Pneumatic Positioner with Fuzzy Control

(;DpYrigth e IFAC )4olioo Control for Intelligent Automation fetUgia, Italy, 0cI0ber 1:1-29, 1992

PNEUMATIC POSITIONER WITH FUZZY CONTROL G. BELFORTE, T. RAPARELLI and M. VELARDOCCHIA

Politecnico di Torino, Department of Mechanics Corso Duca degli Abruzzi 24, I 10129 Torino, llaly

Abstract. A pneumatic positioner with closed loop fuzzy logic control is described. The system consists of a pneumatic cylinder, two proportional valves, a position and speed sensor, a fuzzy controller and an A/D-D/A conversion board. No braking devices for maintaining position are provided on the cylinder rod. The control considers position error and actuator speed as antecedents, and valve control voltages as consequents. Membership functions, the set of rules and the weights of each were obtained by considering the component characteristics and the relationships between _the antecedents and the flow rates to the cylinder chambers with varying control voltages. The latter were calculated using the min-max-center of gravity criteria. Experimental tests were carried out on the positioning system with different reference signal shapes and with different applied loads. Results show good positioning accuracy and repeatability, absence of overshoot and system stability under varying operating conditions. Keywords. Actuators; control applications; fuzzy control; non linear systems; pneumatic power systems; position control; proportional valves.

All investigators have found that the problem of pneumatic actuator motion control is difficult to solve because of air compressibility and the friction force between parts of the cylinder in relative motion.Modelling this positioning system calls for nonlinear equations and hard-to-identify parameters such as seal friction forces, flow parameters for valves and passages, natural frequencies of system components, etc. These difficulties complicate the definition of controller parameters. An attempt to overcome these limitations was made by Belforteand Raparelli (1988), who developed a control algorithm based on rules formalizing the pneumatic positioner's physical behaviour. The algorithm which was implemented on a microprocessor, overcame the problem of mathematical modelling and parameter

1. INTRODUCTION

No entirely satisfactory solution has yet been developed for the problem of implementing continuous pneumatic positioning systems. Indeed, these systems should show accwnte and repeatable positioning throughout the operating range together with insensitivity to disturbance and load variations, and should be provided with an easily defined and implemented control system. A number of authors (e.g. Liu and Bobrow, 1988; Ferraresi, Raparelli and Velardocchia, 1990; Belforte, Ferraresi and Velardocchia, 1990) have investigated the dynamic performance and positioning stability of a continuous pneumatic positioner with a classic control system. All of these investigations have indicated the difficulty of achieving systems which are at once fast. accwnte and stable. Other authors (e.g. Araki and YamamolO, 1990; Bobrow and Jabbari, 1991) have developed positioning systems with adaptive control. These systems are capable of rapid positioning even with varying system operation parameters, though it is difficult to guarantee position stability under all operating conditions.

identificati~.

In other areas of research, a number of authors (e.g. Daley and Gill, 1989; Masui, Terano and Sugaya, 1989; Maedaand Murakami, 1989) have demonstrated that techniques based on fuzzy logic can be used to control systems which are nonlinear, have a large number of input and output variables, are hard to model or have parameters which are not well identified. The, extent to which applying this type of control logic is

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BELroRTE G., RAPAREW T., VELARDOCGllA M.

successful depends on the level of knowledge of the regulated system's physical behaviour. Fuzzy control has been successfully applied in the areas of mechanical system control and industrial automation (e.g. Lim and Hiyama, 1991; Ide, Hosaka and Ohtsuka, 1991). Studies of fuzzy logic application to pneumatic positioning have been made by Matsui, Ishimoto and Takawaki(I990) and by Sanoand Fujita(l991). These studies also provide comparisons between performance levels achieved with different types of control, which show the fuzzy technique to be competitive.

friction material. Cylinder diameter is 20 mm, average rod diameter is around 11 mm and maximum stroke is 200 mm. Tubes connecting cylinder chambers with valves have an internal diameter of 4 mm and a length of 200 mm. Proportional valves are 3-way units with control voltages from 0 to 10 V; with a 5 V control signal, the user is isolated from the other ways. How rate for any given supply and operating pressure depends on valve control voltage. Valves feature 1/4' fittings, while component cutoff frequency is 4 Hz. The position transducer is a wire-wound potentiometer, while the speed transducer is a tachogenerator. Transducers are a press-fit on the same rotary shaft, which is driven by the wire connected rigidly to the cylinder rod. The controller is implemented using an Omron FP3000 digital fuzzy processor, in which control rules and membership function sets for antecedents and consequents are loaded. The l2-bit NO-D/A conversion boards are set to detect voltages varying from -10 V to + IO V and provide a position resolution of 0.097 mm. The test system can vary the traction load on the rod through the addition of a suspended mass connected to the rod via a non-extensible flexible cable and a relay pulley with negligible journal friction as shown in Fig. I. Braking devices for the cylinder rod are not provided.

