Research on the Improvement of Feedback Linearization Control in Suspension System Countering Inductance Variation

Hindawi Mathematical Problems in Engineering Volume 2019, Article ID 5747812, 11 pages https://doi.org/10.1155/2019/5747812 Research Article Research on the Improvement of Feedback Linearization Control in Suspension System Countering Inductance Variation Liwei Zhang , Yue Zhang, Chao Zhang, and He Zhao School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China Correspondence should be addressed to Liwei Zhang; Received 8 February 2019; Revised 7 May 2019; Accepted 13 June 2019; Published 1 July 2019 Academic Editor: Alessandro Contento Copyright © 2019 Liwei Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The safety of the magnetic levitation (maglev) train is closely related to the control performance of the suspension module. However, during operation, the working conditions vary and are vulnerable to the external disturbances. In this work, a large-scale variation of the inductance of the magnetic levitation operation under different air gap conditions is considered, where the transfer function of the system changes nonlinearly. On the basis of the classical feedback linearization method, the algorithm of the first-order derivative for a single equilibrium point is improved, and then a multiequilibrium point feedback linearization method subject to the variation of the inductance is derived. The proposed linearization method can decouple the inductance from the air gap dynamics in any state of levitation, thus, reducing the model error. Using a general linear controller, the closed-loop control performance of the nonlinear hybrid excitation suspension system is run in MATLAB. The simulation results show that the proposed method achieves good dynamic performance under various operating conditions and it improves the robust performance of the system. 1. Introduction For urban low-speed magnetic levitation traffic, the hybrid excitation suspension electromagnet combines the permanent magnet excitation and the electric excitation and is connected in series in the magnetic circuit to generate a control voltage with a varying amplitude and direction through the winding to realize the magnetic circuit. The electric excitation control plays a role in adjusting the magnetic flux density, changing the magnetic attraction force, and adjusting the motion state of the system. Compared with the conventional electric excitation suspension magnet system, the most significant advantage of a hybrid excitation suspension system is energy savings, and the power required to the control system is small [1]. Studying hybrid excitation suspension system has important practical significance for improving the economic benefit and practical value of magnetic suspension technology. In recent years, many scholars have conducted in-depth researches and discussions on the hybrid excitation magnetic levitation technology. Among the hybrid excitation control methods at the present, the Taylor series expansion about an equilibrium point is commonly used in the modeling approach [1–3]. However, at the positions that lie far away from the equilibrium point, especially during the course of events such as levitation and landing, the relative stability of the control system drops significantly. With the largescale application of differential geometry in electrical control theory, nonlinear control methods have emerged. References [3–6] apply the state feedback linearization to magnetic levitation systems, and the control performance is improved compared with Taylor’s linearization method. Among them, references [3, 4] use the current as the control input for being easily measured, but it does not represent the electromagnetic and dynamic changes inside the magnetic levitation system well. References [5, 6] use the air gap magnetic flux density as the internal control input that clearly describes the inherent law of the system. However, on this basis, it is necessary to install a magnetic density measuring device which is very rare in the field to form internal feedback of the system. Through the improvement of the above theoretical basis, references [7, 8] propose a feedback linearization control method based 2 on the rated operating point, which is a first-order derivative transformation process for the nonlinear system at the rated operating point. The simulation showed that the method is more robust to the uncertain systems. Based on the feedback linearization method, references [9–13] robustly optimize the controller according to system characteristics and control requirements. In the design process, the control idea fully considers the uncertainties that appear inside and outside of the system, which include the system parameter perturbation, external noise, and high frequency interference. Combining the nominal and uncertain models with the robust controllers, the design optimization can be implemented for a given class of models. Compared with only considering the nominal model, this control method improves the conservativeness in the nominal design, but the system performance can be well-preserved under the parameter perturbation. For systems that contain nonlinearities or potential bounded time-varying uncertainties, or systems that do not satisfy the global matching conditions, [9] propose an adaptive robust control method with state constraints which is suitable for the nonlinear maglev train suspension control. The method consists of a three-step state transition that converts the maglev train into an interconnected uncertainty system. And then, based on the proposed robust control of transformed system, the overall uncertainty of the adaptive law simulation system is constructed. For the classes of fractional and integer-order systems with mismatched perturbations, a sliding mode control method based on a new fractional-order disturbance observer is proposed in [10]. This method can effectively handle the mismatched disturbance between quadcopters and the magnetic suspension systems, with better control performance, faster response, and reduced overshoot and jitter. Reference [11] proposes a real-time adaptive control method suitable for large-scale mass change of magnetic levitation system. The method uses a fast internal current loop combined with adaptive control to manipulate the suspension control system, and even when the load weight varies widely, the system is still in a stable state. In order to deal with the large-scale parameter perturbation changes, [12] performs inter-partition processing on the parameters. According to the experimental method, the weight functions of each segment are optimized separately to reduce the system conservativeness. In [13], a Takagi-Sugeno (T-S) fuzzy controller based on the improved form of the piecewise Lyapunov function is used to rel (...truncated)