Comparison of servo tracking capability of the interconnected cylinders positioning system with servo pneumatic positioning system

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1 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 214 December 12 th 14 th, 214, IIT Guwahati, Assam, India Comparison of servo tracking capability of the interconnected cylinders positioning system with servo pneumatic positioning system Saravanakumar D 1*, Mohan B 2 1* Department of Production Technology, MIT Campus, Anna University, Chennai, India saravanapoy@gmail.com 2 Department of Mechanical Engineering, CEG Campus, Anna University, Chennai, India mohan@mitindia.edu Abstract Servo pneumatics is a mechatronic approach that enables accurate position control of pneumatic drives with high speed. In the present study, a new method of position manipulator with two interconnected pneumatic cylinders is presented. Nonlinear mathematical model of the system comprising of mass flow rate, pressure dynamics, frictional forces and motion dynamics has been formulated. Using Matlab-Simulink software, the system has been simulated. The positioning performance of the proposed system is compared with the servo pneumatic system with single cylinder. The simulation results shows that the proposed system has better performance indices than existing servo pneumatic system. The interconnected pneumatic cylinders system is observed to have satisfactory regulatory and trajectory tracking performances. Keywords: Servo Pneumatics, Positioning systems, Mechatronics, Modelling and Simulation 1. Introduction Pneumatic actuators are widely used in the field of automation, robotics and manufacturing. Traditionally pneumatic cylinders are used for motion between two hard stops. The pneumatic technology exhibits many advantages such as high speed, high force generation, better efficiency, less maintenance and low operating costs. In order to expand the capabilities of the pneumatic cylinders to be operated as multi-position actuator, servo control techniques are being used. The significant problem is that such drives are nonlinear: the pressure within the pneumatic cylinder, the frictional force, and the compressed air flow rates through the chokes of the pneumatic drive all vary in nonlinear fashion. The dead zone and time delay characteristics of the servo valve also adds to the complexity for designing controller for the system. Mathematical modelling of the system becomes very important for development of controller for the system and also to optimize the parameters in the system. Takosoglu et al. (29 formulated mathematical model for servo pneumatic positioning system. Najafi et al. (29 developed a mathematical model for the pneumatic positioning system also considering the cushioning in the cylinder. Miyajima et al. (27 presented an explicit model for spool movement inside a proportional directional control valve. Saleem et al. (29 developed mathematical model for frictional forces inside pneumatic cylinders. Saravanakumar and Mohan (213 have developed a detailed mathematical model for the servo pneumatic positioning system. In Pneumatic actuators there is always a compromise between speed and the accurate positioning. But the present industry requires the actuators having larger stroke lengths, high speed and better accuracy. Many researchers have tried different types of hybrid actuators which has one actuator to travel the coarse and another for accurate positioning. Chiang et al. (25 developed hybrid pneumaticpiezoelectric actuator for long range and precise positioning. Chiang (21 developed an X-Y dualaxial intelligent servo pneumatic-piezoelectric hybrid actuator for position control with high response, large stroke and nanometer accuracy. Liu and Jiang (27 developed a hybrid actuator comprising of piezoelectric impact force coupled with differential pressure for the pneumatic positioning device. Nishioka et al. (21 proposed a new control method for a multiplex pneumatic transmission constructed with special resonant valves and air tubes with a control system driven by air vibration in air tubes without electrical wires. Juhász and Maas (211 have described a hybrid positioning system consisting of a DC drive and piezoelectric actuator. Michellod et al. (26 have designed a hybrid manipulator with stepper motor and piezoelectric actuator. Bone and Chen (212 have used a hybrid pneumatic-electrical actuator for robot manipulation. But these hybrid actuators do not possess all the advantages of pneumatic actuators. In this study a system comprising of two pneumatic cylinders attached to each other is proposed to solve the problem. One cylinder supplied with high pressure undergoes the coarse movement and another cylinder supplied with low pressure is used to fine movement. The optimal system parameters for accurate positioning of the system are obtained in Saravanakumar and Mohan (213a. 6-1

