Experimental Modeling and Control of Pneumatic Cylinders for Robotic Applications

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1 Experimental Modeling and Control of Pneumatic Cylinders for Robotic Applications Winnie Ngo Mechanical Engineering City College of New York 160 Convent Ave New York, NY USA Milwaukee School of Engineering 1025 N. Broadway Ave. Milwaukee, WI USA Faculty Advisor: Dr. Luis A. Rodriguez Abstract Recently, there has been growth in robotic technology designed to work more closely with humans, such as robotic support for rehabilitation and collaborative robots for production workers. According to the CDC, over 795,000 Americans experience a stroke each year resulting in impaired limb functionality, this increases the demand for robotic technology that can assist in their recovery. TechNavio, a technology and advisory company, projects a high annual growth rate in the market, which suggests an increase demand for collaborative robots in the workforce. High demand for these robots makes safety a priority for people working with them. The current literature suggests that use of compliant robots can limit damage and injury imposed on objects and humans, respectively. Robots should be capable of absorbing unexpected forces and controlling the amount of force applied. The high power to weight ratio and the natural compliance of pneumatics are appealing properties for the design of robots that closely interact with humans. Efforts have been made to control the level of compliance or stiffness in a robotic design to work with patients at different stages of rehabilitation. However, due to the compressibility of air, precise control of pneumatics has been a major challenge. This research focuses on the characterization and control of pneumatic cylinders for robotic applications. To better understand the dynamics of pneumatic cylinders, a custom testbed was developed to acquire experimental data that will be used to create more realistic mathematical models of the pneumatic system. Experimental data for the pressurization a fixed-volume was collected and agreed with observations made of the physical system. Additionally, force feedback control was implemented using an Arduino microcontroller to generate desired cylinder forces. Keywords: Pneumatic cylinder, experimental modeling, force control 1. Introduction According to the American Heart Association, on average, every 40 seconds an American has a stroke and strokes are the leading cause of long-term disability. 1 Advancements in robotics in the medical field have led to more humanrobot interaction to combat this issue. The increasing number of stroke survivors has also raised the demand of robots for rehabilitation. Robotic devices in contrast to traditional therapist are more efficient in carrying out therapy routines and storing information about patients performances and diagnosis 2. In addition, virtual simulation and games integrated into these robotic devices make the rehabilitation process more enjoyable for patients, and emerge patients in their therapy sessions 2. As more robots are designed to meet this demand, pneumatics can be incorporated to take advantage of their low initial cost, inherent compliance, simple and clean operation, and high power to weight ratio 3. Several pneumatic robotic systems, such as the ipam (University of Leeds), RUBERT (Arizona State University),

All these devices also include virtual simulations to engage the patients in activities to train the connection between the brain and the upper limb 4.

2 PNEU-WREX (University of California), and the SRE (University of Salford), were developed to train patients with upper limb disabilities 4. These devices have a gravity compensation mode that can support the weight of the patient's arm to allow the patient to move more freely 4. All these devices also include virtual simulations to engage the patients in activities to train the connection between the brain and the upper limb 4. The advantages found in most of these robotic arms are the comfort, safety, simplicity, and the lightweight quality of the device 4. These applications have demonstrated the qualities of pneumatics to be a sensible option for more safe lightweight and affordable rehabilitation devices. Figure 1. Patient using the ipam 4 Figure 2. Patient using the PNEU-WREX 4 In addition to rehabilitation devices, many companies and corporations have been adapting collaborative robots (cobots) into the work environment to boost the work efficiency of employees. From 2016 to 2021, the co-bot market is estimated to growth from $175.5 million to $ million; the compound annual growth rate is predicted to be 85.08% in that period. 5 This massive growth in the co-bot market indicate a high demand for co-bots, raising the need to further consider the safety of human-robot interaction. Pneumatics can be used to address this challenge, because it can make a co-bot system safer due to its natural compliance, but still have the high-power capabilities to perform various task. Additionally, force control and compliance are necessary to prevent a co-bot from damaging its surroundings and to allow absorption of unexpected forces. These two features have been heavily researched to expand the boundaries of robot or machine capabilities to do specific tasks and to be safer to its surroundings. Many tasks require the human touch that can be both rigid and compliant; most machines that are position based do not have the human touch capabilities and can damage their surroundings. One approach to improve compliance using other forms of actuation include adding an elastic element to the system to provide the compliant factor. 6 Other approaches compare the current command with the actual position and compensate for these unexpected external forces. 7 With the natural compliance of pneumatics, it could minimalize the effort to introduce compliance into a robotic system. It has been shown that pneumatics is beneficial in applications that require variable stiffness, because of the ability of air to compress and adjust the internal pressure; however, it is hard to control. To address the control challenges associated with pneumatics, numerous methods have been proposed in the literature. Many use controllers while others some use different hardware configurations to better control pneumatics 8. Examples of controllers that have been used to control pneumatics include linear and feedback linearization controllers, adaptive position and force controllers, backstepping controllers, twisting algorithm and sliding mode controllers. 9 These multiple efforts to advance pneumatic technology demonstrate a great inclination to further adapt pneumatics into real applications. Additional sensors and instrumentation are required that would require more special signaling, circuitry, and cost that complicates the system. 7 More studies still need to be done to more accurately identify and adjust to the nonlinearities found in pneumatic systems. Towards this goal, this research focuses on the experimental characterization and control of pneumatic cylinders for robotic applications. Experimental results will be used to improve and validate mathematical models of the system. These experiments include finding the mass flow rate in a fixed-volume chamber, calculating the force by measuring the pressure differences in the two chambers of the cylinder and implementing a force-feedback controller to manipulate the force generate by the cylinder. 1.2 Pneumatic Test Stand

