The Active Fractional Order Control for Maglev Suspension System

Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 129129, 8 pages http://dx.doi.org/10.1155/2015/129129 Research Article The Active Fractional Order Control for Maglev Suspension System Peichang Yu, Jie Li, and Jinhui Li College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha 410073, China Correspondence should be addressed to Jie Li; Received 22 October 2014; Revised 4 March 2015; Accepted 5 March 2015 Academic Editor: Andrzej Swierniak Copyright © 2015 Peichang Yu 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. Maglev suspension system is the core part of maglev train. In the practical application, the load uncertainties, inherent nonlinearity, and misalignment between sensors and actuators are the main issues that should be solved carefully. In order to design a suitable controller, the attention is paid to the fractional order controller. Firstly, the mathematical model of a single electromagnetic suspension unit is derived. Then, considering the limitation of the traditional PD controller adaptation, the fractional order controller is developed to obtain more excellent suspension specifications and robust performance. In reality, the nonlinearity affects the structure and the precision of the model after linearization, which will degrade the dynamic performance. So, a fractional order controller is addressed to eliminate the disturbance by adjusting the parameters which are added by the fractional order controller. Furthermore, the controller based on LQR is employed to compare with the fractional order controller. Finally, the performance of them is discussed by simulation. The results illustrated the validity of the fractional order controller. 1. Introduction The developing of maglev train is under a rapid speed around the world. Thanks to no physic contact with guide-way, the maglev system gets the advantage of lower noise, less costly maintenance, less exhaust fumes emission, and so on, which is suitable for the urban transportation. Until now, two commercial maglev routes and several test routes have been built around the world. Suspension control is one of the core technologies in maglev train [1, 2]. The practical model of suspension system is a nonlinear and inherent unstable system due to the fact that the electromagnetic force produced by a constant current is inversely proportional to the square of the levitation gap. Besides, the parameters of the levitation system are varying with the difference of the operating condition. So, it is hard to choose a practicable control strategy to design an ideal controller that can keep satisfied dynamic performance when the train is running under the actual environment. Considering the complicated working situation, many researchers have investigated many new controllers with different theories for the maglev suspension system such as adaptive control [3], nonlinear control [4], fuzzy control [5], and robust control [6]. The quick development of fractional calculus attracts extensive attentions due to its nonlinear feature and unique memory characteristic. In electricity, properties between resistance and capacitance are intermediated by a concept of fractance [7]. Fractional calculus has been applied in the modeling and control of various kinds of physical systems and many real systems are modeled or fitted by fractional order systems. So, in recent years, with the progress of fractional order integral theory, many papers have discussed the design and application of controller design based on fractional order theory. Fractional order 𝑃𝐷 controller attracts increasing attention because of the higher freedom degree provided [8–11]. In paper [8] a 𝑇𝐼𝐷 controller is proposed; this control scheme can improve the robustness of system against disturbances. In paper [9], Oustaloup discussed the 𝐶𝑅𝑂𝑁𝐸 controller. In paper [12], Podlubny focused on the 𝑃𝐼𝜆 𝐷𝜇 controller; this method is the milestone of the 𝐹𝑂𝐶; it increased two parameters for the controller, so, with the 𝑃𝐼𝜆 𝐷𝜇 controller, the system can get desired performance. Since then, many works have been done to apply these new methods to different nonlinear systems. 2 Mathematical Problems in Engineering Cabin Spring Guide-way Unit 1 Unit 2 Module 1 Module 2 Module 3 Absolute reference h(t) z(t) Figure 1: Side view of CMS04. Guide-way 𝛿(t) F(i, 𝛿) Magnet Position sensor i(t) 𝛿(t) (t) Accelerometer ̈ z(t) Figure 2: Electromagnet-track configuration of a single unit. The maglev train, as a typical nonlinear system, is an ideal model for fractional order controller design. This essay paid attention to discussing the usage of fractional order control theory and application of the 𝑃𝐷𝜇 controller on solving the system inherent nonlinearity and parameters uncertain problems of the suspension system. The rest of the paper is organized as follows. The mathematical model of the basic maglev suspension system is developed in Section 2. In Section 3, the design theory and procedure of 𝑃𝐷𝜇 controller based on the simplified model are discussed. In Section 4, simulation is proposed, and we compared the performance with controller based on 𝐿𝑄𝑅. Finally, conclusions are presented in Section 5. The fundamental principle of the electromagnet suspension system (shown in Figure 2) is described as the following: according to the desired suspension gap and status information gotten by position sensor and accelerometer, the controller adjusts the current supply so that the suspension system can produce suitable force 𝐹 that can overcome the gravitation and keep the system stable in the expected operating position. A single electromagnet suspension unit can be simplified as shown in Figure 2. In Figure 2, 𝑚 is the total mass of suspension system. 𝑁 denotes the number of turns of a single electromagnet. 𝐴 is the area of the magnetic pole. 𝑅 is the magnetic resistance. 𝜇0 is the magnetic permeability of atmosphere. 𝑔 is the gravity acceleration. The magnetic inductance is defined as 𝐿. 𝐹 is the force produced by electromagnetic for suspension. 𝛿 is the measured position value from position sensor. 𝑧̈ means the value of measured acceleration from accelerometers. The voltage supplied to magnetic suspension system is expressed by V. The symbol 𝑖 is the current of magnetic suspension system. 𝐵 is the flux density of the gap. 𝑓𝑑 (𝑡) is the disturbance of the load. There are three main relations in the suspension system; there are voltage (V) to current (𝑖), acceleration (𝑧)̈ to electromagnetic force (𝐹), and current (𝑖) to electromagnetic force (𝐹). Based on the electromagnetic theory and dynamics analysis of electromagnet [1], the following equations can be built: V (𝑡) = 𝑅𝑖 (𝑡) + 𝑚𝑧̈ (𝑡) = 𝑚𝑔 − 𝐹 (𝑡, 𝛿) + 𝑓 (𝑡 (...truncated)