Department of Mechanical Engineering, CEG Campus, Anna University, Chennai, India

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1 Applied Mechanics and Materials Online: ISSN: , Vols , pp doi: / Trans Tech Publications, Switzerland Comparison of Servo Positioning Performance of Pneumatic Cylinders using Proportional Valve Method and PWM Control Method Mohan B 1,and Saravanakumar D 2 1 Department of Mechanical Engineering, CEG Campus, Anna University, Chennai, India 2 Department of Production Technology, MIT Campus, Anna University, Chennai, India 1 mohan@mitindia.edu, 2 saravanapoy@gmail.com Keywords: Servo Pneumatic system, Simulation, Position control, Performance comparison, Nonlinear systems, Mechatronics. Abstract. Servo pneumatics is a mechatronic approach that enables accurate position control of pneumatic drives with high speed. The current study presents a comparison of two servo techniques for position control of pneumatic cylinders. One method uses a proportional valve and another method uses PWM controlled solenoid valves. Mathematical models of the system including the nonlinearities such as mass flow rate, pressure in cylinder chambers and frictional forces are presented in this paper. Using the simulation model created in Matlab-Simulink software, the two systems are analyzed for tracking performances. From the responses it is observed that the proportional valve technique has better tracking characteristics than PWM control technique. 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 in designing control system is that the pneumatic system is highly nonlinear. The pressure within the cylinder chambers, the frictional forces and the compressed air flow rates varies in nonlinear fashion. There are mainly two different techniques to establish servo control for the pneumatic drives. The most preferred method is to use a servo or proportional directional control valve. This valve acts both as directional and flow control valves which can be electronically controlled by manipulating the voltage applied to it. The cheaper and economical method for implementing the servo control technology is to utilize ordinary solenoid directional control valves. By modulating the pulse width of the voltage signal applied to these valves, the air flow rate and direction can be controlled. During the selection between these two servo control techniques, there must be always a compromise between cost and performance. The working life of the valve is badly affected when PWM signal is applied. Servo control for pneumatic actuators is an interesting area of research for many scholars over the last decade. Many authors [1-4] presented mathematical models and control techniques for servo pneumatic systems using proportional valves. Analysis of servo systems using PWM controlled solenoid valves has been reported in literatures [5-7]. The objective of the current study is to compare the two servo positioning systems and analyze their tracking capability. Servo Pneumatic Position Systems For precise positioning of pneumatic cylinders in many applications, the preferred method is to use a proportional directional control valve. Fig. 1a shows the schematic diagram of servo positioning system for a pneumatic cylinder with a proportional DCV. The main components of the system are pneumatic cylinder, proportional DCV, position transducer and the fuzzy controller. The position transducer senses the present position value and transmits the value to the controller. The fuzzy All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-10/05/16,09:55:56)

2 1234 Engineering and Manufacturing Technologies controller takes the corrective action by manipulating the voltage applied to the proportional valve. The spool valve movement is controlled as per the applied voltage which in turn varies the air flow rates to the cylinder chambers. This air flow rate variations to the chambers controls the position of the cylinder forming a closed loop servo system. Fig. 1. Schematic diagram of servo pneumatic positioning system using a) Proportional DCV and b) PWM controlled solenoid valves The economical method of obtaining servo positioning control for pneumatic cylinders is by employing pulse width modulation controlled individual directional control valves. In this system, two 3/2 (3 port 2 position) solenoid operated spring return directional control valves are used to produce a pneumatic H-bridge circuit for positioning the cylinder accurately [5].The schematic diagram of the system is shown in Fig. 1b. The important components of the system are pneumatic cylinder, position transducer, two 3/2 solenoid operated DCVs and fuzzy controller. The position transducer senses the cylinder position value and transmits it to the controller. The Controller takes the corrective action by manipulating the duty factor of PWM signals U1 and U2 applied to valves V1and V2 respectively. These valves control the air flow rates to the cylinder chambers and hence controlling the position of the cylinder. Mathematical Model The equation of motion for the cylinder considering the friction effect [1,4] is given in Eq && x = ( A1P1 - A2P2 - Ffric + mgsinθ ) (1) M + m where x is the piston position of the cylinder, M is internal mass of the cylinder, m is external load, A1 and A2 are cross sectional areas of the cylinder chamber 1 and chamber 2 respectively, P1 and P2 are the absolute pressure inside cylinder chambers, Ffric is the frictional force, g is acceleration due to gravity and θ is tilting angle of the piston. The equation for frictional force [4] is given by Eq. 2. v vs F = f v + F sign v + F e sign v + k P P (2) fric 1 k pr p 1 2 where f1 is viscous coefficient of friction, Fk is Kinetic coefficient of friction, vs is Stribeck velocity, Fpr is break away force and kp is friction coefficient due to seals. The equations for pressure in the cylinder chambers [3,4] are given in Eq. 3 and Eq. 4. P& κ = RTm P A v ( & ) A1 l0 x P& κ = RTm + P A v ( & ) A2 l l0 x (3) (4)

