This paper proposes a systematic formulation of inverse optimal control (IOC) law based on a rather straightforward reduction of control Lyapunov function (CLF), applicable to a class of second-order nonlinear systems affine in the input. This method exploits the additional design degrees of freedom resulting from the non-uniqueness of the state dependent coefficient (SDC) formulation, which is widely used in pseudo-linear control techniques. The applicability of the proposed approach necessitates an apparently effortless SDC formulation satisfying an SDC matrix criterion in terms of the structure and characteristics of the state matrix, [Formula: see text]. Subsequently, a sufficient condition for the global asymptotic stability (g.a.s) of the closed-loop system is established. The SDC formulations conforming to the sufficient condition ensure the existence and determination of a smooth radially unbounded polynomial CLF of the form [Formula: see text], while offering a benevolent choice for the gain matrix [Formula: see text], in the CLF. The direct relationship between the gain matrix [Formula: see text] and state weighing matrix [Formula: see text] ensures optimization of an equivalent [Formula: see text]. This feature enables one to rightfully choose the gain matrix [Formula: see text] as per the performance requisites of the system. Finally, the application of the proposed methodology for the speed control of a permanent magnet synchronous motor validates the efficacy and design flexibility of the methodology.

In this paper controller design for voltage sag ride-through in hybrid fuel cell/battery energy storage distributed power generation system has been presented. As the amount of fuel cell power generation and other Distributed Generation (DG) with power electronic in the grid grows, it becomes unacceptable to disconnect generating units every time a disturbance occurs, as was common practice in the past. Keeping the VSC on line during unbalanced voltage sags becomes thus a very critical issue. Hence, modeling, controller design, and simulation study of a hybrid distributed generation system are investigated. Based on the classification of unbalanced faults that can occur in the grid, resulting in voltage sags at the bus where the hybrid power system is connected, the maximum current that the converter valves must be bale to withstand is calculated. Simulation results are given to show the overall system performance including active power control and voltage sag ride-through capability of the hybrid distributed generation system.

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