Sliding Mode Control of Magnetic Levitation System using Nonlinear Time-Varying Sliding Surface Chintu. Gurbani, Dr.Vijay. Kumar, and Anupam. Kumar Abstract - A new sliding surface design approach for magnetic levitation system is proposed that varies the sliding surface in a nonlinear and time-varying fashion. The control law is designed by using the surface that is defined in a new co-ordinate axis. The nonlinear surface is then moved in a proper direction by using a time- varying function. Simulations have been performed on a second- order nonlinear model of a magnetic levitation system. The result of the new design method is compared with the classical sliding mode controller possessing a discretely moving sliding surface. From the results we can conclude that the reaching time has considerably reduced and robustness to disturbance has increased. Also the phase plane portrait has much smoother trajectories. Keywords--- Magnetic levitation system, nonlinear time varying sliding surface, sliding mode control, sliding surface design I. INTRODUCTION AGNETIC levitation systems (MLS) have realistic importance in many engineering systems such as in high-speed maglev trains, frictionless bearings, levitation of wind tunnel models, and vibration isolation of sensitive machinery, levitation of molten metal in induction furnaces, and levitation of metal slabs during manufacturing. The maglev systems can be classified as attractive systems or repulsive systems based on the source of levitation forces. These systems are usually open-loop unstable and are described by highly nonlinear differential equations which present additional difficulties in controlling these systems. This unstable aspect of MLS and its inherent nonlinearities make the modeling and control problems very challenging. Therefore, it is an important task to construct high- performance feedback controllers for regulating the position of the levitated object. During the last 20 years, sliding mode control (SMC) has received significant interest and has become well-established research areas for practical applications. The discontinuous nature of the control law in SMC results in outstanding robust- Chintu. Gurbani, Electronics and Comm. Dept. Indian Institute of Technology,Roorkee,Uttarakhand,India(e-mail :[email protected]). Dr.Vijay Kumar, Electronics and Comm. Dept. Indian Institute of Technology, Roorkee, Uttarakhand, India (e-mail: [email protected]). Anupam Kumar, Electronics and Comm. Dept. Indian Institute of Technology, Roorkee, Uttarakhand, India (e-mail:[email protected]). -ness features for both system stabilization and output tracking problems. The good performance also includes insensitivity to parameter variations and rejection of disturbances. SMC has been applied in many control fields which include robot control, motor control, flight control, control of power systems, and process control. The first application of SMC to magnetic levitation systems was carried out by Cho et al [3]. It was shown that a sliding mode controller provides a better transient response than classical controllers. However, current dynamics was neglected in their model and limited the ball’s motion to a range of 1 mm. Chen et al [2] designed an adaptive sliding mode controller for a rather different type of magnetic levitation system called dual-axis maglev positioning system. Buckner [1] introduced a procedure for estimating the uncertainty bounds using artificial neural network and then applied it to SMC of a magnetic levitation system. Hassan and Mohamed [4] used the reaching law method complemented with the sliding mode equivalence technique to design a variable structure controller for the magnetic levitation system. The main steps of designing a SMC are mainly 1) Determining sliding surface that governs the system dynamics 2) A control law that makes state trajectories approaches the sliding surface. The phase trajectories of an SMC represent two modes of the system [7]. The trajectories starting from a given initial condition off the sliding surface moves towards the sliding surface. This is known as reaching phase, and the system is sensitive to parameter variations in this part of the phase trajectory [6]. When the convergence to the sliding surface take places, the sliding phase starts. In this phase, the trajectories are insensitive to parameter variations and disturbances. [8]. To improve the performance of SMC, two well known sliding surface design methods are used. They are 1) Time varying scheme for constant linear sliding surface 2) Non-linear sliding surface In time varying scheme, sliding surface is shifted and rotated in the state space to improve the tracking problem. This design method is easy but may have performance disadvantages with respect to nonlinear methods. The magnitude of control law required to keep the states on the sliding surface usually increases as the magnitude of the tracking error increases. Thus we need different dynamic M 3rd International Conference on Computational Techniques and Artificial Intelligence (ICCTAI'2014) Feb. 11-12, 2014 Singapore 83
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Sliding Mode Control of Magnetic Levitation
System using Nonlinear Time-Varying
Sliding Surface
Chintu. Gurbani, Dr.Vijay. Kumar, and Anupam. Kumar
Abstract - A new sliding surface design approach for magnetic
levitation system is proposed that varies the sliding surface in a
nonlinear and time-varying fashion. The control law is designed by
using the surface that is defined in a new co-ordinate axis. The
nonlinear surface is then moved in a proper direction by using a time-
varying function. Simulations have been performed on a second-
order nonlinear model of a magnetic levitation system. The result of
the new design method is compared with the classical sliding mode
controller possessing a discretely moving sliding surface. From the
results we can conclude that the reaching time has considerably
reduced and robustness to disturbance has increased. Also the phase
plane portrait has much smoother trajectories.
Keywords--- Magnetic levitation system, nonlinear time varying