3 A custom testbed was designed as a senior project advised by Dr. Daniel Williams. The purpose was to create a testbed as an educational tool for MSOE students to understand and learn more about pneumatics. The pneumatic components of the test stand consisted of an air compressor, an accumulator, a filter regulator (SMC AW20 and AFM20), two SMC electronic-pressure regulators (SMC ITV1050), two pressure switches (SMC ISE40A), two SMC flow switches (SMC PFMB7201), and a pneumatic cylinder. A diagram of the pneumatic circuit is shown in Figure 3. The test stand also included an Arduino to collect sensor data and to send control signals. 2. Methodology Figure 3. Experimental set up for the pneumatic system. 2.1 Pneumatic Model In the following, a mathematical model of the pneumatic cylinder is presented. Variables that include a or b in the subscript indicate whether the variable is representing chamber A or B as displayed in Figure 4. The pressure, area, and volume of chamber A are represented as P a or P b, A a or A b, and V a or V b, respectively. The mass flow rate is denoted as m a or m b, depending on the chamber. The bore diameter, rod diameter, stroke length, position of the piston, and thickness of the piston are represented as B, d, S, x, and t piston, respectively. Figure 4. Model of a Pneumatic Cylinder. The volume of Chamber A and B is given by equation (1) and (2), respectively.

4 V a = π 4 (B2 d 2 ) (S x t piston ) 2 (1) V b = π 4 B2 (x t piston 2 ) (2) From an energy balance, equation (3) and (4) were derived by Bobrow and McDonell 8. The known variables include the temperature of the supplied air as T s = 300 K, and the universal gas constant, R = 287 m 2 /s 2 K. The ratio of specific heat at a constant pressure and constant volume is given as k = (c p / ) = 1.4. P a = R ( c p ) T s m a V a P b = R ( c p ) T s m b P av a ( c p ) V a V b P bv b V b ( c p ) (3) (4) The force of the stroke can be found from equation (5) where P atm is the atmospheric pressure, A s is the cross-sectional area of the stroke, A a and A b are the area of the piston with respect to chamber A and chamber B. F c = P b A b P a A a P atm A s (5) 2.2 Pneumatic Actuator Characterization Fixed Volume Experiment The first experiment involved measuring the pressure with a fixed volume to help determine the mass flow rate of the system. The amount of pressure entering the chambers of the pneumatic cylinder was controlled by the electronicpressure regulators. By keeping the volume constant, equation (3) and (4) becomes equation (6) and (7). These two equations helped determine the mass flow rate of the system by observing that the mass flow is directionally proportional to the rate of change of the chamber pressure. P a = R ( c p ) T s V a m a P b = R ( c p ) T s V b m b (6) (7) Force Feedback Control Experiment A second experiment was performed to determine the force output based on the pressure difference of each chamber. The pressure regulators were used to input and measure the pressure of each chamber and a feedback control algorithm was implemented to maintain the desired force. The force feedback control loop utilized equation (5) to track the force generated by the pneumatic cylinder and followed the procedure shown in Figure 5. To track the force generated from the pneumatic cylinder and to help implement force control equation (8) was used to calculate the error, e, by taking the difference between the desired force and the force generated, denoted as F D and F C, respectively. The controller will use the error and a tuning constant, K p, to make the necessary adjustment. The adjustment sent to the plant to achieve the desired force is proportional to the product of K p and the current error.

5 e = F D F C (8) Figure 5. Force Feedback Control Loop. 3. Results and Discussion Fixed Volume Results For the fixed volume experiment three different pressure values were tested to pressurize chamber B with the cylinder fully extended (V B at max volume). The pressure values used included 5, 10, 15, and 20 psi and were sent to the pressure regulator in a square wave pattern as shown in Figure 6. Sending a square wave helped identify the start and end of the pressure input. Figure 6. Square wave input of a specified pressure value, P. To find the rate of pressure change, the derivative of the pressure data was taken through the numerical central differentiation method. After taking the derivative, the rate of pressure change was applied to equation (7). Figure 7 shows the pressure value collected from the sensor and the mass flow rate calculated taken from the data values. In each experiment with different pressure value, similar trends were found in all experiments. In each experiment, the mass flow rate peaked when the regulator began to pressurize as shown in Figure 7 between 1-2 and seconds. When the chamber depressurized the mass flows back out of the chamber as shown between 6-7 and seconds in Figure 7. After the peak, the mass flow rate would settle to roughly 0 kg/s when the chamber is filled.

