2016 International Conference on Control, Instrumentation, Communication and Computational Technologies (ICCICCT)
Feedback Linearization based Optimal Controller Design for Electromagnetic Levitation System Ravi V.Gandhi
Dipak M.Adhyaru
Ph.D Scholar, Instrumentation & Control Department Institute of Technology, Nirma University Ahmedabad, India
[email protected]
Head, Instrumentation & Control Department Institute of Technology, Nirma University Ahmedabad, India
[email protected]
Abstract— This paper presents the analysis of feedback linearization based optimal controller design for ElectroMagnetic Levitation (EML) system, which is a class of nonlinear and unstable system. Using feedback linearization method, nonlinear model is first converted into controllable linearized model in large operating range under certain conditions. Using linearized model, optimal controller is designed for stabilizing and tracking control of EML system. Feedback linearization based optimal controller shows kind of smooth, stabilizing and tracking response under different trajectories and bounded load variations due to variation of parameters. Simulation results and conditions under which mentioned approach is applicable are presented to validate the contribution in the paper. Keywords— Electromagnetic Levitation System, Optimal Control, Feedback linearization, Nonlinear control, Stabilizing control, Tracking control, Stability analysis.
I.
INTRODUCTION
Now a day, demand and need of mass transportation is on the peak, there should be the availability of such kind of mass transportation system which should be convenient, environment-friendly, low maintenance, compact, light-weight, frictionless. Magnetic levitation (Maglev) train is one of the potential candidates to satisfy those requirements [12] which work as per the principle of Electromagnetic Suspension (EMS) system. Development of such maglev system was first patented in 1934 by Hermann Kemper of Germany [1, 4, 12]. Prof. E. R. Laithwaite in 1965 described levitation and different mechanism related to magnetic levitation in [1]. In, 1960’s maglev system became the favorite topic of research. Maglev phenomena using RLC based tuned circuits with detailed analysis of stability were described in [2, 3, 4]. Transfer function model for maglev system using perturbation method as changes in control voltage to changes in airgap was developed by Henn in [3], to analyze the effect of parameters variations. Applications, control algorithms, types with different structures, guidance, levitation, propulsion and working of maglev trains were reviewed very well in [5, 12]. Wong in 1986, proposed laboratory based small setup of linearized maglev system to stabilize spherical ball near desired position using lead compensator [6]. Dynamics of a maglev system are usually unstable and complicated [22]. Linearized model developed around operating conditions does not work properly under disturbance variations, large operating range, model and parameter uncertainty [7, 8, 9]. In the mid of 1990’s, nonlinear feedback controllers for maglev systems were developed by researches to avoid difficulties of linearized models. Robustness for maglev system can be achieved using exact feedback linearization approach proposed in [7].
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In addition to above work, vertical velocity for spherical ball was estimated using nonlinear state observer [8, 15, 25]. Digital implementation of feedback linearization based nonlinear control for airgap control with dual electromagnets for maglev system was proposed in [9]. Hall effect based position sensor with dual magnets enhances the stability of maglev system with 2-DOF control [25, 27]. Sinha in [10], proposed DSP based adaptive full state feedback control (SFC) for maglev system using stable maximum descent criterion. Mathematical modeling of maglev system on the basis differential geometry and real time nonlinear control based on feedback linearization with force-distance characteristics estimation were designed in [11]. Henly [13], proposed extended Kalman-filter based feedback linearization method for maglev system in his thesis. Coupling effect of guideway and maglev affects the levitation; nonlinear feedback linearization based controllers were developed in [14] to reduce the coupling effect on maglev. Torres and his team [16] developed zero order Takagi-Sugeno based nonlinear controller with feedback linearization method to enhance the overall stability of maglev system. Fuzzy logic based controller algorithm with feedback linearization method to control guided elevator based on maglev concept was designed in [17, 18]. In, [24] Type-1, Type-2 based fuzzy PID controllers were designed for magnetic levitation system. Modeling and exact input-output based feedback linearization for maglev system was designed using simulation in [19, 22]. Stabilizing and sinusoidal trajectory tracking control based on feedback linearization method was presented in [20]. Optimal PID controller for trajectory tracking for maglev system was presented in [23]. II.
MATHEMATICAL MODEL
In this section, nonlinear mathematical model for EML system is presented with Schematic diagram as shown in fig. 1 [23],
Figure 1. Schematic of EML system
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