Model reference adaptive control in fractional order systems using discrete-time approximation methods

• Model reference adaptive control in fractional order systems was studied.
• Fractional order systems were approximated by discrete-time systems.
• Stability analysis of the designed controller was studied using Lyapunov Theorem.
• Plant and reference model with different order of derivative was studied.
• Using higher order approximations resulted in better performance of controller.

In this paper, model reference control of a fractional order system has been discussed. In order to control the fractional order plant, discrete-time approximation methods have been applied. Plant and reference model are discretized by Grünwald–Letnikov definition of the fractional order derivative using “Short Memory Principle”. Unknown parameters of the fractional order system are appeared in the discrete time approximate model as combinations of parameters of the main system. The discrete time MRAC via RLS identification is modified to estimate the parameters and control the fractional order plant. Numerical results show the effectiveness of the proposed method of model reference adaptive control.