A Fractional-Order On-Line Self Optimizing Control Framework and a Benchmark Control System Accelerated Using Fractional-Order Stochasticity

Abstract

This paper presents a design and evaluation of a fractional-order self optimizing control (FOSOC) architecture for process control. It is based on a real-time derivative-free optimization layer that adjusts the parameters of a discrete-time fractional-order proportional integral (FOPI) controller according to an economic cost function. A simulation benchmark is designed to assess the performance of the FOSOC controller based on a first order plus dead time system. Similarly, an acceleration mechanism is proposed for the fractional-order self optimizing control framework employing fractional-order Gaussian noise with long-range dependence given by the Hurst exponent. The obtained results show that the FOSOC controller can improve the system closed-loop response under different operating conditions and reduce the convergence time of the real-time derivative-free optimization algorithm by using fractional-order stochasticity.

Keywords

• self optimizing control
• discrete FOPI controller
• globalized constrained Nelder–Mead algorithm
• fractional-order stochasticity