Generalised Proportional Integral Control for Magnetic Levitation Systems Using a Tangent Linearisation Approach

Abstract

This paper applies a robust generalised proportional integral (GPI) controller to address the problems of stabilisation and position tracking in voltage-controlled magnetic levitation systems, with consideration of the system’s physical parameters, non-linearities and exogenous disturbance signals. The controller has been developed using as a basis a model of the tangent linearised system around an arbitrary unstable equilibrium point. Since the approximate linearised system is differentially flat, it is therefore controllable. This flatness gives the resulting linearised system a relevant cascade characteristic, thus allowing simplification of the control scheme design. The performance of the proposed GPI controller has been analysed by means of numerical simulations and compared with two controllers: (i) a standard proportional integral derivative (PID) control, and (ii) a previously designed exact feedforward-GPI controller. Simulation results show that the proposed GPI control has a better dynamic response than the other two controllers, along with a better performance in terms of the integral squared tracking error (ISE), the integral absolute tracking error (IAE), and the integral time absolute tracking error (ITAE). Finally, experimental results have been included to illustrate the effectiveness of the proposed controller in terms of position stabilisation and tracking performance when appreciable non-linearities and uncertainties exist in the underlying system. Comparative graphs and metrics have shown a superior performance of the proposed GPI scheme to control the magnetic levitation platform.

Design a Robust Optimal Proportional-Integral-Derivative Controller for CE152 Magnetic Levitation System Using Bee Colony Algorithm

“…Suppose that the equilibrium point at (𝑥 10 , 𝑥 20 , 𝑥 30 ) then, 𝑥 20 = 0 and 𝑥 30 = (𝑥 10 − 𝑥 0 ) √ 𝑔 𝐴 1 [2]. A first-order approximation of the Taylor series expansion near the unstable equilibrium point (𝑥 10 , 𝑥 20 , 𝑥 30 ) will be used to linearize equation ( 23) [21,22]. The following nonlinear differential equations can be used to represent the dynamic behavior of the magnetic levitation system in equation (23).…”