2 Comparison of servo tracking capability of the interconnected cylinders positioning system with servo pneumatic positioning system Figure 1 Schematic representation of interconnected pneumatic cylinders system The performance of the proposed system is compared with the existing single cylinder servo pneumatic system. The preliminary study of the study has been given in Saravanakumar and Mohan (213b. The parameters such as rise time, settling time, maximum overshoot, Integral of absolute error (IAE, Integral of the time-weighted absolute error (ITAE, Integral of square of error (ISE and Integral of the time-weighted square of error (ITSE are used for comparing the performance of these two systems as used by Takosoglu et al. ( System description 2.1. System overview The system consists of two pneumatic cylinders A and B which are interconnected to form a series linear manipulator. The master cylinder A is fixed and the cylinder B is coupled to the rod end of the cylinder A. The cylinder A has been utilized mainly for the coarse movement and it is supplied directly from air source with comparatively high pressure. The cylinder B is for the fine movement which has reduced air pressure from the flow control valve as shown in the Figure 1. Two proportional directional control valves (DCV V1 and V2 are used to control the position of cylinders A and B respectively. The position transducer senses the senses the position of the external load connected to the rod end of the cylinder B and feeds it to the control system. The controller manipulates the voltage applied to the proportional control valves thus controlling the position of the manipulator Mathematical model of the system The mathematical model of the system has been derived from physical laws and recent literature information. The system constitutes the nonlinearities of the dead zone, the mass flow rate, the pressure dynamics and the motion equation, that includes the friction dynamics. The position of the entire linear manipulator is the sum of position values of the two individual position values as given by (1. x = x + x (1 a where x is the position of the coupled manipulator, x a and x b are the positions of cylinders A & B respectively. The position of individual cylinders A b and B are given as per Newton s second law of motion by (2 and (3 respectively. Aa1Pa1 Aa2Pa2 Ffa && xa = (2 M + m + M + m L a b b A P A P F b1 b1 b2 b2 fb && xb = (3 ML + mb where A a1 and A a2 are cross sectional area of two chambers of cylinder A, A b1 and A b2 are cross sectional area of two chambers of cylinder B, P a1 and P a2 are absolute pressure in two chambers of cylinder A, P b1 and P b2 are absolute pressure in two chambers of cylinder B, F fa and F fb are frictional forces in two cylinders, m a and m b are internal piston mass of cylinders A and B respectively, M b is the total mass of cylinder B, M L is the external load. The absolute pressure values inside the two chambers of cylinders A and B are given by (4, (5, (6 and (7 respectively. = Rm P A v ( & a1 a1 a1 a1 a A a1(la + x a = Rm + P A v ( ( & + a2 a2 a2 a2 a Aa2 la la xa = Rm P A v ( & b1 b1 b1 b1 b A b1(lb + x b = Rm + P A v ( ( & + b2 b2 b2 b2 b Ab2 lb lb xb (4 (5 (6 (7 where is adiabatic exponent, l a and l b are stroke lengths of cylinders A and B respectively, l a and l b are lengths of dead zone of cylinders A and B respectively, R is specific gas constant, and are mass flow rates to two chambers of cylinder A, and are mass flow rates to two chambers of cylinder B, v a and v b are velocity of cylinders A and B respectively. The mass flow rate values for two chambers of the cylinders A and B are given by (8, (9, (1 and (11 respectively. m& = ρ x C P w C P w (8 ( ( ( ( a1 ra 14 as a1 45 m& = ρ x C P w C P w (9 a2 ra 23 a as 12 m& = ρ x C P w C P w (1 b1 rb 14 bs b1 45 m& = ρ x C P w C P w (11 b2 rb 23 b bs