3 Applied Mechanics and Materials Vols where κ is adiabatic exponent, l0 is length of dead zone of cylinder, l is full stroke length of the cylinder, R is specific gas constant, T is temperature, m& 1and m& 2 are the mass flow rates to the cylinder chambers. For both the servo systems motion and pressure dynamics are the same as shown in Eq The main difference in both the systems is in mass flow rate equations. The equations of mass flow rates through proportional valve [4] to the cylinder chambers are given in Eq. 5 and Eq. 6. m& = x C P w P w (5) 1 0 r s m& = x C P w P w (6) 2 0 r 2 23 s 12 where 0 is air density, xr is spool position (expressed in %) in proportional valve which depend on the control voltage applied to the valve u, Ps is supply air pressure, C is sonic conductance consistent with the standard ISO for critical pressure ratio [4], w14, w45, w23 and w12 are nonlinear flow function (sonic flow and subsonic flow) depending on the pressure ratio and on the critical pressure ratio Cr. The mass flow rates trough the solenoid valves to the cylinder chambers [7] are given in Eq. 7 and Eq. 8. 0C Ps w14 P1 w45 if U1 = 1 m& 1 = (7) 0C Pa w45 P1 w14 if U1 = 0 0C Ps w 23 P2 w12 if U2 = 1 m& 2 = (8) 0C Pa w12 P1 w 23 if U2 = 0 where Pa is the ambient air pressure. Simulation tests and Results Fig. 2. Simulation model for servo pneumatic systems with proportional valve and PWM control using Matlab-Simulink software For comparing the performances of the two servo systems for precise positioning of pneumatic actuator, a simulation model is created using Matlab-Simulink software. The model developed is shown in Fig. 2. This model is developed based on Eq Both the systems have their own closed loop systems comprising of corresponding fuzzy controllers. The same input setpoint functions are applied for both the systems and their responses are obtained. The simulation is carried out using the following parameters.

4 1236 Engineering and Manufacturing Technologies Cylinder Specifications: internal diameter of cylinder d1=0.01m, diameter of piston rod d2=0.0025m, length of cylinder l=0.2m, dead zone length l0=0.01m, mass of the piston rod M=1Kg, External mass m=3kg, inflation angle θ=0. Supply air Parameters: supply pressure Ps= 0.5X10 6 N/m 2, ambient pressure Pa= 0.1X10 6 N/m 2, temperature T= 298K, gas constant R= 288Nm/KgK, air density 0 =1.225Kg/m 3. Valve Parameters: Sonic conductance value C=1.462X10-8 m 4 s/kg and critical pressure ratio Cr=0.32. Frictional Parameters: viscous coefficient of friction f1=250ns/m, Kinetic coefficient of friction Fk=100 N, stribeck velocity vs=0.1m/s, break away force Fpr= 200N and friction coefficient due to seals kp= 3N/Pa. For the comparison of these two systems, the following standard performance indices are used: settling time, IAE, ISE, ITAE and ITSE. The settling time is the time taken to the response to reach steady state value (i.e.) to settle to the desired value. The integral indices normally denote the accumulation of error. Integral Absolute Error (IAE) is accumulation of the absolute error values. Integral Square Error (ISE) accumulates the square value of error. ISE have more effect to errors of higher magnitude. Integral Time Absolute Error (ITAE) and Integral Time Square Error (ITSE) are the time dependent indices which penalizes long time errors. Fig. 3. Responses of the servo systems for a) Step and b) Ramp input functions The displacement of the pneumatic cylinder using two servo control techniques is analyzed when input reference signals are applied. 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. The Performances of the two systems when these input signals are applied are compared using same conditions and parameters at same time. A step change in input signal from 0mm to 180mm is applied to the two servo systems at simulation time 0.5s. The response of the systems for is shown in Fig. 3a. When a ramp input from 0 mm to 180 mm with slope 200 mm/s applied at simulation time 0.1s, the response of these servo systems is shown in Fig. 3b. The Performance indices of the systems subjected to step and ramp signal are given in Table 1.

