ARTICLE Year : 2014  Volume : 4  Issue : 2  Page : 115118 Optimization of Proportional Fuzzy Controller for Servo Pneumatic Positioning System Using Taguchi: Data Envelopment Analysis Based Ranking Methodology D Saravanakumar^{1}, B Mohan^{2}, T Muthuramalingam^{1}, ^{1} Department of Production Technology, Anna University, Chennai, Tamil Nadu, India ^{2} Department of Mechanical Engineering, Anna University, Chennai, Tamil Nadu, India Correspondence Address: Even though pneumatic actuators exhibit many advantages, their usage is limited due to its nonlinear nature. In this paper, a sugeno type proportional fuzzy controller has been designed for the fast and accurate position control of pneumatic cylinder. The servo positioning system for pneumatic cylinder with the optimal fuzzy controller has been simulated using MatlabSimulink software. The design of the fuzzy controller has been optimized by proper selection of range for the membership functions of the input variable of the controller. The objectives for optimizing the controller are to minimize the settling time and the maximum overshoot. This multiobjective optimization problem has been solved by Taguchi based data envelopment analysis based ranking methodology. From the simulation, the optimal controller response for a step input change is obtained as settling time 0.16s and overshoot 0.5%.
1. Introduction Pneumatic actuators are widely used in the field of automation, robotics and manufacturing. The pneumatic technology exhibits many advantages such as high speed, high force generation, better efficiency, less maintenance and low operating costs. The ability of these actuators to be operated in wet, dusty, chemically aggressive and radiation affected atmospheres signifies its practical importance. Traditionally, pneumatic cylinders are used for motion between two hard stops. In order to expand the capabilities of the pneumatic cylinders to be operated as multiposition actuator, servo control techniques are being used. The significant problem in designing the 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. Servo pneumatics is an emerging area which attracted many researchers over the past decade to work in this field. Mathematical model of this complicated system helps in understanding the process parameters and also it is used for development of control system for the system. Najafi et al. [1] and Takosoglu et al. [2] have developed mathematical model for the system. The system is of higher order and exhibits nonlinear behavior which makes it a complex control problem. Many authors attempted to solve the problem with complex control algorithms. Rao and Bone [3] have discussed various issues related to servo control of the pneumatic systems. Bone and Ning [4] have developed two sliding mode controllers for servo pneumatic system. Gao and Feng [5] and Takosoglu et al. [2] have developed fuzzy based controllers for positioning of pneumatic actuators. Optimal design of the controllers enables fast and precise control of the system. Nagi and Perumal [6] have optimized the fuzzy controller for minimum time response. Hsieh et al. [7] have developed optimal fuzzy controller using Taguchihierarchicalgeneticalgorithm method. Nagi et al. [8] have developed optimal time response sugeno fuzzy controller. Rama Mohan Rao and Sivasubramanian [9] have developed a multiresponse optimization technique using particle swarm algorithm. Jeyapaul et al. [10] have reviewed various Taguchi based optimization approaches. AlRefaie et al. [11] described procedure for solving the multiresponse problem in the Taguchi method utilizing two data envelopment analysis (DEA) approaches. Muthuramalingam and Mohan [12] have optimized the electrical parameters in the electrical discharge machining process using TaguchiDEAR algorithm. In the current research, an attempt is made for optimizing the fuzzy controller settings by using Taguchi  data envelopment analysis based ranking (DEAR) methodology. 2. System Description 2.1 Servo pneumatic system The schematic diagram of servo pneumatic position control system is shown in [Figure 1]. The main components in the system are pneumatic cylinder, proportional directional control valve, position transducer and a fuzzy controller. The position of the pneumatic cylinder is controlled by the proportional valve, which regulates the flow rate of the compressed air. The position transducer senses the current position value, which is used by the controller to control the spool movement in the proportional directional control valves (DCV). This spool movement regulates the air flow rate to the cylinder chambers and hence controlling the position and velocity of the cylinder movement.{Figure 1} 2.2 Mathematical model of the system The systematic methodology of the pneumatic actuator nonlinear mathematical modeling is presented from applying physical laws and recent literature information. The full system constitutes a fifth order nonlinear dynamic model of the pneumatic positioning system and considers the nonlinearity of the dead zone, the mass flow rate, the pressure dynamics and the motion equation, that includes the friction dynamics. The state space representation of the system is given in Eqs. 14. [INLINE:1] In the Eqs. 14, x and v are position and velocity of the piston respectively, P 1 and P 2 are absolute pressures in cylinder chambers, M is mass of piston and slide, m is the mass of load, A 1 and A 2 are the crosssectional areas of two chambers of the cylinder, F fric is the nonlinear frictional force, g is acceleration due to gravity, θ is inflation angle, ε is adiabatic exponent, l is stroke length of the cylinder, l 0 is length of dead zone in the cylinder, R is specific gas constant, ∆h is adiabatic heat expansion and f(.) is the nonlinear mass flow rate function which depend on proportional valve spool movement. 