3 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 214 December 12 th 14 th, 214, IIT Guwahati, Assam, India where is air density, x ra and x rb are spool movements in the proportional directional control valves connected to cylinders A and B respectively which depends on the coil voltages u a and u b applied, P as and P bs are absolute pressure values of air supplies to cylinders A and B respectively, C 14, C 45, C 23 and C 12 are sonic conductance consistent with the standard ISO for critical pressure ratio, w 14, w 45, w 23 and w 12 are nonlinear flow function (sonic flow and subsonic flow depending on the pressure ratio and on the critical pressure ratios b 14, b 45, b 23 and b 12. The equations of frictional forces in cylinders A and B are given by (12 and (13 respectively. F = f v + F sign(v fa l a k a v a v sa F e sign(v k (P P + + pr a pa a1 a2 F = f v + F sign(v fb l b k b v b v sb F e sign(v k (P P + + pr b pb b1 b2 (12 (13 where f l is viscous coefficient of friction, F k is Kinetic coefficient of friction, v sa and v sb are Stribeck velocities, F pr is break away force and k pa and k pb are friction coefficients due to seals Control System The structure of the closed loop servo control system of the positioning system comprising two interconnected pneumatic cylinders is shown in Figure 2. The system has two different controllers to control the two cylinders. The cylinder A which is used for coarse movement is controlled by a proportional controller via DCV V1. A Fuzzy PD controller is used for controlling the position of Cylinder B which is used for fine movement via DCV V2. The position transducer measures the total position of the manipulator and compares with the desired position value to generate the position error. This error value is fed to both the controllers to make corrective actions. manipulates the mass flow rate to the cylinder chambers, thus controlling the position of the cylinder. The fuzzy PD controller is designed using fuzzy logic toolbox of Matlab-Simulink software. The Fuzzy controller works on the knowledge base containing IF-THEN rules for undetermined predicates and fuzzy control mechanism. The primary input variable Position error e(k in the range -5 to 5 has five membership functions. They are NB (Negative Big, NS (Negative Small, ZE (Zero Error, PS (Positive Small and PB (Positive Big. The shape and range of the membership functions are shown in Figure 3a. The next input variable Change in Position error e(k in the range -1 to 1 has three membership functions namely NE(Negative Error, ZE(Zero Error and PE(Positive Error. Figure 3b shows these membership functions shape and range. The output variable Control Voltage to the Proportional Valve u(k has the range to 5 and posses seven membership functions. The values of the constant membership functions NB(Negative Big, NS(Negative Small, NVS(Negative Very Small, Z(Zero, PVS(Positive Very Small, PS(Positive Small and PB(Positive Big are shown in Figure 3c. Figure 2 Basic structure of the control system Fuzzy controller which basically work based on the knowledge base similar to a human operator is capable of controlling complex nonlinear system. So a sugeno type discrete fuzzy PD controller is designed for the accurate positioning control of the cylinder B. The controller has two inputs position error e(k and change in position error e(k and one output voltage applied to the proportional valve u(k. The voltage applied to the proportional valve u(k Figure 3 Membership functions of fuzzy PD controller variables aposition error e(k, bchange in position error e(kand cvoltage applied to the proportional valve u(k 6-3

4 Comparison of servo tracking capability of the interconnected cylinders positioning system with servo pneumatic positioning system Figure 4 Simulation model of the system in Matlab-Simulink For convenience the rules of the fuzzy algorithm are shown in Table 1 in a matrix format and should be interpreted as follows: IF e(k is X AND e(k is Y THEN u(k is Z where X, Y and Z are corresponding membership functions. The fuzzy inference method used is MAX MIN method. The Defuzzification method used in the Fuzzy PD controller is Centroid method. Table 1 Rule Base for Fuzzy PD Controller Rule Base Change in Position error e(k NE ZE PE NB NB NS NS NS NS NVS NVS ZE NS Z PS PS PVS PVS PS PB PS PS PB Position error e(k 2.4. Simulation Environment The simulation model of the entire system has been created based on (1 to (13 using Matlab- Simulink software. The simulation model of the positioning system containing two interconnected cylinders is shown in Figure 4. The simulation tests are conducted using the system parameters shown in Table 2. From the simulation