Fuzzy Logic Based Look-Up Table Regulator Manuel Olivares 1 Pedro Albertos Antonio Sala olivares@aii.upv.es pedro@aii.upv.es asala@isa.upv.es Universidad Politécnica de Valencia Dept. of Systems Engineering and Control, Apdo. 22012 E-46071 Valencia, Spain. Phone: +34 96 3879570, Fax: +34 96 3879579 1 On leave from Dept. of Electronics, Universidad Técnica F. Santa María, Valparaíso, Chile. Abstract In this paper, a look-up table control strategy derived from a fuzzy logic controller is developed for output regulation of a SISO linear plant with delay subject to load changes and transfer between different operating points. The strategy considers an off-line trained look-up table for rejection of an unity load step change and another one trained for unity reference step tracking combined in a switched LUT regulator. Also it is shown that any load or reference step change can be rejected or tracked by properly scaling the pre and post processing gains of its corresponding LUT controller. In this way, a non linear regulator is implemented. Keywords: LUT control, self-organising controllers, disturbance rejection. 1 INTRODUCTION Adaptation techniques for fuzzy systems have been extensively studied with the goal of developing practical learning controllers. Here, an iterative learning control strategy that gradually improves the reference and load step response is presented. This problem has been studied by several authors (see for example [2]). The approach in this paper utilises a PI fuzzy look-up table controller [5,6], enhancing the adaptive algorithm [1,3,4] to deal with the regulator problem (disturbance compensation). The Self Organising mechanism yields an improved controller starting from a linear one with poor disturbance rejection performance, by repeated off-line iterations. After a number of learning runs, a satisfactory performance LUT is chosen. The paper is organised as follows: The SOC structure with first order reinforcement learning is presented. Good performance look-up tables (LUT) for unity step reference and unity step load changes are obtained by experimental training. Then the disturbance detection and the scaling method to compensate any step like reference and load change are discussed. The switching between LUTs is easily determined by the a priori knowledge of the set point changes. Finally, some simulating results and conclusions complete the document. 2 SOC STRUCTURE To improve the closed loop response by means of a learning algorithm, a LUT based discrete PI & SOC structure, is implemented. It consists of two main blocks (fig. 1), a discrete dynamic LUT and a SOC algorithm. Details about the SOC structure can be seen in [1]. In addition to the usual 2 input 1 output discrete static LUT, the discrete dynamic LUT has a third input and a second output. CE E z-1 Tz Derivative Tz z-1 Integrator U U* n-d U n-d SOC (G p , τ, T s ) Discrete (d, T) Dynamic Look Up Table GE GCE GCU ce k e k u k Figure 1. Discrete PI & SOC structure The third input * d n U - is used to update the content of the table element taken “d” samples before, and the second output d n U - supplies a copy of the delayed control action signal, sampled each T s sec. The regular U output is computed from the E and CE inputs using linear interpolation. The central element of the table has been kept invariant, and zero to assure a good steady state behaviour. The SOC block produces * d n U - by the reward/penalty n p , the reinforcement required to correct any bad performance detected from n e and n ce . ( ) s n n p n T ce e G p τ + = (1) d n n d n U p U - - + = * (2) where G p is the reinforcement gain and τ the dynamic balance between the error and its change.