2.3 Fuzzy controller For controlling the pneumatic cylinders position, a Sugeno type fuzzy based proportional controller has been designed. The input to the fuzzy controller is position error. The position error is measure of deviation of the current position with the desired position. The output of the fuzzy controller is the voltage level to be applied to the proportional valve. Based on this applied control voltage, the spool movement in the proportional DCV is controlled. The input variable in the range −55 has three triangular membership functions NE, ZE and PE. The output variable, control voltage is in the range 05. It has three constant membership functions NEG, MED and POS whose values are 0, 2.5 and 5 respectively. The rule base of the fuzzy controller consists of three rules which are as following. Rule 1: IF Position error is NE, THEN Control voltage is NEG. Rule 2: IF Position error is ZE, THEN Control voltage is MED. Rule 3: IF Position error is PE, THEN Control voltage is POS. The shape and range of the membership function has a greater influence in the performance of the servo control system. Hence, the range of the membership functions is to be optimized for having better control performance. Thus, three levels for each membership functions are tried. The membership functions for various trails are shown in [Figure 2]. The limits for three triangular membership functions in the format (Lower Limit, Peak Value and Upper Limit) for three levels are shown in [Table 1].{Table 1}{Figure 2} 3. Optimization of Fuzzy Controller 3.1 Simulation tests based on Taguchi design of experiment Based on the mathematical model of the system, a simulation model is created in the MatlabSimulink software. The closed loop response of the system using fuzzy controller is simulated when a step change in input desired value from 0 mm to 100 mm at time 0 s is applied. From the response, the settling time (sec) and the maximum overshoot (%) are computed and taken as output parameters for optimization of controller parameters. Settling time is the time required for the response curve to reach and stay in final steady state value. Overshoot refers to an output exceeding its final steadystate value. The maximum deviation from the steadystate value is the maximum overshoot which will be expressed in percentage. For reducing the number of simulation tests to be carried out, the Taguchi design of experiments is used. L9 orthogonal table design has been selected based on Taguchi design of experiments as shown in [Table 2].{Table 2} The results of the simulation tests for various trails based on the design of experiments are shown in [Table 3].{Table 3} 3.2 DEAR methodology In this method, a set of original responses are mapped into a ratio so that the optimal levels can be found based on this ratio. This value can be treated as multi response performance index (MRPI) value to find the optimal combination of the process parameters. The following steps are involved in DEAR methodology: Determine the weights (w) for each response for all experiments. Weight of a response is the ratio between the responses at any trial to the summation of all responses. Since both the objectives are minimization, the weights are given by the following Eq. 5. [INLINE:2] where W is the weight, x is the output variable value and n is the no of trails.Transform the data of response into weighted data by multiplying the observed data with its own weight as given by Eq. 6. [INLINE:3]Divide the data as larger the better with smaller the better. Treat this value as MRPI. Since both objects are minimization, MRPI is given by the Eq. 7. [INLINE:4] 3.3 Optimization Based on the Taguchi design of experiments, totally nine simulation tests are conducted by varying the limits of membership functions of fuzzy controller. For the optimization, the output parameters considered are settling time (sec) and maximum overshoot (%). This is a multiobjective optimization having the objectives of minimizing both settling time and maximum overshoot. [Table 4] shows the weights for the each output function and the MRPI value for all the trails.{Table 4} [Table 5] shows the consolidated MRPI of all the input factors with all the levels. The values have been computed by the adding the all MRPI values for corresponding level of each process parameters. For example, NE has Level 1 in the trails 1, 2 and 3. So the cumulative MRPI value is given by summation of MRPI values for trails 1, 2 and 3.{Table 5} As it has shown in [Table 5], the maximum level value of each parameter indicates the optimal level of input parameters. So the optimal controller design is obtained by NE in Level 2, ZE in Level 2 and PE in Level 3. 4. Results Based on the multiobjective optimization, the optimal fuzzy controller settings are obtained. The membership functions of the input variable position error showing the optimized limits are shown in [Figure 3].{Figure 3} The designed optimal fuzzy controller has been implemented in the simulation environment of MatlabSimulink software. The simulation result for the servo system when a step input change from 0 mm to 100 mm at simulation time 0 s is shown in [Figure 4].{Figure 4} 5. Conclusion This paper presents an optimal fuzzy controller for the servo control of the pneumatic positioning system. TaguchiDEAR Methodology has been used to solve the multiobjective optimization problem. The objectives of the optimization are to minimize both the settling time and overshoot, so the actuator can have fast and precise movement for the desired position. The developed controller is implemented and simulated using MatlabSimulink software. The response of the optimal controller for a step input change is obtained as settling time 0.16s and overshoot 0.5%. Further research includes real time implementation of the controller to the servo pneumatic positioning system References


