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 sli ding mode controller. Input variables of conventional FLCs are mostly the e rror 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 i nput space. The output of fuzzy inference is applied to the plant as the co ntrol input u or the change of control input Delta u. This scheme came from concepts of linear PD (proportional-derivative) and PI (proportional-integ ral) 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 normali zed input space. Considering these facts, we derive a new variable called t he 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 n umber of rules is greatly reduced compared to two-dimensional FLCs, and hen ce, generations and tuning of control rules are easy. Control performance i s nearly the same as that of conventional FLCs. We also show that this S-FL C 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.