Tuning of PID controller for an automatic regulator voltage system using chaotic optimization approach

Abstract

Despite the popularity, the tuning aspect of proportional–integral-derivative (PID) controllers is a challenge for researchers and plant operators. Various controllers tuning methodologies have been proposed in the literature such as auto-tuning, self-tuning, pattern recognition, artificial intelligence, and optimization methods. Chaotic optimization algorithms as an emergent method of global optimization have attracted much attention in engineering applications. Chaotic optimization algorithms, which have the features of easy implementation, short execution time and robust mechanisms of escaping from local optimum, is a promising tool for engineering applications. In this paper, a tuning method for determining the parameters of PID control for an automatic regulator voltage (AVR) system using a chaotic optimization approach based on Lozi map is proposed. Since chaotic mapping enjoys certainty, ergodicity and the stochastic property, the proposed chaotic optimization introduces chaos mapping using Lozi map chaotic sequences which increases its convergence rate and resulting precision. Simulation results are promising and show the effectiveness of the proposed approach. Numerical simulations based on proposed PID control of an AVR system for nominal system parameters and step reference voltage input demonstrate the good performance of chaotic optimization.

Introduction

During the past decades, process control techniques in the industry have made great advances. Numerous control methods such as: adaptive control, predictive control, neural control, and fuzzy control have been studied. In despite of many efforts, the proportional–integral-derivative (PID) controller continues to be the main component in industrial control systems, included in the following forms: embedded controllers, programmable logic controllers, and distributed control systems. The reason is that it has a simple structure which is easy to be understood by the engineers and it presents robust performance within a wide range of operating conditions.

Van Overschee and De Moor [1] report that 80% of PID type controllers in the industry are poorly/less optimally tuned. They state that 30% of the PID loops operate in the manual mode and 25% of PID loops actually operate under default factory settings. Over the years, many techniques have been suggested for tuning of the PID parameters. In this context there are classical (Ziegler/Nichols, gain-phase margin method, Cohen/Coon and pole placement) [2], [3], [4], [5] and advanced techniques (minimum variance, gain scheduling and predictive) [6], [7], [8], [9], [10]. Some disadvantages of these control techniques for tuning PID controllers are: (i) excessive number of rules to set the gains, (ii) inadequate dynamics of closed loop responses, (iii) difficulty to deal with nonlinear processes, and (iv) mathematical complexity of the control design [10]. Therefore, it is interesting for academic and industrial communities the aspect of tuning PID controllers, especially with a reduced number of parameters to be selected and a good performance to be achieved when dealing with complex processes [9]. Via feedback of the system output the standard PID controller has the ability to eliminate steady-state offsets through integral action and it can also ‘anticipate’ the future through its derivative action.

However, since it is fairly difficult to determine the PID parameters suitably, lots of researches have been reported with respect to PID parameter tuning schemes. Recently, as an alternative to the classical mathematical approaches, modern heuristic optimization techniques such as simulated annealing [11], evolutionary algorithms [12], artificial neural networks [13], particle swarm optimization [14], and fuzzy systems [15] have been given much attention by many researchers due to their ability to find an almost global optimal solution in PID tuning. One of these modern heuristic optimization paradigms is the optimization based on chaotic systems. In this context, the literature [16], [17], [18], [19], [20], [21], [22], [23], [24] contains several algorithms using chaotic sequences for solving optimization problems in engineering applications.

Chaos is a bounded unstable dynamic behavior, which exhibits sensitive dependence on initial conditions and includes infinite unstable periodic motions [21]. Optimization algorithms based on the chaos theory are search methodologies that differ from any of the existing traditional stochastic optimization techniques. Due to the non-repetition of chaos, it can carry out overall searches at higher speeds than stochastic ergodic searches that depend on probabilities.

The application of chaotic sequences in tuning of PID parameters is a powerful strategy to prevent the premature convergence to local minima. The contribution of this paper is the performance analysis of a chaotic optimization method using Lozi map [24], [25] in tuning of a PID controller applied in an automatic regulator voltage (AVR) system. Numerical simulations in tuning of PID controller based on chaotic optimization approach for the AVR demonstrate the effectiveness and robustness of optimization method.

The remainder of this paper is organized as follows. Sections 2 Fundamentals of PID controller, 3 Description of an AVR model describe the PID controller and AVR model, respectively, while Section 4 explains the chaotic optimization concepts based on Lozi map. Numerical simulation and comparisons are provided in Section 5. Lastly, Section 6 outlines the conclusion with a brief summary of simulation results.