Robust Tracker of Hybrid Microgrids by the Invariant-Ellipsoid Set

This paper introduces a new ellipsoidal-based tracker design to control a grid-connected hybrid direct current/alternating current (DC/AC) microgrid (MG). The proposed controller is robust against both parameters and load variations. The studied hybrid MG is modelled as a nonlinear dynamical system. A linearized model around an operating point is developed. The parameter changes are modelled as norm-bounded uncertainties. We apply the new extended version of the attractive (or invariant) ellipsoid for this tracking problem. Convex optimization is used to obtain the region’s minimal size where the tracking error between the state trajectories and the reference states converges. The sufficient conditions for stability are derived and solved based on linear matrix inequalities (LMIs). The proposed controller’s validity is shown via simulating the hybrid MG with various operational scenarios. In each scenario, the performance of the controller is compared with a recently proposed sliding mode controller. The comparison clearly illustrates the superiority of the developed controller in terms of transient and steady-state responses.

LMI-Based Robust Stabilization of a Class of Input-Constrained Uncertain Nonlinear Systems with Application to a Helicopter Model

This paper is concerned with the robust stabilization of a class of continuous-time nonlinear systems, with an application to the pitch dynamics of a simple helicopter model, via an affine state-feedback control law using the linear matrix inequality (LMI) approach. The nonlinear dynamics is subject to norm-bounded parametric uncertainties and disturbances. In addition, the problem of actuator nonlinearity is addressed by considering the saturation effect of the control law. We demonstrate first that the synthesis problem of the saturated controller is expressed in terms of bilinear matrix inequalities (BMIs). Thanks to the Schur complement lemma and the matrix inversion lemma, we convert these BMIs into LMIs allowing the simultaneous computation of the two gains of the affine controller. Furthermore, we address in this work the estimation problem of the domain of attraction using the invariant set concept. This is solved by computing the largest attractive invariant ellipsoid. Compared with previous works, the research procedure of such ellipsoidal set is achieved in a single step with a reduced number of LMI constraints and then with less conservative conditions. A portfolio of numerical results is presented. The effectiveness and robustness of the proposed saturated controller in the stabilization of the adopted helicopter pitch model toward parametric uncertainties and disturbances are illustrated through simulation results.

An implicit class of continuous dynamical system with data-sample outputs: a robust approach

This paper addresses the problem of robust control for a class of nonlinear dynamical systems in the continuous time domain. We deal with nonlinear models described by differential-algebraic equations (DAEs) in the presence of bounded uncertainties. The full model of the control system under consideration is completed by linear sampling-type outputs. The linear feedback control design proposed in this manuscript is created by application of an extended version of the conventional invariant ellipsoid method. Moreover, we also apply some specific Lyapunov-based descriptor techniques from the stability theory of continuous systems. The above combination of the modified invariant ellipsoid approach and descriptor method makes it possible to obtain the robustness of the designed control and to establish some well-known stability properties of dynamical systems under consideration. Finally, the applicability of the proposed method is illustrated by a computational example. A brief discussion on the main implementation issue is also included.

T-S Fuzzy-Based Optimal Control for Minimally Invasive Robotic Surgery with Input Saturation

A minimally invasive surgery robot is difficult to control when actuator saturation exists. In this paper, a Takagi-Sugeno fuzzy model-based controller is designed for a minimally invasive surgery robot with actuator saturation, which is difficult to control. The contractively invariant ellipsoid theorem is applied for the actuator saturation. The proposed scheme can be derived using the H-infinity control theorem and parallel distributed compensation. The result is rebuilt in the form of linear matrix inequalities for easier calculation by computer. Meanwhile, the uniformly ultimately bounded stable and the prescribed H-infinity control performance can be guaranteed. The proposed scheme is simulated in a Novint Falcon haptic device system.