Adaptive multi-controller TSK Fuzzy Structure for Control of Nonlinear MIMO Dynamic Plant Pawel Dworak*. Stanislaw Bańka* *Faculty of Electrical Engineering, West Pomeranian University of Technology, Szczecin, Poland (Tel:+48 91 449 53 38; e-mail: paw el.dworak@ zut.edu.pl, stanislaw.banka@ zut.edu.pl). Abstract: In the paper an adaptive multi-controller control s ystem utilizing a TSK fuzzy rules for a MIMO nonlinear dynamic plant is presented. The prob lems under study are exemplified by synthesis of a position and yaw angle control system for a drillsh ip described by a 3DOF nonlinear mathematical model of low-frequency motions made by the drillship over the drilling point. In the proposed control system use is made of a set of linear modal controllers th at create a multi-controller structure from which a group of controllers appropriate to given operation condi tions is chosen and used to calculate, by using TSK fuzzy rules, control signals. The final part of the paper includes simulation results of system operat ion with an adaptive controller of (stepwise) varying p arameters along with conclusions and final remarks. Key words: MIMO multivariable control systems, nonlinear syste ms, modal control . 1. INTRODUCTION Nonlinear control systems are commonly encountered in many different areas of science and technology. In particular, problems difficult to solve arise in motion and/or position control of various vessels, like drilling platforms and ships, sea ferries, special purpose ships as well as subma rines. Complex motions and/or complex-shaped bodies moving in the water, and in case of ships also at the boundar y between water and air, give rise to resistance forces depen dent in a nonlinear way on velocities and positions, thus cau sing the floating bodies to become strongly nonlinear dynami c plants. In general, there are two basic approaches to solve the control problem for nonlinear plants. The first one called “nonlinear” consists in synthesizing a nonlinear controller tha t would meet certain requirements over the entire range of control signals variability (Fabri and Kadrikamanathan 2001 ; Huba et al. 2011; Khalil 2001; Tzirkel-Hancock and Fallside 1992; Witkowska et al. 2007; Zwierzewicz 2008). The secon d approach called “linear” consists in designing an a daptive linear controller with varying parameters to be sys tematically tuned up in keeping with changing plant operating c onditions determined by system nominal “operating points”. However in practice, the second approach is more co nvenient to use, since advantage can be taken of already pro ven procedures and commonly known mathematical methods employed in design (synthesis) of linear controller s. Here, linearization of nonlinear MIMO plants is a prerequ isite for the methods to be employed. After linearization loc al linear models are obtained valid for small deviations from “operating points” of the plant. Since properties exhibited by linear models at diff erent (distant) “operating points” of the plant may subst antially vary, therefore the controllers used should be eith er robust (Dworak et al. 2009; Dworak and Pietrusewicz 2006;I oannou and Sun 1996) (usually of a very high order as has been observed by (Gierusz 2005)) or adaptive with parame ters being tuned in the process of operation (Äström and Wittenmark 1995). If the description of the nonlinear plant is known, then it is possible to make use of systems with linear control lers prepared earlier for possibly all “operating points ” of the plant. Such controllers can create either a set of controllers with switchable ouputs from among which one control ler designed for the given system “operating point” (Bańka et al. 2010a;Bańka et al. 2010b;Dworak and Pietrusewicz 2010) is chosen, or multi-controller structures the control signal components of which are formed, for example, as wei ghted means of outputs of a selected controller group acc ording to Takagi-Sugeno rules, i.e. with weights being propor tional to the degree of their membership of appropriately fuz zyfied areas of plant outputs or other auxiliary signals ( Tanaka and Sugeno 1992; Tatjewski 2007). What all the above-mentioned multi-controller struc tures, where not all controllers at the moment are utilize d in a closed-loop system, have in common is that all cont rollers employed in these structures must be stable by them selves, in distinction to a single adaptive controller with va rying (tuned) parameters. This means that system strong s tability conditions should be fulfilled (Vidyasagar 1985). Another problem to solve in a practical realization of such a system is the number of controllers used. A number of rules in a Takagi-Sugeno algorithm rise quicly with the n umer of controllers which is often called a “curse of dimen sionality”. Such a system may not be able to implement and run in an confined space of industrial device. To soften this constraints we propose a method for reducing the largeness of a TSK fuzzy structure working with big amount linear cont rollers, necessary to cover all nonlinearities of the plant. 9th IFAC Conference on Manoeuvring and Control of Marine Craft, 2012 The International Federation of Automatic Control September 19-21, 2012. Arenzano, Italy ©2012 IFAC 10.3182/20120919-3-IT-2046.00041 238