New incremental Takagi–Sugeno state model for optimal control of multivariable nonlinear time delay systems

• New incremental state model is proposed for MIMO nonlinear delayed systems.
• The control action in an incremental form guarantees zero steady state errors.
• New Optimal observer is proposed, because not all states are available or measured.

In this work, a novel approach based on incremental state models has been proposed for the modeling of multivariable nonlinear delayed systems expressed by a generalized version of Takagi–Sugeno (T–S) fuzzy model. One of the key features of the new approach is that the proposed incremental state model compared with the no incremental one, naturally solves the problem of computing the target state, since for a desired output vector, a zero incremental state can be taken as an objective. Moreover, the control action in an incremental form is equivalent to introduce an integral action, thereby cancelling the steady state errors. Among other advantages using incremental models are the disappearance of the affine terms. Then, a fuzzy based linear quadratic regulator (FLC-LQR) is designed. Furthermore, a new optimal observer for multivariable fuzzy systems is developed, because not all states of the nonlinear system are fully available or measured. A multivariable thermal mixing tank system is chosen to evaluate the robustness of the proposed controller. The results obtained show a robust, well damped response with zero steady state error in the presence of disturbances and modeling errors.

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