In this paper, the authors propose a nonlinear model for magnetic levitation systems which is validated with experimental measurements. Using this model, a nonlinear control law based on differential geometry is firstly synthesized. Then, its real-time implementation is developed. In order to highlight the performance of the proposed control law, experimental results are given.

Modeling and nonlinear control of magnetic levitation systems

This paper focuses on the design of a real-time particle-swarm-optimization-based proportional-integral-differential (PSO-PID) control scheme for the levitated balancing and propulsive positioning of a magnetic-levitation (maglev) transportation system. The dynamic model of a maglev transportation system, including levitated electromagnets and a propulsive linear induction motor based on the concepts of mechanical geometry and motion dynamics, is first constructed. The control objective is to design a real-time PID control methodology via PSO gain selections and to directly ensure the stability of the controlled system without the requirement of strict constraints, detailed system information, and auxiliary compensated controllers despite the existence of uncertainties. The effectiveness of the proposed PSO-PID control scheme for the maglev transportation system is verified by numerical simulations and experimental results, and its superiority is indicated in comparison with PSO-PID in previous literature and conventional sliding-mode (SM) control strategies. With the proposed PSO-PID control scheme, the controlled maglev transportation system possesses the advantages of favorable control performance without chattering phenomena in SM control and robustness to uncertainties superior to fixed-gain PSO-PID control.

https://www.et.ntust.edu.tw/et/research/wlc20151009213152.pdf

Real-Time PID Control Strategy for Maglev Transportation System via Particle Swarm Optimization

Sliding mode control schemes of the static and dynamic types are proposed for the control of a magnetic levitation system. The proposed controllers guarantee the asymptotic regulation of the statesof the system to their desired values. Simulation results of the proposed controllers are given to illustrate the effectiveness of them. Robustness of the control schemes to changes in the parameters of the system is also investigated.

https://downloads.hindawi.com/journals/mpe/2004/657503.pdf

Sliding mode control of a magnetic levitation system

A feedback linearization controller is presented for a single-degree-of-freedom (DOF) magnetic bearing test rig. The feedback linearization controller is derived from a detailed nonlinear electromagnet model using both analytic relationships and experimental calibration data. The controller is implemented on the test rig in voltage mode, and measured open-loop transfer functions are used to demonstrate the effectiveness of the feedback linearization controller in transforming the nonlinear system to a linear plant. Next, a high-performance controller for the feedback linearized plant is designed with /spl mu/-synthesis to guarantee a beam compliance performance specification. A common problem associated with voltage control in magnetic suspensions and coil resistance variation, is successfully handled by augmenting the feedback linearized plant with a structured uncertainty. Experimental results demonstrate that the /spl mu/ controller with feedback linearization achieves the performance specified during design for the nonlinear plant independent of the disturbance force level or displacement incurred.

Feedback linearization of an active magnetic bearing with voltage control

Vibration control of maglev vehicles traveling over a flexible guideway

In many applications, magnetic suspension systems are required to operate over large variations in air gap. As a result, the nonlinearities inherent in most types of suspensions have a significant impact on performance. Specifically, it may be difficult to design a linear controller which gives satisfactory performance, stability, and disturbance rejection over a wide range of operating points. One way to address this problem is through the use of nonlinear control techniques such as feedback linearization. For most common designs of magnetic suspensions the governing equations are in the so-called companion form, lending themselves to feedback linearization. A single degree of freedom magnetic suspension has been designed and constructed in order to compare the performance of linear and nonlinear digital control schemes in a well-controlled experimental environment. We demonstrate the superiority of nonlinear controllers over conventional controllers for systems with large variations in operating point via experiments on our system.

Linearizing control of magnetic suspension systems

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Linearizing control of magnetic suspension systems