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In this paper, a robust model predictive control (MPC) algorithm is designed for nonlinear uncertain systems in presence of the control input constraint. To achieve this goal, first, the additive and polytopic uncertainties are formulated in the nonlinear uncertain system. Then, the control policy is chosen as a state feedback control law in order to minimize a given cost function at each known sample-time. Finally, the robust MPC problem is transformed into another optimization problem subject to some linear matrix inequality (LMI) constraints. The controller gains are determined via the online solution of the proposed minimization problem in real-time. The suggested method is simulated for a second order nonlinear uncertain system. The closed-loop performance is compared to other control techniques. The simulation results show the effectiveness of the proposed algorithm compared to some existing control methods.
 

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In this paper, a new output feedback control method was used based on a linear matrix inequality to control the angular position of AC servo motor shaft. The proposed control method does not need to measure all of the AC servo motor statuses; it only uses the output feedback and is robust against the uncertain servo motor parameters and the disturbances applied to it. The proposed control method was compared in several scenarios with a Standard Internal Model Control-Sliding Mode Control (SIMC-SMC) method, 2-Degree-of-Freedom Internal Model Control-Sliding Mode Controller (2DOF-IMC-SMC) method, 2-Degree-of-Freedom Internal Model Control-Proportional-Integral-Derivative (2DOF-IMC-PID) method, Standard Internal Model Control-Proportional-Derivatives (SIMC-PD) method, and Internal Model Control-Proportional-Integral-Derivative-Extended State Observer (IMC-PID-ESO) method. The simulation results show that the proposed controller has desirable performance against disturbances and uncertain parameters of the AC servo motor compared with other mentioned controllers. This method relative to other controllers decreased the error of tracking the angular position of the servo motor to 30% .The simulation was performed in the Matlab Software. 

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 In this paper an observer-based robust fault estimation scheme is proposed for a special class of Lipchitz nonlinear systems where the disturbances and faults are assumed to be coupled with the main system states. In the considered model of system, fault is assumed to enter both of the state and output equations as an unmeasured nonlinear function and coupled with the states. The disturbances and the uncertainties are considered as nonlinear functions coupled with the states. To the best of the authors’ knowledge these conditions have not been previously considered in related papers. In the proposed approach, a Luenberger observer is designed for the estimation of faults and states of system simultaneously. The effect of system disturbances is attenuated with the L2  norm. The necessary conditions for the existence of such observer is expressed in the form of Linear Matrix Inequality. The Lipchitz constant of the nonlinear function is obtained by solving the proposed Linear Matrix Inequality. Finally, the performance of the proposed method is simulated on a three-phase induction motor. The results indicate good performance of the proposed method.
 

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In an islanded microgrid, power electronic converters are used to exchange power, and these converters have very low inertia, thus compromising the frequency stability of the microgrid. Virtual inertia control is used to improve the frequency stability of an islanded microgrid. The derivative control technique is usually used to implement virtual inertia control in the microgrid. Factors such as disturbance and uncertainty of parameters of the islanded microgrid compromise the performance of virtual inertia control and may cause system frequency instability. Therefore, the virtual inertia control structure, a complementary controller is needed that can weaken the effect of disturbance on the microgrid as much as possible and be resistant to the uncertainty of parameters of the microgrid. In this paper, a robust control method is used in a virtual inertia control structure that uses system output feedback. The proposed method is expressed based on linear matrix inequality and is proved based on the Lyapunov criterion. Among the advantages of the proposed method is the attenuation of disturbance, resistance to the uncertainty of parameters of the microgrid, and increasing the degree of freedom to control the system in this method. The results of the proposed method to improve the performance of virtual inertia control in several different scenarios by considering the uncertainty of parameters of the two-zone microgrid and disturbances on the microgrid are compared with several methods and the effectiveness of the proposed method in terms of improving frequency stability is shown.