PID-type fuzzy logic controller tuning based on particle swarm optimization

Abstract

In this paper, a new PID-type fuzzy logic controller (FLC) tuning strategy is proposed using a particle swarm optimization (PSO) approach. In order to improve further the performance and robustness properties of the proposed PID-fuzzy approach, two self-tuning mechanisms are introduced. The scaling factors tuning problem of these PID-type FLC structures is formulated and systematically resolved, using a proposed constrained PSO algorithm. The case of an electrical DC drive benchmark is investigated, within a developed real-time framework, to illustrate the efficiency and superiority of the proposed PSO-based fuzzy control approaches. Simulation and experimental results show the advantages of the designed PSO-tuned PID-type FLC structures in terms of efficiency and robustness.

Introduction

The complexity of dynamic system, especially when only qualitative knowledge about the process is available, makes it generally difficult to elaborate an analytic model, which is sufficiently precise enough for the control. Thus, it is interesting to use, for this kind of systems, non-conventional control techniques, such as fuzzy logic, in order to achieve high performances and robustness (Lee, 1990a, Lee, 1990b, Passino and Yurkovich, 1998). Fuzzy logic control approach has been widely used in many successful industrial applications, which demonstrated high robustness and effectiveness properties.

In the literature, various fuzzy logic controller (FLC) structures are proposed and extensively studied. The particular structure given in Qiao and Mizumoto (1996), namely PID-type FLC, is especially established and improved within the practical framework in Eker and Torun (2006), Güzelkaya et al. (2003) and Woo et al. (2000). Such a FLC structure, which retains the characteristics similar to the conventional PID controller, can be decomposed into the equivalent proportional, integral and derivative control components as shown in Qiao and Mizumoto (1996). In order to improve further the performance of the transient and steady state responses of this kind of fuzzy controller, various strategies and methods are proposed to tune the PID-type fuzzy controller parameters.

Indeed, Qiao and Mizumoto (1996) designed a parameter adaptive PID-type FLC based on a peak observer mechanism. This self-tuning mechanism decreases the equivalent integral control component of the fuzzy controller gradually with the system response process time. It allows also increasing the damping of the system when it is about to settle down, meanwhile keeps the proportional control component unchanged so as to guarantee fast reaction against the system's error. The oscillation of the system is strongly reduced and the settling time is shortened considerably. On the other hand, Woo et al. (2000) developed a method to tune the scaling factors related to integral and derivative components of the PID-type FLC structure via two empirical functions and based on the system's error information. To achieve some goals of the strategy originally proposed by Qiao and Mizumoto (1996), the used self-tuning mechanism decreases the equivalent integral control component and increases the damping of the system via the equivalent derivative component. Eksin et al. (2001) and Güzelkaya et al. (2003) proposed a technique that adjusts the scaling factors, corresponding to the derivative and integral components of the PID-type FLC, using a fuzzy inference mechanism. This fuzzy inference-based self-tuning mechanism has two inputs, namely the system's error and a new variable called “normalized acceleration”. Such a variable gives relative rate information about the fastness or slowness of the system response. This method is more efficient since lesser number of parameters is to be tuned and it is more robust to the system parameter or structural changes compared to the other related methods, as shown in Güzelkaya et al. (2003).

However, the major drawback of all these PID-type FLC structures is the difficult choice of their relative scaling factors. Indeed, the fuzzy controller dynamic behavior depends on this adequate choice. The tuning procedure depends on the control experience and knowledge of the human operator, and it is generally achieved based on a classical trials–errors procedure. Up to now there is no clear and systematic method to guide such a choice. So, this tuning problem becomes more delicate and hard as the complexity of the controlled plant increases. Hence, the proposition of a systematic approach to tune the scaling factors of these particular PID-type FLC structures is interesting.

In this paper, a new approach based on the particle swarm optimization (PSO) meta-heuristic technique is proposed for systematically tuning the scaling factors of the PID-type FLC, with and without self-tuning mechanisms. This work can be considered as an extension of the results given in Qiao and Mizumoto (1996), Eker and Torun (2006), Güzelkaya et al. (2003), Woo et al. (2000) and Eksin et al. (2001). The fuzzy control design is formulated as a constrained optimization problem, which is efficiently solved based on the developed PSO algorithm. In order to specify more robustness and performance control objectives of the proposed PSO-tuned PID-type FLC, different optimization criteria are considered and compared subjected to several various control constraints defined in the time-domain framework. The convergence conditions of the proposed and implemented PSO algorithm are analytically guaranteed and verified. The main contribution of this paper consists of proposing a systematic and hybrid control strategy to track reference trajectories using flatness property of linear systems. The proposed approach is based on a robust PID-type fuzzy control method using the PSO technique.

The remainder of this paper is organized as follows. In Section 2, the proposed fuzzy PID-type FLC structures, with and without self-tuning scaling factors mechanisms, are presented and discussed within the discrete-time framework. The optimization-based problems of the PID-type FLC scaling factors tuning are formulated in Section 3. A constrained PSO algorithm, used in solving the formulated problems, is also described. All PSO-based simulation results are compared with those obtained by the classical Genetic Algorithms Optimization (GAO)-based approach. Section 4 is dedicated to apply the proposed fuzzy control approaches on an electrical DC drive benchmark within an experimental real-time framework based on an Advantech PCI-1710 multi-functions board associated with a PC computer and Matlab/Simulink environment.