SENSITIVITY ANALYSIS OF LOW COST FUZZY CONTROLLED SERVO SYSTEMS Stefan Preitl, Radu-Emil Precup and Zsuzsa Preitl “Politehnica” University of Timisoara, Dept. of Automation and Applied Informatics Bd. V. Parvan 2, RO-300223 Timisoara, Romania Phone: +40-256-4032-29, -30, -24, -26, Fax: +40-256-4032-14 E-mail: spreitl@aut.utt.ro, rprecup@aut.utt.ro, zsuzsap@aut.utt.ro Abstract: The paper performs the sensitivity analysis with respect to the parametric variations of the controlled plant in the case of low cost fuzzy control systems dedicated to servo systems, with focus on solving the tracking control problem for a class of wheeled mobile robots with two degrees of freedom used in mining technologies. A new development method for Takagi-Sugeno PI-fuzzy controllers is proposed, based on applying the Extended Symmetrical Optimum method to the basic linear PI controllers in a cascaded control system structure. Original sensitivity models are derived. The approaches are validated by a case study. Copyright © 2005 IFAC Keywords: sensitivity analysis, fuzzy control, second-order systems, PI controllers, servo systems, dynamics. 1. INTRODUCTION The considered class of controlled plants (abbreviated CPs) is characterized by the transfer functions H P (s): )] 1 ( /[ ) ( Σ + = sT s k s H P P , (1) where k P is the plant gain and T Σ represents the small time constant or the sum of parasitic time constants. The CPs with the transfer functions (t.f.s) of the second-order systems in (1) can approximate well enough the servo systems used in several applications including the control of mobile robots. Low cost automation (LCA) involves the use of low cost control equipment and of control solutions that can be developed and implemented relatively easy. LCA solutions employ control structures and algorithms with dynamics that can ensure good control system (CS) performance in many situations. A second-order system (1) can be placed on the lower hierarchical level of complex, large-scale systems. The assurance of good CS performance for these systems by means of LCA solutions represents a necessity. One way to fulfil the goal of good CS performance by means of LCA solutions for the CP (1) is represented by conventional control under the form of PI controllers (Åström and Hägglund, 1995). Another way to fulfil the mentioned goal is represented by the use of fuzzy control with dynamics due to the flexible nonlinear input-output static map ensured by the fuzzy controllers (FCs) that can compensate (based on the designers’ experience) the model uncertainties, nonlinearities and parametric variations of the CP. Actual applications of fuzzy control in the field of mobile robots are those reported in (Saffiotti, 2001; Hwang and Liu, 2004). But, although the reported simulation and experimental results are acceptable, relatively small research effort has been focussed on the systematic analysis of these fuzzy control systems (FCSs) including their stability or sensitivity analysis due to the nonlinearity of the FCs and of the CPs (Gartner and Astolfi, 2000; Cuesta and Ollero, 2002; Precup and Preitl, 2004). The development of fuzzy controllers for the linear CPs (1) is considered as a first step in the development of complex control structures including these plants.