LQR control with integral action applied to a high gain step-up DC-DC converter

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Abstract
This paper presents the linear quadratic regulator (LQR) control technique applied to a high gain boost converter based on three-state switching cell (TSSC). In order to control the state variables of the aforementioned converter, which usually are the current through the filter inductor and voltage across the output capacitor, the small signal average state-space model is used, as the mathematical equations are obtained. Due to the complexity of the converter, the physical circuit formed by semiconductors, magnetic elements, capacitors, and resistors, is initially transformed into an equivalent classical boost converter, and then the matrix equations that reproduce the converter's dynamic behavior are determined. After the modeling, with the aim to obtain the optimal control law that minimizes the predefined cost function, the compensator design is performed using MATLAB. The converter control system is validated through simulation using ORCAD and experimentation by developing a 1-kW laboratory prototype.

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