Abstract
In the paper a control system utilizing Takagi-Sugeno (T-S) fuzzy rules for a MIMO nonlinear dynamic plant is presented. In the proposed control system use is made of a set of linear modal controllers that create a multi-controller structure from which a group of controllers appropriate to given operation conditions is chosen and used to calculate, by employing T-S fuzzy rules, control signals. Stability conditions of the closed-loop system may be checked by the use of the simple, well-known techniques thus the proposed method allows one to simplify the synthesis of the controller. Problems of the controller practical realization and its implementation in, for example, constrained memory of programmable automation devices are discussed. The final part of the paper includes simulation results of system operation with an adaptive controller of (stepwise) varying parameters along with conclusions and final remarks. DOI: http://dx.doi.org/10.5755/j01.eee.20.5.7091
Highlights
Control of a nonlinear dynamic plant is a very difficult task, especially for multi input multi output (MIMO) plants
The T-S fuzzy systems gain its popularity partially because its stability conditions can be tested by the use of linear matrix inequalities (LMIs)
The stability checking procedure does not demand to calculate a huge number of LMI and very simple fuzzy rules adopted allow one to decrease the size of the controller and make the control system easy to implement in any programmable controller
Summary
Control of a nonlinear dynamic plant is a very difficult task, especially for multi input multi output (MIMO) plants. The proposed stability conditions are usually quite restrictive, and no common Lyapunov function exists for many stable fuzzy systems. What many multi-controller structures, where not all controllers at the moment are utilized, have in common is that all controllers employed in these structures must be stable by themselves This means that system strong stability conditions should be fulfilled [16]. To soften these problems a method for reducing the largeness of a T-S fuzzy structure working with a big amount of linear controllers, necessary to cover all nonlinearities of the plant is proposed.
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