طراحی سیستم کنترل غیرخطی راکتور مخزن به طور مداوم هم زده شده با استفاده از الگوریتم کلونی زنبور عسل مصنوعی

This paper proposes a novel controller design method based on using artificial bee colony (ABC) algorithms for an unstable nonlinear continuously stirred tank reactor (CSTR) chemical system. Such CSTR process is highly nonlinear and its dynamic is significantly dominated by system parameters. It is a good challenge to access the controller design performance when the controller is applied in the CSTR control system. The commonly used proportional–integral-derivative (PID) controller is taken into account in this study, and tuning three PID control gains is carried out by the artificial bee colony algorithm. With the use of the optimal ABC algorithm, PID controller gains can be derived suitably by means of minimizing the cost function given in advance. Finally, several control operations are provided to confirm the feasibility and effectiveness of the proposed method. We also discuss the influence of algorithm initial conditions on the control performance with many different tests.

Continuously stirred tank reactor (CSTR) is an important and basic process system in chemical industries. It is a highly nonlinear system and has a rather complex dynamic behavior dominated by its system parameters heavily. To design a suitable controller for such CSTR systems, it is somewhat difficult and need more efforts [1], [2], [3], [4] and [5]. Recently, some novel control strategies have been developed for the CSTR system, for example, Chen and Dai proposed a robust design methodology that combines differential geometric feedback linearization, sliding mode control, and adaptive state feedback to control the CSTR system in the presence of uncertainties, and a Lyapunov-based scheme is utilized to guarantee the stability of the closed-loop system [2]. In [3], they showed an intelligent process control technique to control complex, unknown, and uncertain nonlinear dynamic system, which is based on using fuzzy logic system and neural network. A neuro-fuzzy direct controller is designed to control an open-loop unstable CSTR process system. In addition, an adaptive tracking control was considered for a class of nonlinear systems based on neural networks [5]. The goal of applying neural networks is to realize the feedback linearization approximately. Then the adaptive controller is taken to control the composition of a CSTR. For CSTP control system design, however, this study will focus on the proportional–integral-derivative (PID) controller structure. It is well known that PID controller is rather popular and often utilized in most chemical industry applications due to the advantages of simple architecture and easy implementation. In the structure of PID controller, there are three designed control gains including the proportional gain Kp, integral gain Ki, and derivative gain Kd. Traditionally, the famous design method for PID controller is the Ziegler–Nichols (ZN) tuning method. The process is first modeled by a first-order system plus a transportation delay, and then system constants are determined according to the step response of the process. Finally, based on this process model PID control gains are given according to a decay ration of 0.25 and the limit of stability, respectively [6]. In addition, a large number of new design methods have been developed for PID control systems in recent years, which are based on the swarm intelligence (SI) such as particle swarm optimization (PSO), differential evolution (DE), genetic algorithms (GAs), and other related evolving algorithms [7], [8], [9], [10] and [11]. They search for the optimal (global) solution of the given problem in parallel throughout the search space using respective adjusting mechanisms. This is due to the contribution of population (swarm) concept of the algorithm. Generally, a population comprises a large number of possible candidate solutions called particles used in PSO, parameter vectors in DE, or chromosomes in GAs, respectively. Then the adjusting mechanisms are performed on these candidate solutions to generate a new offspring population with better performance than that of present generation. This procedure continues until the stopping criterion is met. In [8], a modified PSO algorithm was presented to solve the PID control design problem in the tracking control of nonlinear inverted pendulum systems. Simulation results show the applicability of the design scheme. Kim proposed a hybrid method which combines the conventional GA and bacterial foraging (BF) to search for the PID control parameters. The controlled plant is the automatic voltage regulator (AVR) system applied in the power application [9]. Artificial bee colony (ABC) algorithm is one of the newest optimal algorithms initially proposed by Karaboga in 2005 [12]. Like other swarm intelligence methods, it was also a population-based evolutionary computation and has been shown to be a powerful and efficient algorithm for solving the optimization problem. The concept of the ABC algorithm is intuitively motivated by the intelligent behavior of honey bee swarm. In [13], the authors showed that for optimizing multivariable functions the proposed ABC outperforms other algorithms such as GA, PSO, and particle swarm inspired evolutionary algorithm (PS-EA). On the basic of ABC algorithm, researchers have successively developed many applications including digital IIR filter design [14], cluster analysis [15], parametric optimization of non-traditional machining processes [16], etc. Moreover, a good survey on the ABC algorithm and its related applications has just been presented in [17]. Up to now, however, the research which applies the ABC algorithm to the optimal design of PID control tuning has rarely been reported. Consequently, based on using ABC algorithm this paper focuses on the PID control system design for a nonlinear CSTR system. We will perform four different control operations to verify the applicability of the proposed method. The remainder of this paper is organized in the following. In Section 2, the system description of a CSTR is presented in detail, and the PID controller structure is also simply described. In Section 3, we first introduce the basic concept and some central components of the ABC algorithm, and then based on this algorithm a complete design guideline of PID controller is presented for nonlinear CSTR system. Section 4 will show various control operations and some simulation comparisons with the real-coded genetic algorithm (RGA) are also given. Finally, a brief conclusion is addressed in Section 5.

To control a complex and highly nonlinear chemical process, continuous stirred tank reactor (CSTR), is a rather difficult work and also a benchmark for evaluating the proposed controller. In this paper, we have attempted to utilize the PID controller in controlling such a CSTR system, and tuning three control gains has been carried out by the artificial bee colony (ABC) algorithm. During the searching evolution, the defined cost function is successively minimized so that the optimal control parameters eventually occur. In the simulation, different kinds of control cases are provided to show the feasibility of the proposed method. All simulation results reveal the superiority of the proposed PID controller design method in the nonlinear CSTR control. In the future research, it is expected to extend the present form to the multivariable architectures. We wish to propose a design method for multi-input and multi-output (MIMO) PID control systems by means of the ABC algorithm.