POLE ASSIGNMENT CONTROL ON ROBOT ARM USING PNEUMATIC ACTUATORS. Osamu Oyama, Masakazu Harada. Faculty of Engineering Meiji University Kawasaki, Japan

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1 POLE ASSIGNMENT CONTROL ON ROBOT ARM USING PNEUMATIC ACTUATORS Osamu Oyama, Masakazu Harada Faculty of Engineering Meiji University Kawasaki, Japan ABSTRACT Pneumatic actuators are cheaper and lighter and they can drive faster than any other robot actuators. So it is very interesting to use the pneumatic actuators such as air cylinder to the high accuracy robot systems. But in this case, the motion of robot tends to unstable by the air performance. To make stable the system, pole assignment control method is often used and the results by the electro-hydraulic cylinder driving system have been reported (1). The pole assignment method reported in this paper is useful to the electro-pneumatic cylinder driving system theoretically. The experimental results of pole assignment control for actual robot arm system are shown by using air cylinders. 1 ARRANGEMENT OF ROBOT ARM To evaluate the performance of pneumatic cylinder driving robot, the SCARA type two axes arm is made as shown in Fig.1. The dimensions of this arm are similar to human ones. The length and mass of Part" A" is 350 mm and 2.51 kg,part"b" is 300 mm and 1.22 kg. These parts are driven individually with 40 mm bore and 150 mm stroke air cylinders("a" and"b" respectively). The top of arm moves within almost 500 mm radius and 70 degree angle, and this range is not sufficient for practical uses. The cylinders are connected to the electro-pneumatic converters (2) and they are driven by electric proportional controllers. KEYWORDS Electro-pneumatic drive, Observer regulator, Pole assignment control, Robot arm, Precision positioning NOMENCLATURE A: Effective cross section [m3] C: Capacitance coefficient [Pa/V] D: Viscosity coefficient [N/mi] e: Input voltage of E/P converter [VI F: Feed back coefficient [v/..] f: Friction [N] G: Gain J: Inertial moment [Nm2] K: Feed back gain of regulator k: Sensitivity of E/P converter [Pa/V] 1: Length [m] m: Mass [kg] : Angle of axis [deg] e Fig.1 Two axes robot arm driven by pneumatic cylinders

2 The converter is consisted of a solenoid, a nozzle flapper mechanism and a Diaphragm as shown in Fig.2, and converts electric signal to proportional air pressure. The supply pressure of converters are 200 kpa. The axis angles are detected by the rotary potentiometers and are fed back to controllers to compose the closed loop. Fig.4 Distribution of positioning e1 axis Fig.2 Proportional electro-pneumatic converter by using diaphragm Fig.5 Illustration of the arm about mainly part"a" Fig.3 Path of arm when it moves along two dimentional continuous assigned path In Fig.3, the path of the top of arm is shown when the arm moves very slowly along the desired path determined by the spline function about 17 assigned points. It is shown that the two dimentional continuous positioning by pneumatic actuator is possible too as another electric or hydrauric actuators. The accuracy of positioning at a certain point is tested when only cylinder"a" moves and cylinder"b" is locked. The distribution of positioning 01 angle for 50 times is shown in Fig.4.In this case, the standard derivation of e1 angle is almost 0.14 degree and it corresponds to 0.85 mm at the top of arm. When the arm moves fast, the motion of arm tends to become vibratile. 2 POLE ASSIGNMENT CONTROL The scheme about mainly part"a" of the arm is illustrated in Fig.5 In order to examine the fundamental performance of the arm easily, it was tested under the condition that only cylinder"a" moves and part"b" is locked at 90 degree place against "A". In this case the top of arm moves on the circular path which center is e1 axis. The state equation of this condition is represented by:

