Linearization Method of Nonlinear Magnetic Levitation System

Abstract

Linearized model of the system is often used in control design. It is generally believed that we can obtain the linearized model as long as the Taylor expansion method is used for the nonlinear model. This paper points out that the Taylor expansion method is only applicable to the linearization of the original nonlinear function. If the Taylor expansion is used for the derived nonlinear equation, wrong results are often obtained. Taking the linearization model of the maglev system as an example, it is shown that the linearization should be carried out with the process of equation derivation. The model is verified by nonlinear system simulation in Simulink. The method in this paper is helpful to write the linearized equation of the control system correctly.

Discrete-Time Pole-Region Robust Controller for Magnetic Levitation Plant

“…In this section we design the state feedback robust controller by solving LMI (15) and (17) for the AE region defined by matrices ( 7)-( 9), adding the stability degree requirement. We systematically changed the AE design parameters: The evaluation of the corresponding closed-loop performance of the real plant for changing design parameters is presented and the respective step responses are compared.…”

“…Magnetic levitation belongs to challenging plants to control, due to its nonlinearity, instability and fast dynamics, with broad application area. Many authors devoted their research to modeling and control of a magnetic levitation system, [17][18][19][20][21][22][23][24]. In [17,21], a linearized model of magnetic levitation is derived based on first principles, the former uses Jacobian linearization, while the latter applies a general linearization technique.…”

“…Many authors devoted their research to modeling and control of a magnetic levitation system, [17][18][19][20][21][22][23][24]. In [17,21], a linearized model of magnetic levitation is derived based on first principles, the former uses Jacobian linearization, while the latter applies a general linearization technique. Various continuous-time control schemes for magnetic levitation can be found, for example, feedback linearization approach in [18], CDM based design in [19], adaptive state feedback [20]; in all these papers, the results were verified by simulation.…”

Sliding Mode Control Design for Magnetic Levitation System

“…Besides, a linear controller, such as PID and FOPID, needs a linear model, although it is plausible to be obtained from a linearization [30]- [38]. Another controller that needs the system to be modeled in a linear one is the widely known state feedback [39]- [42]. Meanwhile, a controller based on fuzzy logic control is not easy to design [43], needs practical data reference or additional knowledge from other controllers [44] and requires high computation to run the fuzzy [45].…”

Development of a new linearizing controller using Lyapunov stability theory and model reference control

“…The efficient control of a Maglev system can reduce the operating cost, fuel economy, driving range and performance in various industries [9], [10]. One of the most efficient methods to stabilize and ensure robustness of the Maglev system is the linearization technique [11]- [13]. The linearization method draws deductions about the local stability of a nonlinear system around an operating point from the stability characteristics of the system's linear estimation.…”