A Novel Fractional-Order PIλDμAν Controller and Its Design Optimization Based on Spiritual Search

Abstract

A novel fractional-order PIλDμAν controller involving fractional-order integrator, fractional-order differentiator and fractional-order accelerator is proposed for higher-order systems. The proposed PIλDμAν controller is a successor of the fractional-order PIλDμ and the integer-order PIDA controllers. In this paper, time-domain and frequency-domain responses of the PIλDμAν controller are characterized. With the design optimization framework, seven parameters of the PIλDμAν controller, i.e. proportional gain, integral gain, derivative gain, accelerated gain, fractional order of integrator, fractional order of differentiator and fractional order of accelerator, are optimized by the spiritual search (SS), one of the most efficient hybrid metaheuristic optimizers. To perform its benefits and effectiveness, the PIλDμAν controller and its SS-based design optimization are applied to three real-world higher-order control systems. Results obtained by the PIλDμAν controller are compared with those obtained by the PIDA and PIλDμA controllers. As results, it was found that the proposed PIλDμAν controller exhibits very satisfactory responses superior to the PIDA and PIλDμA controllers, significantly.