AN AUTOMATIC DEPTH CONTROL SYSTEM FOR ON-LINE MEASUREMENT OF SPATIAL VARIATION IN SOIL COMPACTION

Transcription

1 AN AUTOMATIC DEPTH CONTROL SYSTEM FOR ON-LINE MEASUREMENT OF SPATIAL VARIATION IN SOIL COMPACTION W. Saeys, A. M. Mouazen, J. Anthonis, H. Ramon Department of Agro-Engineering and Economics, Faculty of Agricultural and Applied Biological Sciences, Kasteelpark Arenberg 30, B-3001 Heverlee, Belgium; INTRODUCTION Problem Soil compaction is usually measured manually by means of different penetrometers and core samplers, referring to soil penetration resistance and dry bulk density, respectively. Based on these measurements 2D and 3D soil compaction maps can be constructed regardless of soil surface unevenness. Since these manual measurements are difficult and time costly, some trials have recently started to focus on the on-line measurement of soil compaction, using different mathematical models and measurement techniques. Mouazen et al. (2003) developed a model to calculate soil compaction indicated as dry bulk based on measured draught of a subsoiler, soil moisture content and depth. Since the formula for prediction of the soil compaction based on the draught measurement also depends on the cutting depth, the depth variations of 0.07 m when using two depth wheels are too large to obtain reliable soil compaction predictions. As a consequence, it is impossible without depth measurement to distinguish whether a higher draught is the result of a higher compaction or of a deeper measurement. This makes these compaction maps difficult to interpret and rather useless for the farmer. An automatic depth control system will eliminate the depth variation problem during the on-line measurement of soil compaction, allowing the development of fixed depth soil compaction maps. Literature review Various control systems have been developed and tested to control the working depth of an agricultural machine by means of a hydraulic actuator (Lee et al., 1998; Condon et al., 2001). Each control system consists of three parts: a depth sensor, an actuator to change the working depth and a controller. The depth sensors are classified as contact and non-contact sensors. The non-contact ultrasonic and infrared sensors were intensively used for this purpose (Yasin, et al., 1992; Lee et al., 1998). Most researchers working on depth control systems on agricultural machinery obtained good results using simple linear controllers. Weatherly and Bowers (1997) developed a proportional controller for depth control of a seed planter. Condon et al. (2001) tuned a PID controller (Proportional Integrative Derivative) for a depth control system of a peat milling machine. Lee et al. (1998) designed an on-off controller for the depth control of rotary implements. Sφgaard (1998) developed an automatic depth control system for a finger weeder. Since each implement or machine type has its own dynamics and actuators, a new type of implement will require another controller. Objective In this paper a model based control system is designed to maintain the cutting depth of a subsoiler used as on-line compaction sensor, as constant as possible. Since soil compaction is measured on-line after harvesting the previous crop, the presence of stubble and plant residue makes the readings of non-contact sensors to detect the frame vertical distance unreliable. Therefore, the first objective of this study was to

