Tuning of Fractional-order Lead-lag Compensators

Abstract

This part of the book will concentrate on the tuning and auto-tuning of fractional-order lead-lag compensators, that is, a generalization of the classical lead-lag compensator. The similarities between this structure and the fractional-order PI^λD^μ controller in the frequency domain will be discussed. The design method proposed here will avoid the nonlinear minimization and initial conditions problems presented in Part II of the book.

In this chapter, a design method for fractional-order lead-lag compensators (FOLLC) is presented. Simple relations among the parameters of the fractional-order controller are obtained and specifications of steady-state error constant K_ss, phase margin ϕ_m, and gain crossover frequency ω_cg are fulfilled, following a robustness criterion based on the flatness of the phase curve of the compensator. The tuning method proposed will be taken as a first step for a later generalization of these lead-lag compensators to the fractional-order PI^λD^μ controllers, as will be explained in Chapter 9.