Fractional-order lead networks to avoid limit cycle in control loops with dead zone and plant servo system

The fractional-order controllers (FOCs) have recently had a significant impact on control applications. However, they still need further research for feedback systems with hard nonlinearities, such as dead zones. The above compelling evidence motivates the design of a new robust FOC to avoid limit cycles caused by dead zones in the control loops. The proposed FOC consists of the cascade of two shifted in frequency, fractional-order lead networks. They provide high-value and sufficiently flat phase leads in sufficiently large frequency intervals. In this way, the linear part of the control loop can be easily shaped to achieve avoidance of limit cycles. The article applies classical concepts, such as the Nyquist plot and describing function method, to derive guidelines for designing the free parameters of the FOC. Moreover, a realization algorithm and a parameter setting procedure make the new FOC easily implementable in engineering practice.