Hybrid fuzzy logic control with genetic optimisation for a single-link flexible manipulator

Abstract

To reduce the end-point vibration of a single-link flexible manipulator without sacrificing its speed of response is a very challenging problem since the faster the motion, the larger the level of vibration. A conventional controller can hardly meet these two conflicting objectives simultaneously. This paper presents a genetic algorithm (GA)-based hybrid fuzzy logic control strategy to achieve that goal. A proportional-derivative (PD) type fuzzy logic controller utilising hub-angle error and hub-velocity feedback is designed for input tracking of the system. GA is used to extract and optimise the rule base of the fuzzy logic controller. The GA fitness function is formed by taking the weighted sum of multiple objectives to trade off between system overshoot and rise time. Moreover, scaling factors of the fuzzy controller are tuned with GA to improve its performance. A GA-based multi-modal command shaper is then designed and augmented with the fuzzy logic controller to reduce the end-point vibration of the system. The performance of the hybrid control scheme is assessed in terms of its input-tracking capability and vibration suppression at the end point. A significant amount of vibration reduction has been achieved at the end point, especially at the first three resonance modes of the rig structure, with satisfactory level of overshoot, rise time, settling time, and steady-state error.

Introduction

Flexible manipulators are lighter, faster and less expensive than rigid ones, but they pose various challenges in research as compared with rigid manipulators, ranging from system design, structural optimisation, and vibration control. In order to achieve high-speed and accurate positioning, it is necessary to control the manipulator's response in a cost effective manner.

Numerous control approaches have been adopted and used for flexible structure systems. These include, but are not limited to, the linear quadratic regulator (LQR) (Cannon and Schmitz, 1984), hybrid-collocated and non-collocated control methods (Tokhi and Azad, 1996a), H_∞ control (Sutton et al., 1999), iterative learning control (Tokhi et al., 2004), hybrid learning control (Alam et al., 2005; Tokhi and Zain, 2006), adaptive inverse and neuro-inverse active control (Shaheed et al., 2005), command shaping (Singer and Seering, 1990; Mohamed and Tokhi, 2002; Romano et al., 2002; Zain et al., 2006), and many others (Benosman and Vey, 2004).

Conventional control techniques require accurate mathematical models describing the dynamics of the system under study. One of the major limitations of conventional control systems is the change in the plant dynamics with time and actuator saturation, which add to the nonlinearity of the system (Lin et al., 1996). These techniques result in tracking error when the load varies fast and overshoot during transients. An interesting alternative that could be investigated is the use of fuzzy logic control (FLC) methods (Zadeh, 1965, Zadeh, 1973; Mamdani, 1974; Mamdani and Assilian, 1975). In recent years, FLC has attracted considerable attention as a tool for a novel control approach because of the variety of advantages that it offers over the classical control techniques (Zadeh, 1973). The FLC paradigm has been developed as an alternative to conventional model-based control systems (Mamdani, 1974). It does not require a mathematical model of the plant and can be applied equally to linear and nonlinear systems. In the past two decades, fuzzy control has been successfully applied to many control problems (Cohen et al., 2002; Jnifene and Andrews, 2004; Karr and Gentry, 1993; Lee, 1990).

Fuzzy control can be viewed as a way of converting expert knowledge into an automatic control strategy in the absence of detailed knowledge of the plant (Zadeh, 1973). Kwak and Sciulli (1996) used a fuzzy logic-based method for vibration suppression of a cantilever beam with surface-bound collocated piezoceramic sensors and actuators. Jnifene and Andrews (2005) used an active control strategy based on fuzzy logic and neural networks to dampen the end-point vibration of a single-link flexible manipulator mounted on a two degrees-of-freedom platform. Sun and Er (2004) proposed a hybrid fuzzy controller for robotic systems by combining a fuzzy gain scheduling method and a fuzzy proportional–integral-derivative (PID) controller to solve the nonlinear control problems, such as pole balancing and multilink robot manipulation.

A feedforward control scheme based on input command shaping, introduced by Singer and Seering (1990), has created considerable interest among researchers. Since its introduction, the method has been applied to the control of different types of flexible structure systems for either vibration reduction or trajectory tracking, or occasionally both (Singhose, 1992). A properly designed command shaper (CS) cancels the resonance poles of the system regardless of given reference input to the system. The command shaping method involves convolving a desired command with a sequence of impulses. However, designing an effective CS requires a priori knowledge of the system characteristic parameters, such as resonance frequencies and corresponding damping ratios, to produce a command that results in zero residual vibration (Singer and Seering, 1990; Singhose, 1992; Singh and Singhose, 2002).

The objective of this work is to develop a hybrid FLC strategy based on genetic algorithm (GA) whereby a flexible robotic arm is moved from one position to another in the least amount of time with minimum vibration. It is difficult to find a suitable solution through analytical means meeting these two objectives simultaneously. So, GAs with different types of objective functions and their sum of weighted values are used to find an effective solution that trades off between these conflicting features.

Firstly, a GA-based fuzzy logic controller is designed for input tracking of the flexible manipulator. An automated design of the fuzzy rule base is presented. Learning a fuzzy rule base can be considered as an optimisation problem in which the search space is constituted by the set of fuzzy if–then rules. Moreover, input and output scaling factors are tuned to minimise the overshoot and rise time of the system's response.

Secondly, assuming no prior knowledge is available on the system, a GA-based multi-modal CS is designed with the view to reduce vibration at the end point and is augmented as a feedforward component with the fuzzy controlled closed loop system.

The paper is organised as follows. Section 2 gives a description of the experimental set-up. Section 3 presents the proposed hybrid fuzzy logic controller. The theoretical background of the conventional command shaping technique is presented in Section 4. Section 5 describes the design procedure and performance analysis of GA-based fuzzy logic controllers. A GA-based CS is presented in Section 6. Performances of the hybrid FLC and a comparative assessment of the control approach are presented in Section 7, and the paper is concluded in Section 8.