This paper presents a continuous pneumatic positioning system with fuzzy logic control. Applying this control technique called for a knowle~ge of the operation of system components and their data sheets. No form of parameter identification was required, nor was it necessary to write a detailed model of the system. The actuator and control valves used were commercial units. A number of experimental tests were carried out in which system performance data with varying reference signal forms and load conditions were recorded. The electropneumatic system, rules, membership functions and results are presented and discussed below.

3. FUZZY MECHANICAL SYSTEM REGULATION

2. SYSTEM DESCRIPTION

In order to apply fuzzy control logic to the positioning system described above, it is necessary to establish the fuzzy inference rules by considering the relationships between position error and actuator speed (antecedents) and valve control voltages (consequents). Position error is the difference between reference signal and position signal. To establish these relationships. it is necessary to consider system operation and the commands which an operator would give the valves as antecedents vary. In general, reducing a position error involves directing air to one chamber of the cylinder and exhausting air from the other. The greater the error, the greater the air flow to or from the c ham bers m ust be in order to reduce rod positioning time. For position control purposes, using only the link between position error and control voltages can lead to overshoot and instability as a result of valve response times. the dynamic response of the pneumatic circuit (lines. fittings, chambers. etc.) and the mechanical system's dynamic behaviour (friction, inertia, etc.). To offset these phenomena, it is important to link control voltages to actuator speed as well as to position error. In this way, control action can cope with the speed with which error changes, and thus prevent the problems indicated above from occurring. In any case, an operator would react differently to position errors occurring with the system in motion or stationary, and the action would differ according to changes in the sign and modulus of velocity.

A schematic view of the positioning system is shown in Figure 1. The system consists chiefly of a pneumatic cylinder, two proportional solenoid valves, a position and speed transducer and a fuzzy controller, and incorporates provision for varying the load acting on the actuator rod. Pl\4lumolic cylinder

Fig. 1. Pneumatic posilioner

The pneumatic cylinder is a double-acting unit with an anti-rotation feature. This characteristic simplifies the system's mechanical confi guration, though the friction force is higher than it would be on an equivalent cylinder without anti-rotation. Sliding seals are conventional types, rather than consisting of special low

230

PNEUMATIC POSITIONER wrrn FUZZY CONmOL

The fuzzy rules were also established considering the overall effect of air flow to the cylinder chambers on the position etror. In addition, the rules make it possible to adapt conbol voltages to variations in the load acting on the rod for any given target position. A number of different rule sets were tested while maintaining the membership functions constant. The best performance was achieved with the set shown for front chamber valve control in Figme 2 and for the rear chamber valve in Figme 3. The labels shown in the figures are to be interpreted as follows: NM : negative medium; NS : negative small; ZR : zero; PS : positive small; PM : positive medium. ~

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Figures 2 and 3 also contain an activation rule for membership function PS or for one valve or the other independently of speed. When the error is NS, the rule is activated for the front chamber valve, while if the error is PS it is activated for the rear cylinder valve. These two rules serve to ensme that the control system directs an air flow to the actuator chambers which reduces position error independently of the other conditions. This independence from velocity prevents the conbol from exercizing an insufficient control action on the valves in certain situations. In this way, the system's response speed and repeatability was improved. The fuzzy variable membership functions shown in Figme ' 4 were initially determined on the basis of experience and a knowledge of system components, and subsequently refined in the light of test results.

