Fractional-order Control to Prevent Limit Cycles due to Saturation Nonlinearity

Many control systems show deteriorated performance because of hard nonlinearities that are common in different applications. Fractional-order control can find new results to compensate nonlinearities, but control design methods are still at infancy. This paper addresses the issue of limit cycles determined by saturation elements in nonlinear control loops including plant servo systems. The fractional-order controller consists of two lead networks in series, one shifted with respect to the other on the frequency axis, and both of non-integer order. They are designed in the frequency domain to provide a high phase lead at the resulting gain crossover frequency and a Bode plot of the loop transfer function with phase varying slowly around that frequency. Robust prevention of the limit cycle is obtained such that the Nyquist plot of the linear elements in the loop does not intersect the negative inverse describing function plot.