Fractional order automatic tuning of PI^λD controller for stable processes

This paper presents modified fractional order relay based automatic tuning of PI^λD controller for stable processes with load disturbance. The modified relay comprises of PI^λcontroller introduced with the ideal relay in series. The proportional gain of PI^λ controller is assumed as unity and the integral time constant is chosen such that, the system attains minimum 0° phase margin. λ of PI^λ controller helps in reducing the harmonics in the output which ultimately leads to improvement in the accuracy of the proposed scheme. The limit cycle, thus, obtained helps in extracting the critical frequency and peak amplitude which helps in controller design. The designing of PI^λD controller is based on the measured parameters from modified relay. Subsequently, the derivative time constant is derived in the design of PI^λD controller using phase margin criteria and Nyquist curve is used to obtain the proportional gain. The integral time constant for PI^λD controller is same as that of PI^λ controller for auto tuning test. The auto tuning method and PI^λD controller design, thus proposed, is validated using typical examples through simulation.