Stabilization of the Magnetic Levitation System

Abstract

This paper contributes toward research on the control of the magnetic levitation plant, representing a typical nonlinear unstable system that can be controlled by various methods. This paper shows two various approaches to the solution of the controller design based on different closed loop requirements. Starting from a known unstable linear plant model—the first method is based on the two-step procedure. In the first step, the transfer function of the controlled system is modified to get a stable non-oscillatory system. In the next step, the required first-order dynamic is defined and a model-based PI controller is proposed. The closed loop time constant of this first-order model-based approach can then be used as a tuning parameter. The second set of methods is based on a simplified ultra-local linear approximation of the plant dynamics by the double-integrator plus dead-time (DIPDT) model. Similar to the first method, one possible solution is to stabilize the system by a PD controller combined with a low-pass filter. To eliminate the offset, the stabilized system is supplemented by a simple static feedforward, or by a controller proposed by means of an internal model control (IMC). Another possible approach is to apply for the DIPDT model directly a stabilizing PID controller. The considered solutions are compared to the magnetic levitation system, controlled via the MATLAB/Simulink environment. It is shown that, all three controllers, with integral action, yield much slower dynamics than the stabilizing PD control, which gives one motivation to look for alternative ways of steady-state error compensation, guaranteeing faster setpoint step responses.

Performance Portrait Method: An Intelligent PID Controller Design Based on a Database of Relevant Systems Behaviors

“…In addition, when neglecting the possible control saturation by considering and taking into account that all other delays arising in the transmission and processing of information, in the actuators, filters, and sensors can be denoted as a model dead-time , the double integrator plus dead time (DIPDT) model [ 28 , 41 ] can be written as: …”

“…Here, represents a measurement, or estimate of the equivalent disturbance . Analysis of an optimal controller tuning for a DIPDT system by the triple real dominant pole method can be found in [ 41 , 43 ]. In [ 44 ], the PD controller has been proposed by modification of PI control for an IPDT system based on the relative time-delay margin.…”

“…Next, the analytical controller tuning will be based on the quadruple real dominant pole (QRDP) method [ 28 , 41 , 42 ]. If, for simplicity, we omit the index “ p ” from the parameter designation, application of the parallel PID controller ( 17 ) leads to the closed-loop transfer functions: …”

Control of the Magnetic Levitation System in Conditions of Stochastic Disturbances

“…W literaturze można znaleźć również badania wykorzystującego kilka jego wariantów: regulator PD z aproksymacją bazującą na DIPDT (ang. Double-Integrator Plus Dead-Time) [4], regulator PID połączony z regulatorem kompensacji rozmytej [14], czy połączenie PID z regulatorem ślizgowym SMC (ang. Sliding Mode Control) [22].…”

Toward Optimal Control of a Multivariable Magnetic Levitation System

“…It should be emphasized that examined methodology is of great importance in modern public transports, in particular rail transport, where the magnetic levitation process phenomenon is observed. The solution presented here is based on the EDS (electrodynamic suspension) and EMS (electromagnetic suspension) systems, so it requires a comprehensive expert supervision [8][9][10][11]. The instability and nonlinearity of multivariable plants are just some of the aspects that should be considered in the process of design of control systems.…”