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Error membership functions were symmetrically distributed relative to zero. Five membership functions are envisaged. Two further functions, PL (positive large) and NL (negative large) were originally provided. However, as experiments showed that large error conditions called for the same consequent actions as envisaged by functions PM and NM, functions PL and NL were incorporated in PM and NM respectively. The main difficulties in optimizing position error membership functions are due to the need to provide a group of fuzzy variables permitting satisfactory control with an error varying from around 0.1 mm to 200 mm. Error can in fact become very large following a step command, or be very small in the approach stage to the desired position. As position and error resolution is 0.097 mm, the effects of variations of even a few bits on the membership function configuration limits can have clear consequences on positioning. For example, a larger area assigned to function ZR can lead 10 less fmal precision, while excessively reducing this error can cause instability. To improve system accuracy and stability, membership functions NS and PS cross at

PS Fig. 3. Rule set for the rear chamber valve

The frrst line of the figures shows the position error membership functions (e), while the frrst column shows speed membership functions (v) used as antecedents of the fuzzy inference rules. The other terms include the output membership functions (V., V 2) consequent on the application of a rule. Rules can be found in Figmes 2 and 3 by postulating the membership functions of the antecedents and determining the consequent membership function as the intersection of the line and the col umn showing the antecedents. In Figme 2, for example, we have: ife=NM andv=NS then V.=PM if e = NS and v = ZR then V. = PM if e = ZR and v = PS then V. = PS

231

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BELFORTE G., RAPAREW T., VELARJXX:CHIA M.

zero error. In this way, an error which is very close to zero belongs to both functions, and to one of them to an extent such that the control action is significant. The three velocity membership functions were configured maintaining symmetrical distribution around zero and to avoid overlap between functions NS and PS. The control is thus sensitive to the sign of the velocity, and is not affected by transducer signal disturbance. Tests showed that varying the values of the velocity membership functions has less impact on system performance than varying the error membership functions. A symmetrical distribution around zero was also chosen for the voltage command membership functions. The five envisaged membership functions are identical for the two valves. Unlike those discussed above, the functions have constant value, as the fuzzy controller used dictates this configuration. Functions NM and PM, when are exercised alone, make it possible to place the chamber connected to the valve almost completely in exhaust or in supply. As in these cases the command is sufficient to make one of the two operating conditions prevail, it was not necessary to use PL (positive large) or NL (negative large) membership functions. More careful definition called for NS and PS membership functions, which are used to manage error reduction, position maintenance in the presence of disturbance, and positioner speed regulation in the vicinity of the desired condition. Values of these variables were:selected considering the natural frequency of the valves and delays for the pneumatic system and the system as a whole. Values were refined through experimental tests. Positioning instability may occur if NS and PS are too far from the ZR function, while a reduction in dynamic performance, a lessened capacity to oppose disturbance and a loss of accuracy may occur if they are too close. The membership functions which were found to be most satisfactory are shown in Figure 4. The fuzzy inference used to determine control voltages is the min-max-center of gravity method. The method is exemplified in Figure 5 for the case of two rules with two antecedents and one consequent. In the figure, XI and X2 denote the membership functions for position error and actuator velocity respectively, while Y is the consequent membership function for valve control voltage. The result produced by the two fuzzy inference rules is shown at the bottom of Figure 5.

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The control receives values for position error and velocity and determines the degree of membership Cl) with the antecedent fuzzy variables indicated in the rules. The minimum between the degrees of membership with the antecedents of a rule limits the consequent fuzzy variables Y to values ro..w,. If the same consequent variable is the result of different rules, the maximum a of the degrees of membership ro..w, which activate the variable is chosen. Commands sent from the control are calculated as

where subscript i indicates a generic output membership function. In the case at hand, i varies from one to five. 4. EXPERIMENTAL RESULTS Tests were carried out using a supply pressure of 0,6 MPa. Rules and membership functions were optimized for this pressure. Tests consisted of subjecting the system to different reference signal shapes and recording both the reference signal and system response. The reference signal is the voltage output of a function generator. In the diagrams, signals are shown in mm; the reference signal is indicated with 1 and the position signal with 2. For tests conducted without load, Figure 6 shows typical system response to a positive and negative step signal (gives as a square wave signal).

232

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Fig. 8. Ramp signal. without load Fig. 6. Positive and negative step signals. without load

The positive step corresponds to rod extension, while the negative step corresponds to retraction. On the average, system response time to the positive step is 0.25 s, while response time to the negative step is 0.2 s. Response time was measure at 50% of the value of the steady~state output signal. Note that in steady-state conditions the system shows no over-elongation, and the stationary error is maintained constant at around

Here again, system response is satisfactory: during the actuator extension ramp, the positioning error is virtually constant. During the retraction ramp, on the other hand, actuator response shows discontinuities due to the greater weight of stick-slip, as the thrust section is reduced by the presence of the rod. During ramp reversal, the system accumulated a marked delay due to the time required to adapt chamber pressures to the reversal of the sign of the friction force. System performance with a 2.5 kg load on the rod can be deduced from the curves shown in Figures 9 and 10.

