Design of Fractional-order QFT Controllers for Unstable Plants Based on Automatic Loop Shaping

This paper introduces a quantitative robust fractional order controller designing applicable to the unstable plant. The plant is with only one unstable pole. In this work, the main idea consists in the study of the fractional-order compensator, which gives singular properties to automatically shape the open loop gain function in Nichols by using a minimum set of parameters. The fractional order controller is designed for not only minimum phase system but also uncertain non-minimum phase and unstable plants in QFT. It has been demonstrated that the fractional order controller can provide smaller high frequency gain than the integer order controller due to its extra tunable parameters. An automatic loop-shaping based on Particle Swarm Optimization (PSO) is developed and employed in quantitative feedback theory (QFT).