A procedure is presented for designing fuzzy controllers based upon variable structures techniques. Three such controllers are presented: the fuzzy equivalents of sliding-mode controllers, saturating controllers, and tanh controllers. By using an approach based upon variables structures (VSS) techniques, the stability of each of these controllers is assured. By using a sliding surface, the order of the rule base is reduced to size r/spl times/m, where r is the number of inputs and m is the number of fuzzification levels. This combination makes the proposed design procedure able to generate simple controllers with guaranteed stability properties. To illustrate the proposed design procedure, fuzzy controllers are designed for a ball-and-beam system. It is demonstrated that in spite of this system being a fourth-order unstable system, the proposed design procedure results in simple stable fuzzy controllers.

A simple control law is proposed to maintain the movement of a trotting quadruped. The assumption behind this control law is that one should be able to rely upon the quadruped's momentum for stability. The control law should only serve to redirect or maintain the quadruped's momentum. The result is a control law that works well so long as the quadruped is moving.