Design of Robust Fractional PID Controller Using Triangular Strip Operational Matrices

Abstract

Abstract The present article proposes a simple tuning technique aimed to produce a robust non-integer order PID controller exhibiting iso-damping property during reparameterization of a plant. The required robustness property is achieved by letting the fractional PID control system to imitate the dynamics of a reference system having Bode’s ideal transfer function in its forward path. The objective of designing robust controller by tracking the dynamics of reference control system is defined mathematically as an H∞- optimal control problem. Fractional differential systems are transformed into algebraic equations by the use of triangular strip operational matrices. The H∞-optimal control problem is then changed to an ∞-norm minimization of a parameter (Kc,KI,Kd, λ, μ) varying square matrix. Global optimization techniques, Luus-Jaakola direct search and particle swarm optimization are employed to find the optimum values of fractional PID controller parameters. The proposed method of control system design is implemented in heating furnace temperature control, automatic voltage regulator system and some integer and fractional order process models. Fractional PI, fractional PD and various versions of fractional PID controllers are designed as optimal controllers using the triangular strip operational matrix based control design method.