Fractional PIλD Controller Design for a Magnetic Levitation System

Abstract

Currently, there are no formalized methods for tuning non-integer order controllers. This is due to the fact that implementing these systems requires using an approximation of the non-integer order terms. The Oustaloup approximation method of the sα fractional derivative is intuitive and widely adopted in the design of fractional-order PIλD controllers. It requires special considerations for real-time implementations as it is prone to numerical instability. In this paper, for design and tuning of fractional regulators, we propose two methods.The first method relies on Nyquist stability criterion and stability margins. We base the second on parametric optimization via Simulated Annealing of multiple performance indicators. We illustrate our methods with a case study of the PIλD controller for the Magnetic Levitation System. We illustrate our methods’ efficiency with both simulations and experimental verification in both nominal and disturbed operation.

Tuning rules: Graphical analysis and experimental validation of a simplified fractional order controller for a class of open‐loop unstable systems

“…The applicability of the proposed method is shown by the experimental results of the two well-known test bench setups: one is rotary inverted pendulum (ROTPEN), and another is the magnetic levitation system (MAGLEV). Number of controllers based on the FO control [9,11,12,14,15] and some other nonlinear control methods [37][38][39] have been reported in the literature for the nonlinear system, and for comparison purpose, the sliding mode controller (SMC) has been taken in account to validate the superiority of proposed FO controller tuning.…”

“…KEYWORDS fractional order controller, MAGLEV, ROTPEN, tuning Abbreviations: ROTPEN, Rotary inverted pendulum; MAGLEV, Magnetic levitation system; PM, Phase margin of the system under consideration; GM, Gain margin of the system under consideration; GCF, Gain crossover frequency of the system under consideration; SMC, Sliding mode controller; FOMCON, Fractional order modeling and control toolbox; FOPID, Fractional order PID controller; k p , Proportional controller gain; k i , Integral controller gain; k d , Derivative controller gain; , Order of fractional integrator; , Order of fractional differentiator; q 1 and q 2 , Feed forward controller gain parameters.of many scholars in the previous years from academic as well as the industry. Fractional order (FO) controller has been studied, tested, and successfully implemented on the experimental setups such as the inverted pendulum, magnetic levitation system, manipulators, direct current (DC) motors, oscillators, and other electrical circuits [2,4,[8][9][10][11][12][13][14][15][16][17]. It has been validated in the abovementioned…”

“…of many scholars in the previous years from academic as well as the industry. Fractional order (FO) controller has been studied, tested, and successfully implemented on the experimental setups such as the inverted pendulum, magnetic levitation system, manipulators, direct current (DC) motors, oscillators, and other electrical circuits [2,4,[8][9][10][11][12][13][14][15][16][17]. It has been validated in the abovementioned…”

Design of Low-Voltage FO-[PD] Controller for Motion Systems

“…where λ, µ ∈ R provide the controller with two extra degrees of freedom and thereby, with a better adjustment of its characteristics [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

“…Studies over the past few decades have provided important information on the way in which variations of the FO-PID controller contribute to the development of the industry of motion-control systems [18][19][20][21][22][23]. On the basis of values of λ, µ, the main subcategories of FO-PID controllers, employed towards this purpose, are summarized in Table 1.…”