6 Pressure (psi) Pressure (psi) Mass Flow (kg/s) Pressure of Chamber and Mass Flow Pressure of Chamber B Mass Flow from Pressure Time (seconds) Figure 7. Graph illustrates the measured pressure value and mass flow rate when rod is fully extended and a pressure of 5 psi is sent to the cylinder. Force Feedback Control Results A simple force feedback control was implemented to generate the desired force. As the pneumatic system was cycling through the control loop, data of the measured pressure values in each chamber was collected using an oscilloscope. Multiple desired forces, that included 5, 10, and 15 psi, were tested through this control loop and all had similar trends. Figure 8 is the pressure data collected under a control loop that aimed to generate 10 lb. of force with a tuning constant of K p = 0.9. Since the time of piston travel was approximately one second, it was difficult to implement multiple force control cycles between the start and end of travel Pressure A Pressure B Pressure of Chambers Time (seconds) Figure 8. Graph displays the measured pressure values of each chambers during force feedback loop with tuning constant of K p = 0.9 and desired force F = 10 lb. These pressure values were then used to find the force by using equation (5) to generate the graph shown in Figure 9. When observing the Figure 9, the control loop did maintain a force close to the desired force between seconds,

7 Force (lb) seconds, seconds. However, once the piston had reached the end of the travel the force value doubled because there was no longer a back pressure in chamber A. When the piston could no longer travel any further, chamber B and A was depressurized and pressurized, respectively, to return the rod to the retracted state. Force Generated Time (seconds) Figure 9. Graph displays the calculated force values based on pressure values in Figure Conclusion and Future Work Experimental data for the pressurization a fixed-volume was collected and agreed with observations made of the physical system. This data will be used in the future to validate simulated results from a mathematical model. One of the problems that was observed in experiments was the large amount of sensor noise that skewed the measured values; further work will include the development of a filter to limit the sensor noise. Additionally, through multiple attempts to control the pneumatic cylinder with an Arduino microcontroller, a consistent force was generated for each cycle. Due to the response time of the pressure regulator and the limited travel of the piston, it was difficult to have the Arduino keep up with the rapid motion. A pneumatic cylinder with a longer stroke length would be beneficial to test force control over a longer period of travel in future experiments. Further experiments are needed to completely characterize the dynamics of the pneumatic cylinder and will be addressed in future studies. 5. Acknowledgements The author would like to thank the National Science Foundation for the grant provided to this research and SMC for the generous donation of components for the pneumatic test stand. A special thanks to Dr. Luis A. Rodriguez (Advisor), Dr. Subha Kumpaty PE (Principal Investigator), Betty Albrecht, and all MSOE staff and REU participants for their support. The material is based upon work supported by The National Science Foundation under Grant No. EEC Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of The National Science Foundation. The material is based upon work using pneumatic components donated by SMC. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of SMC. 6. References [1] E. J. Benjamin and On behalf of the American Heart Association Statistics Committee and Stroke Statistics Subcommittee et al., Heart Disease and Stroke Statistics-2017 Update: A Report From the American Heart

8 Association, Circulation, 01-Jan [Online]. Available: [Accessed: 06-Jul-2017]. [2] K. D. O. Andrade, J. Martins, G. A. P. Caurin, R. C. Joaquim, and G. Fernandes, Relative performance analysis for robot rehabilitation procedure with two simultaneous users, th IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob), [3] B. Trinkel, CHAPTER 5: Pneumatic and hydraulic systems, Hydraulics & Pneumatics, 15-Oct [Online]. Available: [Accessed: 06-Jul-2017]. [4] R. Morales et al, Pneumatic robotic systems for upper limb rehabilitation, Medical & Biological Engineering & Computing, vol. 49, no. 10, pp , Aug [5] "Research and Markets; Global Cobots Market Growth at CAGR of 85.08%, with ABB, Bionic Robotics, Blue Ocean Robotics and Omron Adept Technologies Dominating the $3.81 Billion Market - Research and Markets,"Journal of Engineering, pp. 465, Available: [6] W. Roozing, Z. Li, D. G. Caldwell, and N. G. Tsagarakis, Design Optimisation and Control of Compliant Actuation Arrangements in Articulated Robots for Improved Energy Efficiency, IEEE Robotics and Automation Letters, vol. 1, no. 2, pp , [7] C. Trakarnchaiyo and A. M. S. Abeykoon, Vibration suppression design for virtual compliance control in bilateral teleoperation, nd International Conference on Control and Robotics Engineering (ICCRE), [8] J. E. Bobrow and B. W. McDonell, Modeling, identification, and control of a pneumatically actuated, force controllable robot, IEEE Transactions on Robotics and Automation, vol. 14, no. 6, pp , [9] T. Driver and X. Shen, Pressure Estimation-Based Robust Force Control of Pneumatic Actuators, International Journal of Fluid Power, vol. 14, no. 1, pp , 2013.

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