response of the system, the rise time (T r, the settling time (T s, maximum overshoot (OS max, Integral of absolute error (IAE, Integral of the time-weighted absolute error (ITAE, Integral of square of error (ISE and Integral of the time-weighted square of error (ITSE are computed. These parameters are used to analyze the speed and accuracy of the system. Rise time is the time required for the response to rise from 1% to 9% of its final value. Settling time is the time required for the response curve to reach and stay in final steady state value with ± 2% error. Thus rise time and settling time indirectly refers to speed of the positioning system. Overshoot refers to an output exceeding its final steady-state value. The maximum deviation from the steady-state value is the maximum overshoot which will be expressed in percentage. Thus overshoot is measure for accuracy of the system. Table 2 System Parameters used in the numerical simulations Parameters Values A a1 64 X 1-5 m 2 A a2 45 X 1-5 m 2 A b1 25 X 1-5 m 2 A b2 18 X 1-5 m 2 P as.6 MPa P bs.2 MPa m a and m b.5 kg M b.4 kg M L 2 kg 1.4 R 288 Nm/kgK kg/m 3 l a and l b.2 m l a and l b.2 m C 14, C 45, C 23 and C X 1-8 m 4 s/kg b 14,b 45,b 23 and b f l 25 Ns/m F k 1 N v sa and v sb.1 m/s F pr 2 N k pa and k pb 3 N/Pa Integral of absolute error (IAE is accumulation of the absolute error values which is given by (14. Integral of square of error (ISE accumulates the square value of error which is given by (15. ISE have more effect to errors of higher magnitude. Integral of the time-weighted absolute error (ITAE and Integral of the time-weighted square of error (ITSE are the time dependent indices which penalizes long time errors. ITAE and ITSE are the integral time weighted parameters which are depends on time which is combined measure of both speed and accuracy of the 6-4

5 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 214 December 12 th 14 th, 214, IIT Guwahati, Assam, India Reference change Step Ramp Table 3 Performance indices of the systems from simulation results System T r (s T s (s OS max IAE ISE ITAE ITSE (% (m (m 2 (sm (sm 2 Interconnected cylinders system P s =.6MPa P s =.4MPa P s =.2MPa Interconnected cylinders system P s =.6MPa P s =.4MPa P s =.2MPa system. ITAE and ITSE are given by (16 and (17 respectively. IAE = e( t dt (14 ( e t 2 ISE = ( dt (15 ITAE = t e( t dt (16 ( 2 ITSE = t e( t dt (17 where t is simulation time and e(t is position error at the time t. 3. Results and discussions The performance of the positioning ability of the proposed system with two pneumatic cylinders interconnected is compared with the servo pneumatic system with single cylinder. For this comparison the mathematical model of the single cylinder servo positioning system given in Saravanakumar and Mohan (213 has been used. The fuzzy PD controller as described in Saravanakumar and Mohan (212 has been used for controlling the system. The same system parameters are used for both the systems and all simulation tests are carried out simultaneously. Figure 5 Response of the systems when a step change in reference signal from m to.1m is applied at simulation time.1s Figure 6 Response of the systems when a ramp change in reference signal from m to.1m with slope.3m/s is applied at simulation time s The performance of the positioning ability of the two systems is analyzed by applying change in input reference signals (setpoint. For testing the regulatory performance of the systems, a step input signal is applied. Similarly to test the setpoint tracking capabilities of the systems, ramp input reference signal are applied. A step change in input signal from m to.1m is applied to the two systems at simulation time.1s. The response of the interconnected pneumatic cylinders system and servo pneumatic system at different supply pressures (.2MPa,.4MPa and.6mpa are shown in Figure 5. When a ramp input from m to.1m with slope.3m/s applied at simulation time s, the response of the systems is shown in Figure 6. The Performance indices of the systems subjected to step and ramp signal are given in Table 3. In the single cylinder pneumatic servo system, there will be a compromise between speed and accuracy of the system. When the supply pressure to the system is low, the speed is reduced to have a better positioning accuracy. If the supply pressure is high, the system operates in high speed which produces more errors and overshoots. From the Table 3, the above facts are observed to be true. The proposed two interconnected pneumatic cylinders system overcomes this problem. It has better speed 6-5

