DESIGN OF FUZZY CONTROLLER FOR INVERTED PENDULUM BASED ON LQR-MAPPED SENSORY FUSION

Abstract

"Rule number explosion" in fuzzy controller and "uncertainty" in the model are two main issues in the design of fuzzy control systems. To overcome these problems, a method has been applied in which a linear sensory fusion function has been used to reduce the dimensions of fuzzy controller's inputs and simultaneously use the features of LQR control. By using fusion, the output variables of the system with four dimensions (in LIP and RIP) are synthesized as two variables: error and variation of error. As a result the design process of fuzzy controller has been much simplified and the control quality improved significantly. The method has been tested for control of the benchmark nonlinear systems such as linear 1-stage inverted pendulum (LIP), rotary inverted pendulum (RIP). A model based on LQR mapping with heuristic fuzzy and ANFIS respectively are first designed and compared their control performance with those obtained from LQR control. Since the fusion block utilizes the features of LQR control, the control quality obtained in case of fuzzy control using LQR mapped fusion will be better in every aspect (also satisfied by simulation results). Complex under-actuated systems (number of joints greater than that of actuating signals) e.g. LIP, RIP, DIP are inherently nonlinear and much affected from the uncertainty in the model. Since, in type-2 fuzzy control the degree of fuzziness increased and it can better handle the uncertainty in the model compared to conventional fuzzy,. so the method of sensory fusion with type-2 fuzzy control scheme has been combined to make the controller more robust w.r.t. the parameters variation, perturbance and uncertainty in the model. Performance criteria like IAE, ISE and ITAE have been used to compare the control performance obtained from conventional fuzzy and type-2 fuzzy controller. The method has been applied to the approximate linear model, and the experimental results show that this method has better tracking performance, disturbance resisting performance, and robustness against model uncertainties. Such kinds of fuzzy controllers have clear design ideas, satisfactory reliability and practicability.