A simple robust sliding-mode fuzzy-logic controller of the diagonal type

This paper derives and analyzes a new robust fuzzy-logic sliding-mode controller of the diagonal type, which does not need the prior design of the rule base. The basic objective of the controller is to keep the system on the sliding surface so as to ensure the asympotic stability of the closed-loop system. The control law consists of two rules: (i) IF sign(e(t)(e) over dot(t)) < 0 THEN maintain the control action, and (ii) IF sign(e(t)(e) over dot(t)) > 0 THEN change the control action, where e(t) = x(t) - x(d)(t) is the system state error, and the control action can be either an increase or decrease of the control signal, which is realized through the use of fuzzy rules. The proposed controller, which does not need the prior knowledge of the system model and the prior design of the membership functions' shape, was tested, by simulation, on linear and nonlinear systems. The performance was in all cases excellent (very fast trajectory tracking, no chattering) . Of course, as in traditional control, there was a trade-off between the rise-time and the overshoot of the system response.