Um controlador ótimo robusto aplicado a inversores conectados à rede

Abstract

This thesis deals with a robust optimum control obtained through linear matrix inequalities applied to inverters connected to the grid through LCL filters. First, the plant is modeled in the state space, and the uncertainty in the grid inductance is taken into account, leading to a polytopic model of the plant. This model is validated by simulations. After, the delay of implementation of the control law in digital signal processor is included. Finally, resonant controllers in state space are inserted, generating a suitable model for state feedback design to control the current injected into the grid. Then, one presents conditions based on linear matrix inequalities for stability analysis and for design of state feedback controllers. These conditions are specialized to compute a robust optimal controller of the discrete quadratic linear regulator type, being the main contribution of this thesis in the applied control theme. Simulation results in the time domain and the frequency domain are shown, confirming the reference tracing of injected current in the grid, rejection of disturbances with harmonics, with transient results and satisfactory continuous regime results. Experimental results in a grid-connected inverter prototype confirm the practical viability of the control technique for this application, with currents injected into the grid presenting total harmonic distortion and harmonic content within the limits prescribed by the IEEE 1547.