Design of a single-input fuzzy logic controller and its properties

We suggest a simple but powerful FLC (Fuzzy Logic Controller) design method using a single fuzzy input variable, which is equivalent to the pseudo sliding mode controller. Input variables of conventional FLCs are mostly the error e and the change-of-error (e) over dot regardless of the complexity of controlled plants. A rule table is then constructed in a two-dimensional input space. The output of fuzzy inference is applied to the plant as the control input u or the change of control input Delta u. This scheme came from concepts of linear PD (proportional-derivative) and PI (proportional-integral) controllers. We found that rule tables of most FLCs have skew-symmetry property, and the absolute magnitude of the control input \u\ or \Delta u\ is proportional to the distance from its main diagonal line in the normalized input space. Considering these facts, we derive a new variable called the signed distance, which is a sole fuzzy input variable in our simple FLC called single-input FLC (S-FLC). The S-FLC has many advantages: The total number of rules is greatly reduced compared to two-dimensional FLCs, and hence, generations and tuning of control rules are easy. Control performance is nearly the same as that of conventional FLCs. We also show that this S-FLC is equivalent to the pseudo SMC (sliding mode controller), and hence, the stability is guaranteed using the Lyapunov stability. The performance of S-FLC is revealed via computer simulations using a nonlinear plant. (C) 1999 Elsevier Science B.V. All rights reserved.