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this paper presents the modelling, controller design and a steady-state analysis algorithm for a wind-driven induction generator system. An output feedback linear quadratic controller is designed for the static synchronous compensator (STATCOM) and the variable blade pitch in a wind energy conversion system (WECS) in order to reach the voltage and mechanical power control under both grid-connection and islanding conditions. A two-reference-frame model is proposed to decouple the STATCOM real and reactive power control loops for the output feedback controller. To ensure zero steady-state voltage errors for the output feedback controller, the integrals of load bus voltage deviation and dc-capacitor voltage deviation are employed as the additional state variables. Pole-placement technique is used to determine a proper weighting matrix for the linear quadratic controller such that satisfactory damping characteristics can be achieved for the closed-loop system. Effects of various system disturbances on the dynamic performance have been simulated, and the results reveal that the proposed controller is effective in regulating the load voltage and stabilizing the generator rotating speed for the WECS either connected with or disconnected from the power grid. In addition, proper steady-state operating points for an isolated induction generator can be determined by the proposed steady-state analysis algorithm. Constant output frequency control using the derived steady-state characteristics of the isolated induction generator is then demonstrated in this paper.

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In this paper, we perform safety and performance analysis of an autonomous vehicle that implements reactive planner and controller for navigating a race lap. Unlike traditional planning algorithms that have access to a map of the environment, reactive planner generates the plan purely based on the current input from sensors. Our reactive planner selects a waypoint on the local Voronoi diagram and we use a pure-pursuit controller to navigate towards the waypoint. Our safety and performance analysis has two parts. The first part demonstrates that the reactive planner computes a plan that is locally consistent with the Voronoi plan computed with full map. The second part involves modeling of the evolution of vehicle navigating along the Voronoi diagram as a hybrid automata. For proving the safety and performance specification, we compute the reachable set of this hybrid automata and employ some enhancements that make this computation easier. We demonstrate that an autonomous vehicle implementing our reactive planner and controller is safe and successfully completes a lap for five different circuits. In addition, we have implemented our planner and controller in a simulation environment as well as a scaled down autonomous vehicle and demonstrate that our planner works well for a wide variety of circuits.