2 develop and evaluate a pendulum-type metal wheel sensor on different surfaces. The hydraulic three point linkage system of a New Holland 8160 agricultural tractor with attached soil compaction sensing tool, was used as the actuator for depth control. To be able to develop an adequate controller a model was build. This model combines the dynamics of the hydraulic system with the tractor dynamics to be able to simulate the influence of all possible inputs on the controller performance. Finally, several types of linear controllers were developed, evaluated and compared on the resulting model and validated in the field for their ability to reduce the depth variations of the compaction sensor. WHEEL SENSOR Methodology The pendulum-type metal wheel sensor consists of a heavy wheel with a diameter of 0 4 m and a weight of 175 N, to make the distance measurement less sensitive for the presence of stubble and plant residue than the non contact sensors. An LVDT displacement transducer realises a vertical connection between the frame and the wheel shaft. The wheel sensor is calibrated by measuring the Volt signal of the LVDT displacement transducer at different frame heights and performing a polynomial fit on the obtained data. The wheel sensor constitutes of a pendulum mechanism, of which the equations of motion are found in almost every textbook of control theory or mechanical vibrations (Franklin et al., 1994; Meirovitch, L., 2001). The bandwidth of the sensor depends on the natural frequency and the damping of the pendulum. From a pendulum experiment a natural frequency of 1.3 Hz and a damping ratio of were measured. Since this damping ratio is so small, one would expect the useful bandwidth of this sensor to be lower than the resonance frequency, because near the resonance frequency the wheel would bounce heavier than the soil undulations. However, this damping ratio of didn t take the damping effect of the soil into account. When applying a load (wheel) to it, the soil behaves rather plastic than elastic. This plastic behaviour causes energy dissipation preventing or at least reducing the bouncing of the wheel, which is a form of damping. Therefore, the functional bandwidth of the wheel sensor depends on the soil conditions and was determined experimentally on different running surfaces. With respect to the spatial resolution of the sensor, the wheel diameter plays a dominant role. When a larger wheel is used, undulations close to each other cannot be measured anymore, but a smaller wheel would be more sensitive for the crop residues and stubble. Since most sudden variations are limited in height to 0.05 m, the spatial variation was calculated to be approximately 0 26 m. A commercially available UC2000 ultrasonic sensor with a spatial resolution of 0.1 m was fixed to the same frame just 0 25 m ahead of the wheel sensor to be able to compare their performance on different running surfaces (namely, asphalt road, soil road and wet silty clay loam field). On the field the subsoiler was fixed on the frame and pulled into the soil throughout four lines at 0 15 m depth, whereas two other lines were measured without soil cutting by the subsoiler. For a detailed description of this sensor design the reader is referred to Mouazen et al. (2004). Results and discussion When the wheel distance sensor rotated on the hard and even surface of the asphalt road, no deformation of the road occurred beneath its relatively heavy mass. Therefore, a perfect coincidence of the frame height measurement variation was found between the ultrasonic and displacement sensors, and a standard deviation of m was

3 found between the two measurements. The relatively uneven surface of the soil road resulted in reasonably oscillating measurements of the frame height change. The tendency of the frame height change coincided well for both sensor measurements. Compared to the asphalt road, a higher standard deviation of m was found between the two-sensor measurements. At some locations, the wheel sensor system provided millimetre-scale over measurement of height variation compared to the ultrasonic sensor. This was attributed to the small sinkage of the wheel in the softer soil surface, due to its relatively large weight of 175 N. On the stubble covered field, this large weight resulted in a very small influence of the maize stubble on the wheel sensor output, where the ultrasonic sensor signal showed radical fluctuations. A standard deviation of m was calculated between these two measurements. This effect will be important during measurements of soil compaction, performed after the harvest of previous crop, when the soil surface is covered with dense stubble or plant residue. Very similar frame distance variations were measured with both sensors when crossing a clean soil surface, with draught sensor installed and without draught sensor installed. In comparison with the standard deviation (0 039 m) of the measurement line with maize stubble, smaller standard deviations of 0 007, , , and m were found for the five lines with clean surface. This also clearly indicates that the draught sensor has no significant influence on the frame height measurement from the ground surface obtained from both sensors. In spite of the fact that the large mass of the wheel sensor assists to overcome the problem of stubble presence, the distance between the frame and soil surface is over measured due to the wheel sinkage in the deformable wet soil with clean surface. The mean extra height measured by the wheel sensor ranges between and m. A mean correction factor of m is calculated for the five measured lines. This correction factor is subtracted from the displacement sensor measurement, leading to high coincidences between the two sensor measurements for the three measurement lines performed with draught sensor installed and the two measurement lines without draught sensor installed. This encourages adopting the pendulum-type metal-wheel displacement sensor for the measurement of the frame height distance from the soil surface, particularly when the measurement is performed on a dense stubble soil surface after the harvest of the previous crop. MODEL Since the hydraulic system of the three point linkage connects the subsoiler to the tractor, any force acting on the subsoiler has its reaction force acting on the tractor and vice versa. This means that the movement of the subsoiler and the control actions of the actuator can excite the dynamics of the tractor, while the displacements under the tyres will be transferred to the subsoiler. Therefore, the depth control system was modelled in two distinct parts: one for the electrohydraulic subsystem and one for the tractor dynamics. The equations of motion for the tractor were developed using a simplified kinematic model based on generalised Lagrange coordinates (Qiu et al., 1999; Anthonis et al., 2003). The model structure for the electrohydraulic system was developed using a mechanistic approach (Anderson, 1988; Wu et al., 1998; Qiu et al., 1999), but the parameters were estimated by means of frequency domain identification techniques (Clijmans et al., 2000; Pintelon & Schoukens, 2001). For a detailed description of the modelling the reader is referred to Saeys et al. (2004). Kinematic analysis of an agricultural tractor Since only the motions in the vertical XY plane influence the depth of the subsoiler, the tractor with subsoiler is considered as a planar mechanism. The determination of the

