Abstract
Many studies have been conducted by researchers globally in the recent past on the control scheme to stabilize the levitated object of magnetic levitation system (MLS) at the unstable equilibrium point though very small amount of work has been reported regarding the design and tuning of fractional order controller for unstable process, especially in the presence of actuator saturation. In this paper, a novel methodology of fractional order \(PI^\lambda -PD^\mu \) controller for MLS is proposed for both stabilizing the system and removing the actuator saturation. Fractional order control facilitates an extra degree of freedom to change the order of integrator, arise a new concept to diminish the error windup during actuator saturation. The tuning of gain parameter of PID controller is done using the conventional pole placement technique, while a simple tuning method is proposed here to tune fractional parameter using stability margin and sensitivity function. Stability of the proposed controller scheme employed to MLS is analyzed on the basis of Riemann sheets concept in w-plane. To compensate for saturation due to integral term, back-calculation anti-windup scheme is used here. Experimental demonstration of proposed scheme on magnetic levitation confirms the ability of the controller to reject the external random perturbations as well as its robustness against the variation of system parameters.
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Abbreviations
- SM:
-
Sensitivity margin
- PM:
-
Phase margin
- GM:
-
Gain margin
- MLS:
-
Magnetic levitation system
- RTW:
-
Real-time workshop
- RTWT:
-
Real-time windows target
- IOPID:
-
Integer order proportional integral derivative
- AWPID:
-
Anti-windup proportional integral derivative
- FOPID:
-
Fractional order proportional integral derivative
- FOCAW:
-
Fractional order controller with anti-windup
- FOMCON:
-
Fractional order modeling and control toolbox
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Pandey, S., Dwivedi, P. & Junghare, A. Anti-windup Fractional Order \(\textit{PI}^\lambda -\textit{PD}^\mu \) Controller Design for Unstable Process: A Magnetic Levitation Study Case Under Actuator Saturation. Arab J Sci Eng 42, 5015–5029 (2017). https://doi.org/10.1007/s13369-017-2535-x
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DOI: https://doi.org/10.1007/s13369-017-2535-x