6 Comparison of servo tracking capability of the interconnected cylinders positioning system with servo pneumatic positioning system and accuracy as described by the performance indices. This system has the speed of high pressure servo system and the overshoot is much less as in low pressure servo system. All the other integral performance indices have low values for the proposed system which signifies the better positioning performance of the system. The proposed interconnected pneumatic cylinders system is observed to have satisfactory regulatory and trajectory tracking performances. 4. Conclusions A new method of position manipulator with two interconnected pneumatic cylinders has been presented in the current research. The mathematical model of the system comprising of motion dynamics, pressure dynamics, mass flow rate variations and frictional forces has been developed. The positioning performance of the proposed system is compared with the servo pneumatic system with single cylinder. The proposed system overcomes the speed/accuracy preference problem in servo pneumatic system with high speed and better accuracy. The simulation results shows that the proposed system has better performance indices than existing servo pneumatic system. The interconnected pneumatic cylinders system is observed to have satisfactory regulatory and trajectory tracking performances. References Bone, G.M. and Chen, X. (212, Position Control of Hybrid Pneumatic-Electric Actuators, Proceedings of American Control Conference (ACC 212, pp Chiang, M., Chen, C. and Tsou, T. (25, Large stroke and high precision pneumatic piezoelectric hybrid positioning control using adaptive discrete variable structure control, Mechatronics, Vol. 15, pp Chiang, M.H. (21, Development of X-Y Servo Pneumatic-Piezoelectric Hybrid Actuators for Position Control with High Response, Large Stroke and Nanometer Accuracy, Sensors, Vol. 1, pp Juhász, L. and Maas, J. (211, Online Controller Optimization for Piezoelectric Hybrid Micropositioning Systems. Proceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM 211, pp Liu, Y.T. and Jiang, C.C. (27, Pneumatic actuating device with nanopositioning ability utilizing PZT impact force coupled with differential pressure, Precision Engineering, Vol. 31, pp Michellod, Y., Mullhaupt, P. and Gillet, D. (26, Strategy for the Control of a Dual-stage Nanopositioning System with a Single Metrology. Proceedings of 26 IEEE Conference on Robotics, Automation and Mechatronics, pp Miyajima, T., Fujita, T., Sakaki, K., Kawashima, K. and Kagawa, T. (27, Development of a digital control system for high-performance pneumatic servo valve, Precision Engineering, Vol. 31, pp Najafi, F., Fathi, M. and Saadat, M. (29, Dynamic modeling of servo pneumatic actuators with cushioning, International Journal of Advanced Manufacturing Technology, Vol. 42, pp Nishioka, Y., Suzumori, K., Kanda, T. and Wakimoto, S. (21, Multiplex pneumatic control method for multi-drive system, Sensors and Actuators A, Vol. 164, pp Saleem, A., Wong, C.B., Pu, P. and Moore, P.R. (29, Mixed-reality Environment for Frictional Parameters Identification in Servo-Pneumatic System, Simulation Modelling Practice Theory, Vol. 17, pp Saravanakumar, D. and Mohan, B. (213, Nonlinear Mathematical Modelling of Servo Pneumatic Positioning System, Applied Mechanics and Materials, Vol , pp Saravanakumar, D. and Mohan, B. (213a, Optimization of Size Parameters for Interconnected Pneumatic Cylinders Positioning System, Proceedings of the 1st International and 16th National Conference on Machines and Mechanisms (inacomm213, pp Saravanakumar, D. and Mohan, B. (213b, Performance Comparison of Interconnected Pneumatic Cylinders Servo Positioning System, Proceedings of Indian Conference on Applied Mechanics (INCAM 213. Saravanakumar, D. and Mohan, B. (212, Simulation Study of Servo Control of Pneumatic Positioning System using Fuzzy PD Controller, Proceedings of International conference on Emerging Trends in Science, Engineering and Technology (INCOSET 212, pp Takosoglu, J.E., Dindorf, R.F. and Lashi, P.A. (29, Rapid Prototyping of fuzzy controller pneumatic servo system, International Journal of Advanced Manufacturing Technology, Vol. 4, pp Takosoglu, J.E., Laski P.A. and Blasiak, S. (212, A fuzzy logic controller for the positioning control of an electropneumatic servo-drive, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, Vol. 226, pp