4 equations of motion for the tractor-subsoiler system is based on the calculation of the kinetic energy of the mechanism and the calculation of the virtual work of all discrete internal and external forces performed on the mechanism (Petyt, 1990; Anthonis & Ramon, 2003). In order to calculate the kinetic energy and the virtual work, the tractorsubsoiler system was divided into 6 rigid bodies having at least one degree of freedom to all other bodies linked to. All model parameters were determined experimentally by direct measurement and modal analysis. The resulting model has only 2 generalised coordinates instead of the 7 initial generalised coordinates. These two generalised coordinates are the vertical translation (bounce) and the rotation (pitch) of the tractor multibody system. A third degree of freedom comes from the translation α of the actuator resulting in a rotation of the subsoiler with respect to the tractor. This variable acts as an input of the kinematic model together with its first and second derivative. This input of the kinematic tractor subsystem model is the output of the hydraulic subsystem model and was used to couple both subsystem models to obtain a global model. A fourth input of the system is the force f s exerted by the soil on the cutting tool of the subsoiler. This tractor model was validated by comparing the modal frequencies obtained from a one poster shaker experiment with the subsoiler attached to the tractor with the calculated modal frequencies for this multibody system. Identification of the hydraulic subsystem The hydraulic system of the three point linkage of the New Holland 8160 agricultural tractor has a proportional relative position controller, which converts the voltage corresponding to a certain position set point to a certain relative angular position of the two lower linkage bars. Since the specifications of the hydraulic components of this system were proprietary and not readily available, the model structure was determined based on theoretical considerations. First, the model structure of the uncontrolled three point linkage was determined. This hydraulic subsystem converts a voltage applied to the proportional valve to a position of the lower linkage bars. Since the electronics are much faster than the hydraulics, and since the inertial force and the Coulomb friction force are negligible compared to the spring force and the viscous friction force, the model was simplified. Therefore, the transfer by the proportional valve of an applied voltage to an oil flow rate through the valve was modelled as a first order system. Since the velocity of the hydraulic actuator is proportional to the oil flow rate, it acts as an integrator for the transfer from oil flow rate to actuator position and to the position of the linkage bars attached to it. This means that the open loop hydraulic subsystem can be modelled as a second order system: ϕ( s) K G0 ( s) = = V ( s) s( s + τ ) (1) Adding the proportional relative position controller results in the following second order model for the controlled hydraulic subsystem: K0K s( s + τ ) K0K G( s) = = 2 K0K 1+ s + τ s + K0K s( s + τ ) (2) The parameters of this model were determined by experimental frequency domain identification. To obtain sufficient information about the system in a relatively small measurement time, the system was excited with a full optimized multisine. A multisine

