A Particle Swarm Optimization Approach for Optimum Design of PID Controller for nonlinear systems Taeib Adel Research Unit on Control, Monitoring and Safety of Systems (C3S) High School ESSTT Email: taeibadel@live.fr Chaari Abdelkader Research Unit on Control, Monitoring and Safety of Systems (C3S) High School ESSTT Email: abdelkader.chaari@yahoo.fr Abstract—In this paper,a novel design method for determining the optimal proportional-integral-derivative (PID) controller pa- rameters for Takagi-Sugeno fuzzy model using the particle swarm optimization (PSO) algorithm is presented. In order to assist estimating the performance of the proposed PSO-PID controller,a new timedomain performance criterion function has been used. The proposed approach yields better solution in term of rise time, settling time,maximum overshoot and steady state error condition of the system.the proposed method was indeed more efficient and robust in improving the step response. I. I NTRODUCTION During the past decades,the process control techniques in the industry have made great advances. Numerous con- trol methods such as adaptive control,neural control,and fuzzy control have been studied [1][2].(93-103). Among them,proportional-Integral-Derivative (PID) controllers have been widely used for speed and position control of various applications. Among the conventional PID tuning methods, the ZieglerNichols method [3] may be the most well known technique,but,In general,it is often hard to determine optimal or near optimal PID parameters with the Ziegler-Nichols for- mula in many industrial plants [4][5]. For these reasons,People have made lots of research, and proposed some advanced PID control methods,such as expert PID control based on knowledge inference[6],self-learning PID control based on regulation, neural network PID control based on connection mechanism[7],and intelligent PID control based on fuzzy logic[8,9]. Genetic algorithm (GA) has (566) been applied to self-tuning of PID parameters,too [10]. However,GA has the disadvantages of premature and slow convergence rate,and the need to set up many parameters. Recently,the computational intelligence has proposed particle swarm optimization (PSO) [11, 12] as opened paths to a new generation of advanced process control. The PSO algorithm, proposed by Kennedy and Eberhart [11] in 1995,was an evolution computation tech- nology based on population intelligent methods. In comparison with genetic algorithm,PSO is simple,easy to realize and has very deep intelligent background. It is not only suitable for sci- entific research,but also suitable for engineering applications in particular. Thus,PSO received widely attentions from evolution computation field and other fields. Now the PSO has become a hotspot of research. Various objective functions based on error performance criterion are used to evaluate the performance of PSO algorithms. Each objective function is fundamentally the same except for the section of code that defines the specific error performance criterion being implemented to optimize the performance of a PID controlled system. Performance indices used to estimate the best parameters of PID controller are given by:,,and . The main aim of this research paper is to establish a methodology for optimal design of PID controllers for Takagi-Sugeno (T-S) fuzzy model. the T-S fuzzy model is widely used in many research areas because of its excellent ability of nonlinear system description. It has a great capacity to approximate any nonlinear system [9]. for this,a particle swarm optimization (PSO) algorithm are proposed to improve controller by adjusting transfer function parameters. The rest of the paper is organized as follows. In section 2,a brief review of the TS fuzzy model formulation is given. In section 3,describes the standard PSO.PID controller design by the proposed PSO algorithm is described in Section 4. Some simulation results is shown in Section 5. Finally,some conclusions are made in section 6. II. T-S FUZZY MODEL OF NONLINEAR SYSTEM We consider a class of nonlinear systems defined by: ( + 1) =  (()) (1) With the regression vector represented by: ()=[(),(−1), ..., (−),(),(−1), ..., (−)] (2) Here,k denotes the discrete time,and n define the number of delayed output. Through this contribution, the unknown function  (()) is approximated by a T-S fuzzy model which is charities by rule consequents that are linear function of the input variables [13]. The rule base comprises r rules of the form: U.S. Government work not protected by U.S. copyright