Fuzzy sliding control with non-linear observer for magnetic levitation systems

Magnetic levitation (Maglev) systems make significant contribution to industrial applications due their reduced power consumption, increased power efficiency and reduced cost of maintenance. Common applications include Maglev power generation (e.g. wind turbine), Maglev trains and medical devices (e.g. magnetically suspended artificial heart pump). This paper proposes fuzzy sliding-mode controller `FSMC' with a nonlinear observer been used to estimate the unmeasured states. Simulations are performed with nonlinear mathematical model of the Maglev system, and the results show that the proposed observer and control strategy perform well.


I. INTRODUCTION
Magnetically levitated train constitutes one of the significant advance made due to Maglev Experimental results of Maglev (VAWT) in [1] show that system vibration can be reduced by 37.5%, and power generating capability of the system is increased by 12% using Maglev concept. A combination of sliding mode control (SMC) with fuzzy logic is used in this work as, it is difficult to prove the stability of fuzzy logic controller (FSMC). Moreover, SMC is insensitive to external disturbance and to parametervariations, and able to decouple systems high-dimensionalsystem into lowerdimensional sub-systems. This feature canhelp reduce the size of rule base of an FLC. Finally thiscombination can effectively alleviate the prevalent chatteringproblem of SMC [2].Slidingmode control is used in [3] to control the linearized magnetic ball levitation system over a fixed set of operating points using singular perturbation method. In this paper two kinds of traditional fuzzy sliding-mode control (FSMC) are first introduced, based on calculation of the control action using error / change of error e/ ˙e in the first instance and secondly the sliding function S. Then a novel fuzzy sliding mode control (NFSMC) is proposed in which the fuzzy natural control is calculated using sliding function with integration of an adjustable gain.
The simulation results show the superior performance can be achieved to the NFSMC in comparison to the traditional FSMC.
A modified dynamic sliding-mode control has been reported in [4]

MAGLEV SYSTEM
The Maglev system consider here serves to keep a small steel ball in stable levitation at some steady-state operating position. An electromagnet is used to produce forces to support the ball (see Fig. 1). The electromagnetic forces are related to the electrical current passing through the electromagnet coil; where fem is the electromagnetic forces, L is the additional inductance, x0 is an arbitrary of the object and i is the coil current. The object is suspended by balancing between the force of gravity and electromagnetic force.
Applying Newtons 3 rd law of motion, the dynamic form of the mechanical system can be written as The nonlinear state space model of Maglev system can be expressed as

III. SLIDING-MODE CONTROL
The state variables for the magnetic ball Considering the fuzzy input and output, the rules-base to produce the desired natural control can be set up as in Table I  To design an optimal controller based on state feedback for such a nonlinear system; all states need to be measured or estimated.
The object position can be measured by an appropriate sensor and coil current. The velocity measurement, however, is not Verification of this kind of observer is considered as a difficult task as it requires that the right side of equation (3) should ascertain the global Lipschitz condition. For this reason this type of observer is considered only as local stable observer, which means that the estimation error dynamics of equation (17) should have a finite escape time (observer error converges to zero within a finite time). Thus in this paper the gains G were constructed in such a way, that the observer dynamics (High-Gain Observer HGO) are much faster than the system dynamics (at least five-times). The estimated states which are obtained from the nonlinear observer are used to implement the control law of the exact linearizing controller (see Fig. 4).

VI. SIMULATION RESULTS
A block diagram representation of active magnetic levitation with the proposed controller is shown in Fig. 3. Step responses of the magnetic ball system with these two controllers are shown in Figures 7-10 in presence of different percentage mass uncertainties. Figures 11 and 12 show the control efforts of SMC and FSMC with mass percentages of 80% and 120% respectively.
As it can FSMC delivered a smooth the control signal and overcome the phenomena of chartering.

VII. CONCLUSION
A nonlinear full-order observer-based controller with fuzzy sliding-mode controller has been proposed FSMC to stabilise an active magnetic levitation system. The