5 Applied Mechanics and Materials Vols Table 1. Performance indices for two systems for step and ramp responses Input Signal Servo System using Settling Time (s) IAE ISE ITAE ITSE Step Proportional Valve PWM control Ramp Proportional Valve PWM control From the various responses and indices it is observed that the servo control method using the proportional valve have better performance than the servo control method using PWM control. Under similar conditions, the servo system with PWM control takes approximately 10% more time to reach the steady state desired value than the servo system using proportional valve. From the performance indices it is shown that the systems have better setpoint tracking characteristics. Conclusion The nonlinear mathematical models for servo positioning systems using proportional valve and PWM controlled solenoid valves have been presented in this paper. The nonlinearities such as mass flow rate variations, pressure dynamics and frictional forces are included in the models. For comparing the performances of two servo systems, simulation tests are carried out in Matlab-Simulink software. The systems are analyzed by applying standard input functions such as step and ramp signals. From the responses and performance indices it is noted that the servo system using proportional valve have minimum settling time and better performance. In similar conditions, the cheaper servo system using PWM controlled solenoid valves takes approximately 10% more time to settle to the desired value than the servo system using proportional valve. The simulations results encourage having a real-time implementation and comparison of these systems. References [1] J. Wang, D.J.D. Wang, P.R. Moore and J. Pu, Modelling study, analysis and robust servo control of pneumatic cylinder actuator systems, IEEE Proc. Contr. Th. Appl. Vol. 148 (2001), p [2] T. Miyajima, T.Fujita, K. Sakaki, K. Kawashima and T. Kagawa, Development of a digital control system for high-performance pneumatic servo valve, Precis. Eng. Vol. 31 (2007), p [3] F. Najafi, M. Fathi and M. Saadat, Dynamic modelling of servo pneumatic actuators with cushioning, Int. J. Adv. Manuf. Technol. Vol. 42 (2009), p [4] J.E. Takosoglu, R.F. Dindorf and P.A. Lashi, Rapid prototyping of fuzzy controller pneumatic servo-system, Int. J. Adv. Manuf. Technol. Vol. 40 (2009), p [5] Z. Rao and G.M. Bone, Nonlinear Modeling and Control of Servo Pneumatic Actuators, IEEE Trans. Contr. Syst. T. Vol. 16 (2008), p [6] M. Taghizadeh, F. Najafi and A. Ghaffari, Increased tracking ability of pulse width modulation-driven pneumatic servo systems via a modified pneumatic circuit, Elect. Eng., Vol. 91 (2009), p [7] M.Q. Le, M.T. Pham, R. Moreau and T. Redarce, Comparison of a PWM and a hybrid force control for a pneumatic actuator using on/off solenoid valves, Proc. IEEE/ASME Int. Conf. Adv. Intelligent Mechatronics (2010), p

6 Engineering and Manufacturing Technologies / Comparison of Servo Positioning Performance of Pneumatic Cylinders Using Proportional Valve Method and PWM Control Method /