Design of PID Controller for Higher Order Continuous Systems using MPSO based Model Formulation Technique

This paper proposes a new algebraic scheme to design a PID controller for higher order linear time invariant continuous systems. Modified PSO (MPSO) based model order formulation techniques have applied to obtain the effective formulated second order system. A controller is tuned to meet the desired performance specification by using pole-zero cancellation method. Proposed PID controller is attached with both higher order system and formulated second order system. The closed loop response is observed for stabilization process and compared with general PSO based formulated second order system. The proposed method is illustrated through numerical example from literature. Keywords—Higher Order Systems, Model Order Formulation, Modified Particle Swarm Optimization, PID controller, Pole-Zero Cancellation. I.INTRODUCTION ID controllers have been widely used in industries for various applications and it plays a vital role in automation. It has been a crucial problem to tune properly the gains of the PID controller because many industrial plants are often burdened with the characteristics such as higher order, time delay and nonlinearities [1]. While modeling the complex systems like aircraft mechanism, Atomic plant process monitoring, fuel injector and spark timing of auto mobiles it can be noted that the system order is increased. The analysis and synthesis of higher order systems are difficult and generally not desirable on economic and computational considerations. Thus, it is necessary to obtain a lower order system so that the obtained lower order maintains the characteristics of the original system. This helps in minimizing the variations during design and realization of suitable control system components to be attached to the original system. Model order formulation is the process of deriving the lower order model from the higher order model. Model order formulation approximates the complex system by simple one. The main aim of the formulation is to find the best possible approximation of the output of the original system. During the past four decades, numerous impressive varieties of new techniques [2] [6] have been developed for obtaining lower Dr. S. N. Deepa is working as an Associate Professor in the Department of Electrical and Electronics Engineering, Anna University of TechnologyCoimbatore, Coimbatore 641 047, Tamil Nadu, India (e-mail: deepapsg@ gmail.com). G. Sugumaran is a Senior Engineering Research Fellow with the Department of Electrical and Electronics, Anna University of TechnologyCoimbatore, Coimbatore 641 047, Tamil Nadu, India (e-mail: urssugu@ gmail.com). order models from higher order linear system. Each of these methods has both advantages and disadvantages when tried on a particular system. Several methods have been developed for designing a PID controller. Ziegler et al., [7] have proposed the frequency response method by using information from the Nyquist curve of the system. The method is only suitable for systems with monotonic step response. Hang et al., [8] have reexamined the Ziegler-Nichols method and proposed new tuning formulae, in which setting point weight for systems with PID controllers are introduced. Zhuang et al., [9] proposed an optimal design of PID controllers based on the minimization of an integral criterion. Yeung et al., [10] presented the graphical method for common continuous time and discrete time compensators. Various methods are developed by employing frequency response matching techniques for designing the controllers. Rattan et al., [11] proposed a method based on complex curve fitting and involves the matching of frequency response of closed loop system with the reference model. Tschauner [12] has proposed the jury stability conditions derived from Routh and Fuller tables. The digital controller design method proposed by Inooka et al., [13] is based on series expansion of pulse transfer function. Aguirre [14] introduced a method for the design of continuous time controllers by matching a combination of time moments and Markov parameters of the closed loop system. The main purpose of the approach is to reduce the excessive overshoot of the system to be compensated. To enhance the capabilities of traditional PID parameter tuning techniques, several intelligent approaches have been suggested to improve the PID tuning, such as those using Genetic Algorithms (GA) [15] and the Particle Swarm Optimization (PSO) [16]. With the advance of computational methods in the recent times, optimization algorithms are often proposed to tune the control parameters in order to find an optimal performance [17]. In this paper a simple algebraic scheme is proposed to design a PID controller for Linear Time Invariant Continuous System (LTICS). Adjunct Polynomial scheme is used for deriving the basic second order system from the original higher order system, and to obtain a fine tuned second order system depicting the original characteristics of the system, Modified Particle Swarm Optimization (MPSO) algorithm is proposed. Pole-zero cancellation method is employed for initialize the PID gain values. Matlab simulation procedures are used to obtain the optimal PID gain values. The robustness S. N. Deepa, G. Sugumaran Design of PID Controller for Higher Order Continuous Systems using MPSO based Model Formulation Technique P World Academy of Science, Engineering and Technology International Journal of Computer, Electrical, Automation, Control and Information Engineering Vol:5, No:8, 2011 949 International Scholarly and Scientific Research & Innovation 5(8) 2011 scholar.waset.org/1999.4/2109 In te rn at io na l S ci en ce I nd ex , C on tr ol a nd I nf or m at io n E ng in ee ri ng V ol :5 , N o: 8, 2 01 1 w as et .o rg /P ub lic at io n/ 21 09 of the proposed scheme is compared with general PSO based formulated second order model. II.DESCRIPTION OF THE PROBLEM A. PID Controller Transfer Function The standard block diagram of PID controller is shown in Fig.1. PID controller can be mathematically represented as [18], ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ∫ + + = ) ( ) ( ) ( 1 ) ( ) ( 0 t d t de T d e T t e K t u t