LQR based Optimal Passive Fault-Tolerant Nonlinear Fractional-Order PID

In this study, a passive fault-tolerant controller is designed for the dynamic system based on nonlinear fractional-order theory. The closed-loop control structure contains a linear quadratic regulator for calculating the optimum input signal based on physical criteria as well as nonlinear fractional-order PID. In fact, the summation of the controlling inputs, which are computed by the optimized robust nonlinear fractional-order PID controllers (NFOC), is modified by the LQR unit to achieve higher reliability and robustness. Using optimized robust NFOC along with LQR, the desired controller robustness and performance are evaluated by comparing its quantified performance indicator and optimized simple and fractional-order PID controllers' efficiency. This controller can improve the system’s tracking performance by less amount of control effort and reject the effects of the faulty actuator on the system’s dynamics.