Decoupling Control Design for the Module Suspension Control System in Maglev Train

Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 865650, 13 pages http://dx.doi.org/10.1155/2015/865650 Research Article Decoupling Control Design for the Module Suspension Control System in Maglev Train Guang He, Jie Li, and Peng Cui College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha 410073, China Correspondence should be addressed to Jie Li; Received 26 August 2014; Revised 11 December 2014; Accepted 26 December 2014 Academic Editor: Dan Ye Copyright © 2015 Guang He 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. An engineering oriented decoupling control method for the module suspension system is proposed to solve the coupling issues of the two levitation units of the module in magnetic levitation (maglev) train. According to the format of the system transfer matrix, a modified adjoint transfer matrix based decoupler is designed. Then, a compensated controller is obtained in the light of a desired close loop system performance. Optimization between the performance index and robustness index is also carried out to determine the controller parameters. However, due to the high orders and complexity of the obtained resultant controller, model reduction method is adopted to get a simplified controller with PID structure. Considering the modeling errors of the module suspension system as the uncertainties, experiments have been performed to obtain the weighting function of the system uncertainties. By using this, the robust stability of the decoupled module suspension control system is checked. Finally, the effectiveness of the proposed decoupling design method is validated by simulations and physical experiments. The results illustrate that the presented decoupling design can result in a satisfactory decoupling and better dynamic performance, especially promoting the reliability of the suspension control system in practical engineering application. 1. Introduction As an urban track transportation vehicle with large application prospect, low speed maglev trains have been developed for almost 30 years [1, 2] and there have already been several commercial operation lines or test lines [3– 8]. Maglev train utilizes suspension controllers to adjust the electromagnetic forces between the electromagnets and the track for stable levitation. Hence, the electromagnetic suspension control system is the most pivotal component of the maglev train, which attracts tremendous attention [9–12]. As of today, the stability problem of the suspension control system has been basically solved. The major work on suspension control is excepted be transferred to the performance promotion and the practical problem existing in engineering applications. On the basis of the mechanical decoupling in bogie, levitation modules can be considered as the foundational elements of the low speed maglev train. At present, the main existing suspension control methods decompose the module into two single-suspension-control units. However, due to the physical stiffness structure of levitation module, direct coupling between the two singlesuspension-control units will attenuate disturbance rejection capability of the levitation control system and also becomes a serious obstacle to the performance promotion. To some extent, the adjustment of one levitation unit may destabilize the whole module suspension system. Therefore, it is essential to develop some decoupling control strategy for the module suspension control system. By viewing the module as an integrated object, the suspension control system is a two-input-two-output (TITO) control system. The engineering oriented research on the decoupling control of the module suspension system has rarely been reported. Fortunately, considerable efforts have already been devoted to the decoupling control of the multiple-input-multiple-output (MIMO) system for several decades. Different control strategies have been developed to overcome the complicated couplings between control loops, such as inverse Nyquist array [13], internal model control [14], inverse based decoupling control [15], and other decoupler based methods. Those methods can allow parameter perturbation and uncertainties in system model with robust 2 requirement, which benefits the decoupling design of the module suspension system. Besides, although the differential geometry technique is also a feasible approach to deal with the multivariable decoupling control problems [16, 17], their need for precise mathematical model is an obstacle to apply it to practical engineering. The general decoupling control approach is to design the decoupler so that the MIMO control system can be treated as multiple single-input-single-output (SISO) loops, which allows us to use well developed single loop controller design methods. Many decoupling control design methods are developed based on this view as well [18– 22]. The ideal decoupler is to be designed as the inverse of the transfer function matrix. However, this kind of decoupler needs to calculate the inverse of the process transfer function matrix resulting in too complicated calculation. Shen et al. considered the adjoint transfer matrix of the original multivariable system as the decoupler [23], where it can avoid complicated computation, especially for TITO system. In this paper, a modified adjoint transfer matrix based decoupler was presented. First, the existing coupling in the module suspension control system is analyzed and the dynamic model is also given. By adopting the modified adjoint transfer matrix as the decoupler, we divide the module suspension control system into two independent SISO control systems. Then, compensated controllers are designed to meet the desired loop performance and robustness demand of the module suspension control system. The formulation of a resultant decoupling controller is obtained by combing the decoupler and the compensated controller. Multivariable PID structure controller is the most effective technology in engineering applications because of adequate performance with simple structure [18, 19, 24, 25], which is also adopted in our practical CMS04 low speed maglev train. Hence, the resultant decoupling controller is transformed to PID type controller by model reduction. Given the parameters uncertainties and nonlinear characteristic in the magnetic suspension system, the modeling errors between the linearized model and practical physical model have been taken into account. The modeling errors are measured by frequency sweeping experiments on a real full-scale single bogie of CMS-04 maglev train, based on which the robust stability of the decoupled module suspension control system is validated. Furthermore, simulations and experimental results show that the p (...truncated)