Optimal output feedback for chaos improvement in AC variable active passive reactance system

Variable active passive reactance (VAPAR) is nonlinear time varying system which can generate virtual variable inductance including negative values in power circuits. AC source of VAPAR causes sinusoidal states in the circuit then the circuit does not have one fixed point in source period. So modified poincare map have to be used for modeling of these systems. In VAPAR Analytical methods cannot find optimal controller because, resultant state matrix is very complex. Also numerical methods have to be introduced. In this paper VAPAR with AC source and capacitor mode consideration in its inverter is modeled and three optimal feedback gains are computed with Gradient Descent algorithm. Characteristic multipliers in modified poincare map are moved to optimal locations and in the physical system, chaotic behaviors of the system are minimized with Applying optimal gains. The fixed point on each period is calculated by averaging theory.