DESIGN OF FRACTIONAL ORDER PID CONTROLLER FOR SELECTED TYPE OF SYSTEMS

Abstract

Fractional order calculus is a natural generalization of integer order calculus having the orders of the differential and integral operations as non-integers, which could be real as well as complex numbers. Over the past few decades, the concepts of fractional calculus have been integrated into various academic disciplines especially control systems branch of electrical engineering. In this work, an attempt has been made to explore and formulate two widely different control techniques, namely fractional order internal model control (FOIMC) and active disturbance rejection control (ADRC) approach. The proposed fractional order IMC scheme incorporates the concept of CRONE principle and fractional order filter to formulate a fractional order PID controller, that can be expressed as a series combination of integer or fractional order PID controller and fractional order low pass filter. To further enhance the control performance, a novel scheme namely active disturbance rejection control technique is extended to fractional and integer order time delayed systems. The mathematical formulae for the proposed fractional order ADRC are derived for a generalized time delayed fractional order system for the first time in this thesis. The proposed fractional order active disturbance rejection control(FOADRC) uses a limited plant information, i.e. high frequency gain and the relative order and treats everything else as a generalized disturbance. It incorporates an extended state observer (ESO) to measure the states of the plant as well as the disturbance and subsequently designs a control law that can effectively reject the disturbance and ensure an efficient set point tracking. Further, the proposed FOADRC has an added advantage that it does not require any approximation of time delayed term, which is traditionally adopted for PID based control techniques. ADRC inherits the quality of PID like error driven control law, easy to tune with extra advantages of handling capability of nonlinear disturbance, tracking error, noise degradation in derivative control. .To demonstrate the superiority and effectiveness of the proposed FOIMC and FOADRC scheme, four different numerical examples have been taken from the literature. An extensive qualitative and quantitative comparison has been undertaken in time domain. The robustness of the proposed design criteria is verified via the scrutiny of system response upon perturbation of system parameters. The simulation results indicate the strength and efficacy of the proposed control scheme.