1-4244-0361-8/06/$20.00 ©2006 IEEE MRAC and FMRLC for a plant with time varying parameters S. E. Oltean 1 , M. Abrudean 2 , A. Gligor 1 1 Petru Maior University of Targu Mures, soltean@upm.ro, agligor@upm.ro 2 Technical University of Cluj Napoca, Mihai.Abrudean@aut.utcluj.ro Abstract - This paper pr esents a compar ative analysis of two adaptive contr ol methods used in case of time var ying plant par ameters. The first adaptive contr ol method is based on the stability theor y of L yapunov and the other one is based on fuzzy logic. Also, the per for mances of the pr oposed contr ol algor ithms ar e evaluated with simulation envir onment. These contr ol str uctur es ar e designed for local compensation of the non-linear interactions and unknown payload variations in flexible-link gear dr ive. I. I NTRODUCTION In automation literature more plants need newer and modern control strategies to obtain the technical demands and desired performances. Some plants have time varying or unknown parameters, other are partially known or are altered by disturbance. A solution for these problems is to adapt the parameters of the initial controller and to obtain a so-called adaptive controller. In this paper is presented the implementation of the two adaptive control strategies (model reference adaptive control MRAC and fuzzy model reference learning control FMRLC) and the comparison of their performances. In MRAC, as in FM RLC, the technical demands and the desired input-output behavior of the closed l oop system is given via the corresponding dynamics of the reference model. Therefore, the basic task is to design such a control, which will ensure the minimal error between the reference model and the plant outputs (adaptation error) despite the uncertainties or variations in the plant parameters and working conditions. The design of controllers, using conventional techniques, for plants with non-linear dynamics and modeling uncertainties can be often quite difficult. The first approach is the design of the model reference adaptive control MRAC using the stability theory of Lyapunov. This theory assures that the adaptation error 0 is asymptotically stable. Of course, fuzzy control is a practical alternative for a variety of challenging control applications, since it provides a convenient method for constructing non-linear controllers via the use of heuristic information. However, some of the problems encountered in practical control problems, such as model uncertainties or the diffi culty to choose some of the fuzzy controller parameters, demand a way to automatically tune the fuzzy controller so that it can adapt to different operating conditions [1,2]. Based on fuzzy logic controller we then focus on the design of the second adaptive controller named fuzzy model reference learning controller FMRLC. The term learning is used as opposed to adaptive to distinguish the two control structures. In particular, the distinction is drawn since the FMRLC, which is a direct model reference adaptive controller too, will tune and to some extent will remember the values it had tuned in the past, while the conventional adaptive approach (MRAC) will continue to tune the controller parameters. In the end the performances of the two proposed control algorithms are evaluated in a local adaptive control structure for a flexible-link gear drive. Robot control is a complex process, which needs knowledge from different domains. The control of the robot can be done in the free workspace or in the constrained workspace. Flexible- link gear drive with high reduction ratio provides a linearization of the robot system dynamics. Further, this gear drive offers the possibility to use the decoupling control method or the local compensation of the non-linear interactions between different motion axes. II. DYNAMICAL MODEL OF THE P LANT The kinematics of the serial robot has a special construction. The forces and the moments of the different arms of the serial robot are interacting. A solution for resolving the non-linear interactions is the parallel robots. If this physical solution is not possibl e, an alternative is obtained with the combination between gear drive and adaptive controller. The modern adaptive controller assures the robustness of the global system even in presence of the model uncertainties or payload variations. We suppose that each flexible-link of the robot is gear driven by a dc motor. So, our plant used in digital simulation is in fact a dc motor. The dynamic equations of the dc motor with independent excitation are:         ) ( ) ( , ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( t t dt t d t t C t B dt t d J t i k t k dt t di L t i R t u dc dc dc r dc dc m dc e . (1) Where the plant parameters are voltage u , current i, circuit resistance R (1.025 ), circuit inductance L (0.1H), electromotive voltage k e (k e = 0.5247V·min/rot), motor torque