An adaptive optimal linear quadratic regulator applied to three phases PWM AC-DC converter

It is difficult to get analytical closed-form solutions of the ac-dc voltage source converter, because their model is time-variant, non linear and includes switching functions. However, to solve these problems, three steps are applied to model it. First, the system is further divided into two parts, the steady-state dc model and the small-signal ac model and the second parts, an adaptive optimal linear quadratic regulator (LQ) to the ac - dc voltage source converter is applied. The LQR regulator is a useful tool in modem optimal control design, consisting of an explicit matrix design equation based on Ricatti equation easily solved in a digital computer assure an improvement in power factor (P.F), harmonic reduction in case of the load variation.