Fractional-order Control: Nyquist Constrained Optimization

Abstract

The adoption of fractional calculus in control systems has enabled the synthesis of new controllers with fractional-order derivatives and integrals. Several optimization-based methods for tuning of linear fractional-order controllers have been explored. However, few have considered the stability of the closed-loop system during optimization. This paper presents a model-driven method for tuning of fractional-order controllers based on a heuristic optimization technique and the experimental use of Nyquist’s stability criterion to enforce closed-loop stability of fractional-order systems. The proposed frequency domain tuning method enables tuning of linear fractional-order controllers with few to medium number of parameters. The method can handle both fractional-order linear and integer-order linear plant models and controllers. To assist the experimental use of Nyquist’s stability criterion, a function for drawing a Logarithmic amplitude polar diagram has been developed. Simulation results of the method applied to a nanopositioning system in atomic force microscopy suggest that the proposed method can be used for optimization of fractional-order controllers while enforcing closed-loop stability. Given that the system can be stabilized with the given controller. Matlab code building on the FOTF toolbox and global optimization toolbox is provided.