5 is a summation of sine waves with a certain spectrum. The phases of these sine waves were optimised (Pintelon & Schoukens, 2001). The frequency range of the signal had an upper limit of 1.1 Hz, because this was found to be the highest frequency to which the system responds. The sample frequency was set at 30 Hz. The measurement file was loaded into Matlab and the non-parametric errors-in-variables estimator for the Frequency Response Function (FRF) was calculated. The model parameters were then determined by an absolute nonlinear least squares estimation (Pintelon & Schoukens, 2001). The absolute nonlinear least squares model estimation G M after 14 iterations on the nonparametric FRF was calculated from the measurement data for an engine speed of 1450 min -1 as: GM ( s) = s s (3) where, s is the Laplace operator. This model provided a good prediction of the measured FRF. Combination of both models The model for the tractor subsystem and the model for the hydraulic subsystem were converted to state space and combined to obtain a global model. The inputs of this model are the uncontrollable inputs u: the displacements under the tyres (w 1, dw 1 /dt, w 2, dw 2 /dt) and the downward force f s on the cutting tool, and the controllable input: voltage v applied to the hydraulic subsystem. The output y t is the absolute vertical position of the cutting tool measured by the wheel sensor. For displacements under the tyres with a frequency lower than 10 rad/s or 1.6 Hz, the tractor was found to behave as a rigid body. This means that all disturbances under the tyres with a frequency higher than 1.6 Hz will be transmitted unchanged through the body to the cutting tool. The transfer function from the applied voltage v to the absolute depth of the cutting tool y t was derived from the state space model as: G ( s )( s )( s s )( s s ) ( s s 275.5)( s 1.301s 325.6) T ( s) = 2 2 (4) The complex poles and zeroes are close together and far away from the upper frequency limit of the hydraulic subsystem at 1.1 Hz. Therefore, they were cancelled out to simplify the transfer function: 197 GT ( s) = ( s )( s ) (5) where, the poles are those of the hydraulic subsystem. Comparison of the bode plots for Eqn (4) and (5) shows that the second order model of the hydraulic subsystem multiplied by a conversion factor is a good approximation for the full model in the frequency range of the hydraulic subsystem. This simplified model was used for the controller design.

6 CONTROLLER Methodology The different controllers were designed based on the root locus or Evans diagram (Nise, 2000; Franklin et al., 1994). Time domain performance criteria for controller design such as rise time, overshoot and settling time were incorporated in the diagram and the desired gain was selected from the plot. Owing to the two real poles of the system, the root locus is a straight line parallel to the imaginary axis when leaving the real axis. As the settling time is inversely proportional to the real part of the poles (Franklin et al., 1994), this implies that with a simple Proportional controller the settling time could not be changed. An acceptable trade-off between overshoot and static error was found at a static error of around 20% and a damping ratio of 0.5. A lead compensator has more degrees of freedom than a P-controller such that no trade-off between overshoot and static error had to be made. This is actually a PD (Proportional Derivative) controller with filtering of the high frequency noise, which is most of the time present in practical set-ups. The location of the pole and the zero were determined by the pole placement method proposed by Nise (2000). For the lead compensator a settling time of 0.78 s (half the settling time of the P-controller) and an overshoot of 10 % (corresponds to a damping ratio of 0.6) were used as design criteria. With a PIDcontroller (Proportional Integrative and Derivative controller), the static error could be made zero and the bandwidth can be increased. Reducing the static error to zero was achieved by the I-action, while the PD part of the controller added a zero to improve the transient response of the system. The same design specifications were imposed as for the lead-compensator i.e. a settling time of 0.78 s and an overshoot of 10 %. The PID controller was designed by making use of the root locus based methodology described in Nise (2000). As the amplification curve of the bode plot increased with 20 db per decade, a possible problem of the PID controller was the amplification of high frequency noise. A stationary experiment on the tractor revealed that this was indeed a problem. Thererfore, a first order low-pass filter was added to the D-action similarly to the lead-compensator. The controllers were first evaluated on the design model described in the previous section. As disturbance signal, a measured depth variation of the subsoiler was added to the output of the design model. This depth variation had been measured in previous field experiments on the subsoiler without depth control at a speed of 0.28 m/s. Finally, the controllers were transformed to the Z-domain (discrete) and implemented on the system. The controllers were evaluated in field conditions by crossing 70 m on a wet silty clay loam harvested maize field in April at a speed of 0.5 m/s. A speed of around 0.5 m/s is often used by the authors to measure soil compaction. Because of hardware limitations, the reaction of the depth control system is limited to 1.1 Hz. By this, only variations in depth below 1.1 Hz could be compensated by the controller and provided information about the performance of the controller. On the other hand, the variations of the depth above 1.1 Hz delivered information about the performance requirements of the hardware. In case the amplitude of these variations would have been too high, the hardware (in this case the three point hitch) needed to be improved. Note that the bandwidth of the depth sensor was restricted to 1.3 Hz. Increase of the dynamics of the three point hitch would also require a sensor with a higher bandwidth. To investigate the performance of the PID controller at high speed measurement, an experiment has been performed at 6 km/h with and without controller. This experiment was performed at the end of August on a dry silty clay loam field after wheat. The soil crust was broken by a tooth harrow. A lot of dry clods were present on the soil surface, which were not broken by the wheel sensor. For a detailed description of the controller design and validation the reader is referred to Anthonis et al. (2004).

