Disturbance Rejection Fractional Order PID Controller Design in v-domain by Particle Swarm Optimization

Design and stabilization problems of fractional order PID (FOPID) controllers have been generally solved in frequency, time and s-domains. This study presents a design scheme in v-domain for optimal disturbance reject FOPID controller tuning problem. The proposed method is based on optimally placement of minimum angle system poles inside stability region of the first Riemann sheet to improve disturbance rejection control performance. For a given stabilizing target angle of minimum angle system pole, the purposed design approach maximizes reference to disturbance rate (RDR) index. For this purpose, optimization problem is defined as maximization of RDR index subject to minimum angle pole placement constraint. This constraint ensures stability of resulting FOPID control system by placing the minimum angle system pole into stability region of v-domain. Particle swarm optimization (PSO) is implemented to solve this optimization problem. An illustrative design example is presented to show effectiveness of the proposed design method.