66 15,89 44,21 42,62 11, ,206 31,109 11,70 66,94 28,61 11,76 38,39 31,26 9, ,113 25,767 9,69 55,45 23,70 9,74 37,30 25,90 L.1

76 Appendix M CURRENT ACTUATOR ATLAS COPCO ROTARY MOTORIZED VALVES ACTUATOR SERIES ARA600 PROPORTIONAL ESBE Actuator Series ARA600 for operating ESBE mixing valves DN The actuators have an operating range of 90 and can easily be manually operated. Patented + Registered design. Proportional OPERATION The ESBE series ARA600 is a compact actuator designed for operating rotary mixing valves DN The actuators ARA6X9 are controlled by proportional signal, and are recommended for mixing applications. The actuator has an operating range of 90 and the valve can easily be manually operated by the pull-and-turn knob on the front of the actuator. In addition to the proportional signal control, actuators series ARA639 can also be used for 3- and 2-point signal control. VERSIONS The actuators ARA6X9 are available for 24 V AC/DC, 50/60 Hz power supply. An auxiliary switch, which can be set in any position, is available as an optional kit to be ordered separately. The auxiliary switch is easily set by a unique solution, by just lifting off the turning knob the switch cam is accessible, no tools or disassembly required. The ARA659 can be set to running times of 45 and 120 seconds and is supplied with a 1.5 m cable attached. The ARA639 can be set to running times of 15, 30, 60 and 120 seconds. The ARA639 also have the additional features of proportional analogue output signal for monitoring devices etc, optional advanced noise reduction of the input signal and positioning memory for fast startup after power failure. SUITABLE MIXING VALVES Thanks to the special interface between the actuator series ARA600 and the ESBE valve series VRG and VRB, the unit as a whole has a unique stability and precision when regulating. The actuator series ARA600 is also easily mounted on the ESBE valve series MG, G, F, BIV, T, TM, H and HG. Series VRB100 Series BIV Series T and TM ADAPTOR KITS The actuator is supplied complete with an adaptor kit for easily fitting onto an ESBE rotary mixing valve. Adaptor kits can also be ordered separately. Art. No ESBE valve series G, MG, F, BIV, T, TM, H, HG (= supplied with actuator) ESBE valve series VRG, VRB, G, MG, F, BIV, T, TM, H, HG TECHNICAL DATA Ambient temperature: max. +55ºC min. -5ºC Power supply: 24 ± 10% V AC/DC, 50/60 Hz Enclosure rating: IP41 Protection class: II Torque: See table WIRING The actuator should be preceded by a multi-pole contact breaker in the fixed installation. Power consumption - Operation, AC: 5 W DC: 2.5 W Power consumption - Dimensioning, AC: ARA639, 11 VA ARA659, 8 VA DC: ARA639, 6 VA ARA659, 4 VA Rating auxiliary switch: 6(3) A 250 V AC Weight: 0.4 kg LVD 2006/95/EC EMC 2004/108/EC RoHS 2011/65/EC 6 24 V 5 N M 0-10 V, 2-10 V, 0-20 ma, 4-20 ma M 4 Y 0-10 V/2-10 V/0-20 ma/4-20 ma T 3 Y 2 X 2-10 V 1 N Actuator series ARA659 Actuator series ARA639 Copyright. Rights reserved to make alterations. 1 Figure Appendices-10: Datasheet of the current actuator of Atlas Copco M.1

77 Appendix N IRIS VALVE ACTUATOR EGGER IRIS Valve EGGER TURO PUMPS North America, Inc. IRIS Diaphragm Control Valve Design Features / Range Available Sizes: 1-24 Pressure : up to 87 psi higher upon request Temperature : up to 248 F higher upon request Designs IRIS Valve advantages Energy cost saving and low noise emissions through enhanced design Due to the almost free passage and low turbulences in our valve energy costs and noise emmissions are reduced to a minimum. Robust Construction Designed for continouos operation, particularly suitable for variable duties. Simple installation and commissioning. Non-clogging and self cleaning Due to the free, central flow design and automatic self cleaning feature of the segment edges during valve operation. Flushing connections are provided. Hysteresis-free and excellent regulation characteristics are the prerequisites for regulating tasks. This is achieved by the continually variable aperture from 0-100%, similar to the IRIS diaphragm of a camera, always maintaining a central flow axis and by an enhanced segment edge design. Several actuator designs available Electrical actuator for precise regulation permitting up to 1200 operations per hour. Optional pneumatic actuator, hand wheel or lever. Various fields of applications The valve may be used for liquids, gases, granuls or powders. Available with integrated flow measurement for gases (refer to back sided) EGGER TURO PUMPS P.O. Box Salt Lake City, UT Figure Appendices-11: Datasheet of Egger actuator N.1