0.2 mm for both extension and retraction. These

(mm)

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performance levels can be regarded as satisfactory in

2

view of the actuator used (standard seals with high

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friction levels varying with operating pressures and

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speeds) and in view of the valve response times.

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Figure 7 shows response to a square wave signal at 0.4

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Fig. 7. Square wave signal, without load

The system reaches the desired position with the response times and error indicated above, showing high

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positioning repeatability. In Figure 8, the signal is a ramp.

Fig. 10. Square wave signal. with load

233

(5)

BELFORTE G., RAPAREW T., VELARDOCCHIA M .

Figure 9 shows the response toa square wave command at 0.2 Hz. while Figure 10 shows the response to a square wave at 0.4 Hz. Performance is still satisfactory even though response times to the extension and retraction signal increase slightly. and the stationary error exceeds the no-load error only in certain conditions.

Ferraresi. C .• T. Raparelli and M. Velardocchia (1990). Studio della stabilita e della prontezza di sistemi di posizionamento pneumatici. Proceedings of X Congresso Nazionale AIMETA (Ed.). Vo!. 2. pp. 511-516. Belforte. G .• C. Ferraresi and M. Velardocchia (1990). Linear electro-pneumatic axis with position control. Japanese Journal Advanced Automation Technology. 2. 80-85. Araki. K. and A. Yamamoto (1990). Model reference adapti ve con trol of a pneumatic servo wi th a constant trace algorithm. The J. of Fluid Control. 20. 30-48. Bobrow. J.E. and F. Jabbari (1991). Adaptive pneumatic force actuation and position control. J. of Dynamic Systems. Measurement and Control. Transactions of the AS ME. 113.267-272. Belforte. G. and T. Raparelli (1988). Electrical control of pneumatic positioner without seals. The J. of Fluid Conl1ol. 18.7-18. Daley. S. and K.F. Gill (1989). Comparison of a fuzzy logic controller with a P+D control law. J. of Dynamic Systems. Measurement and Control. Transactions of the AS ME. 111. 128-137. Masui. S .• T. Terano and Y. Sugaya (1989). Identification of fuzzy rules in a manual control system. Proc. IFSA. pi. M2. 71-74. Maeda. M. and S. Murakami (1989). Steering control and speed control of an automobile with a fuzzy logic. Proc. IFSA. pi. M2. 75-78. Lim. C.M and T. Hiyama (1991). Application offuzzy logic control to a manipulator. IEEE Transactions on Robotics and Automation. 7. 688-691. Ide. H .• R. Hosaka and M. Ohtsuka (1991). Fuzzy Control of Robot Hand Based on EMG. Journal of Robotics and Mechatronics. 3. 435-436. Matsui. T .• E. Ishimoto and M. Takawaki (1990). Learning position control of a pneumatic cylinder using fuzzy reasoning. The J. of Fluid Control. 20. 7-29. Sano. M. and T. Fujita (1991). Fuzzy control of pneumatic cylinder by PCM driving mode. Int. Symposium on Fluid Power Transmission and Control. Beijing Institute of Technology Press. Beijing. China. pp. 330-334.

5. CONCLUSIONS The behaviour of a continuous pneumatic positioner consisting of commercial components without external braking systems and controlled using fuzzy logic techniques was analyzed. Physical knowledge of the system. as formalized in rules and membership function. was transferred to the fuzzy controller. It was not necessary to model mathematically the system. which is highly nonlinear and involves a number of hard-todetermine parameters. It was likewise unnecessary to identify system parameters. A number of different rule sets were tested. and the rules and membership functions with which the best experimental results were achieved are presented. It is entirely possible that there are better rule sets that those indicated herein. Experimental results show that the control logic is effective. as a fast. repetitive system showing good positioning accuracy was achieved.

This work was sponsored by Italian Ministry of Universityand Scientific Research and by the Omron Italy Company.

REFERENCES Liu. S. and J. E. Bobrow (1988). An analysis of a pneumatic servo system and its application to a computer-controlled robot. Journal of Dynamic Systems. Measurement and Control. Transactions of the ASME. 110. 228-235.

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