3 where The motion of el axis of arm to step reference signal when controlled by proportional action is shown by the solid line in Fig.6. Where Gp is a proportional gain of analogue controller. In both cases about Gn, the axis moves with overshoot acti6n and when G becomes larger, the motion becomes unstable. The theoretical values of Eq.(1) are shown by dotted lines. They agree with experimental ones well when Gn is less than 4, but they don't agree when G is larger the reason is supposred because of system nonlinearity. In order to reduce the overshoot of motion, the regulator system of angle should be composed by feeding back the all of state variables. In this study, Pc is set to constant and the state equation (1) is shifted to single input system. Then A and B is modified to A' (3x3),b' (3x1) with equilibrium about Pc. e is given as: Where e1 is the angle of axis, f is the force generated by cylinder, r and r' are the lengths between connecting points respectively, D1 and D are the viscose coefficients of e1 axis and cylinder "a" respectively, Ah and Ar are the effective cross section areas of head side and rod side of cylinder "a" respectively. Pc is the pressure of head side of cylinder, e,k and C are the input voltage, the sensitivity and the capacitance coefficient of electro-pneumatic converter respectively. And M is the mass of piston, J is the inertial moment, m and 1 are the mass and the length of part of the arm. Eq.(1) is linearlized near the moving point. Where F1,F2 and F3 are variables to chan9e the system pole. The signals of e1 and f cannot be obtained directly, so the observer is provided to estimate these signals. The summations and multiplications of Eq.(6) are executed by analogue circuits. shown in Fig.7. The observer is composed of analogue circuits and has the same order of the arm although required outputs are only two. The reason why the third order observer is used, is to assure the accuracy of the output by comparing with the estimated e1 and experimantal e1. Where K1,K2 and K3 are variables to assign the observer poles. The real part of these poles are tuned to be smaller than that of the arm system poles. Fig.6 Motion of e1 axis when step input is yielded Fig.7 Combination of observer and proportional controller made by analogue circuit

4 3 EXPERIMENTAL RESULTS The comparison estimated outputs and calculated values when the step signal is given to the observer as input is shown in Fig.8. The experimental value (the solid line) and calculated one (the dotted) shows rather good agreeme9,t for e, but not good agreement for 8. But it can't be improved because of the saturation of analogue circuits. Fig.9 Motion of 91 axis with pole assignment control Fig.8 Comparison obtained outputs of observer and theoretical outputs when the step signal is given The eigenvalues of matrix:a'-bif are selected to assign the system pole by changing the F1,F2 and F3. When the poles are assigned to and i, the theoretically motion to step reference input is suppressed to no overshoot condition shown by the dotted line in Fig.9. But as the experimental result shown by solid line, the overshoot action still remains. When the poles are assigned to and i although the theoretical motion responses with a small overshoot, the experimental motion can responses as desired. The reason of difference between theory and experiment is consider that it is effected by the nonlinearity of the system parameters. The distribution of positioning angle to a certain Place when the poles are assigned to and i is shown in Fig.10. The standard derivation is degree and it corresponds to 0.38 mm at top of arm. The distribution when the poles are assigned to and i, and it is the optimal condition of stability as experiment, is shown in Fig.11. The standard derivation of angle is degree and then the accuracy of positioning becomes wrong than the upper case. The positioning accuracy is estimated to have relation with the velocity of piston and to have no relation with Fig.10 Distribution of positioning 91 axis when pole is assigned to and }1.56i Fig.11 Distribution of positioning el axis when pole is assigned to and }+4.00i

5 the stability near the stopping position. 4.CONCLUSION In order to use the pneumatic actuators for the high accuracy robot system the SCARA type two axes arm is prepaired and tested. As a result it is possible to use the pneumatic cylinder for this arm as same accuracy as the other actuaters. But, When the speed of motion becomes fast the arm moves with the overshoot action. Then the pole assignment control method are attempted to stabilize the motion. The third order observer and the proportional controller are proposed, and then the regulator system is composed. It has been shown that the motion of the arm can be stabilized by pole assignment control with feeding back the all state variables. But the positioning accuracy when the arm moves vibratile is better than that of when the arm moves without overshoot action. The positioning representaion accuracy of top of the arm under optimal stability condition is within }0.75 mm, and this value is not sufficient for practical use. But, it seems to be possible to improve the accuracy by applying higher feed forward gain. It is necessary to realize the following subjects. The observer and controller must be replaced with digital circuits to avoid the saturation of the signal. ACKNOWLEDGMENTS We are grateful for the cooperation during the students of Meiji University, to Mr. Tosikatsu Akiba, Mr. Makoto Nakatsugawa, Mr. Yasuyuki Tominaga and Mr. Ikuo Taguchi. REFERENCES 1 J. W. Fi nney and M. S. Bloor and G. S. Gill, A Pole-Assignment Controller for an Electrohydraulic Cylinder Drive, Trans. of ASME, Vol.107, June 1985, 145/150 2 O. Oyama and H. Mitsuda and M. Harada, Positioning of Piston with Electro- Pneumatic Servo-System, Journal of JHPS, Vol.16 No.4, 1985, 275/280