An algorithm to compute an optimally robust controller and its stability radius

A delay-dependent robust fuzzy control approach is developed for a class of nonlinear uncertain interconnected time delay large systems in this paper. First, an equivalent T–S fuzzy model is extended in order to accurately represent nonlinear dynamics of the large system. Then, a decentralized state feedback robust controller is proposed to guarantee system stabilization with a prescribedH∞disturbance attenuation level. Furthermore, taking into account the time delays in large system, based on a less conservative delay-dependent Lyapunov function approach combining with linear matrix inequalities (LMI) technique, some sufficient conditions for the existence ofH∞robust controller are presented in terms of LMI dependent on the upper bound of time delays. The upper bound of time-delay and minimizedH∞performance index can be obtained by using convex optimization such that the system can be stabilized and for all time delays whose sizes are not larger than the bound. Finally, the effectiveness of the proposed controller is demonstrated through simulation example.

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Doubly fed induction generators to enhance inter-area damping based on a Robust controller: $${{\varvec{H}}}_{2}/{{\varvec{H}}}_{\infty }$$ Control

SN Applied Sciences ◽

10.1007/s42452-021-04150-1 ◽

2021 ◽

Vol 3 (1) ◽

Author(s):

Ali Goodarzi ◽

Ali Mohammad Ranjbar ◽

Moslem Dehghani ◽

Mina GhasemiGarpachi ◽

Mohammad Ghiasi

Keyword(s):

Working Conditions ◽

Reactive Power ◽

Wind Farms ◽

System Stability ◽

Pole Placement ◽

Linear Matrix ◽

Robust Controller ◽

Induction Generators ◽

Doubly Fed ◽

Oscillation Damping

AbstractIn this study, an auxiliary damping controller based on a robust controller considering the active and reactive power control loops for a doubly-fed induction generator for wind farms is proposed. The presented controller is able to improve the inter-area oscillation damping. In addition, the proposed controller applies only one accessible local signal as the input; however, it can improve the inter-area oscillation damping and, consequently the system stability for the various working conditions and uncertainties. The oscillatory modes of the system are appointed using the linear analysis. Then, the controller’s parameters are determined using the robust control approaches ($${H}_{\infty }/{H}_{2})$$ H ∞ / H 2 ) with the pole placement and linear matrix inequality method. The results of the modal analysis and time-domain simulations confirm that the controller develops the inter-area oscillation damping under the various working conditions and uncertainties.

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