7 Results Without controller, depth variations of around 0.12 m were observed. All controllers achieved a considerable improvement and kept the depth variation within 0.02 m (0.04 m range). The PID with D-filter controller showed the best performance. It maintained the range in depth within a band of 0.02 m (0.01 m variation). The depth variations beyond 1.1 Hz generally remained within a range of 0.02 m, which is acceptable. Taking into account that measurement of depth variations on sub centimetre level is practically infeasible and certainly doesn t make sense, given the size of soil granulates, it was concluded that the dynamics of the three point hitch are sufficient to control the depth of the subsoiler. Furthermore, implementation of a more complex controller doesn t make sense for this hardware. A more advanced controller could possibly reduce the depth variations below 1.1 Hz to sub-centimetre level. However, as the depth variation beyond 1.1 Hz cannot be controlled, the over-all range of depth variation would still be within a band of 0.02 m, which is the over-all depth variation of the PID controller with filter on the D action. During the high speed measurements the depth variations below 1.1 Hz without control had a range of 0.1 m, whereas the controller reduced this band to 0.03 m. Because of the clods on the field, the variations beyond 1.1 Hz varied in a range of 0.04 m. Again, the difference between the depth controlled subsoiler and the uncontrolled were significant. Therefore, it was concluded that the depth control system preserves its performance at higher speeds. CONCLUSIONS A depth control system for a subsoiler for online measurement of soil resistance has been designed. The cutting depth was measured with pendulum-type wheel sensor, which signal is less influenced by the stubble and crop residues than non contact distance sensors. A model for the simulation of the influence of all the controllable and uncontrollable inputs on the performance of the depth control system was developed. The operation of the hydraulic subsystem was found not to excite the tractor dynamics when the subsoiler was attached to it. Based on a simplified model several modelbased controllers have been conceived and tested. Without controller, changes in the subsoiler cutting depth of about 0.12 m (0.06 m variation) were observed. With a simple P controller, already a good performance was achieved (0.02 m depth variation). A PID-controller with filter on the D-action further reduced the depth variations by a factor of 2 (0.01m). With the actual hardware i.e. depth sensor and three point hitch, only depth variations below 1.1 Hz can be compensated. Design of a more advanced controller than the PID-controller with filter on the D-action doesn t make sense, as the measured depth variations beyond 1.1 Hz were in the same range as the regulated depth by the controller. These variations were in the range of 0.01 m, which is actually the maximum achievable accuracy on a field that makes sense. Therefore, it can be concluded that the dynamics of a simple three point hitch and the developed wheel sensor are sufficient to control the depth of a subsoiler to measure soil compaction. Even for high speed applications, the control system was found to be successful in maintaining the desired depth of the implement.

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