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

TL;DR: This paper proposes fuzzy sliding-mode controller `FSMC' with a nonlinear observer been used to estimate the unmeasured states of the Maglev system and results show that the proposed observer and control strategy perform well.

Abstract: 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.

## Summary (2 min read)

### Introduction

- Magnetically levitated train constitutes one of the significant advance made due to Maglev technologies.
- This feature can help reduce the size of rule base of an FLC.
- A modified dynamic sliding-mode control has been reported in [4] to overcome the chattering problem of SMC, where the proposed controller is used to stabilize the dynamic of Maglev system in the new coordinates using feedback linearisation control.
- The results show that the modified dynamic SMC can provide smoother control action compared to classic dynamic SMC and up to 25% more robustness to parameter variations.

### II. NONLINEAR DYNAMIC MODEL OF 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 object is suspended by balancing between the force of gravity and electromagnetic force.

### III. SLIDING-MODE CONTROL

- For a 3rd order system, the time varying surface σ(t) can be defined as σ(t) = ( d dt + s )3−1 E (7) where s is strictly positive constant and indicates the slope of sliding surface.
- The general form of the control law for the sliding mode controller can be written as u = ueq + un (10) where ueq and un are the equivalent control and natural control receptively.
- The equivalent control is augmented by auxiliary control effort termed as hitting the sliding surface and determined as ueq = −(S ĝ(x))−1S f̂(x, t) (12).
- The natural control is used to maintain the status trajectory on sliding surfaces using signum function which requires infinite switching on the part of actuator and the control signal, and this is expressed [7] as un = −K(S ĝ(x))−1sign(σ) (13).

### V. NONLINEAR OBSERVER DESIGN FOR MLS

- The object position can be measured by an appropriate sensor and coil current.
- The velocity measurement, however, is not straight forward.
- The difficulties associated with unmeasured states can be solved through a state estimation process.
- 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).

### VI. SIMULATION RESULTS

- A block diagram representation of active magnetic levitation with the proposed controller is shown in Fig.
- Moreover, FSMC generated much smoother control signal than SMC as shown in Fig. 6 Table II explores the effect of uncertainty in the mass of object in the system with set-point of 15 mm, as the mass was decreased to the limit of 70% and increased up to around 255%.
- It is noted that FSMC achieved the minimum Integral Absolute Error (IAE) as well as minimum Mean Square Error (MSE).
- 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.

### 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 results show that the generated control signals using FSMC are much smoother than those with SMC, and this has improved the regulation and quality of control provided by FSMC with nonlinear observer.

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##### Citations

12 citations

### Cites methods from "Fuzzy sliding control with non-line..."

...[16] presented a fuzzy sliding mode controller with a nonlinear observer for a MAGLEV system....

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6 citations

3 citations

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### Cites methods from "Fuzzy sliding control with non-line..."

...The magnetic field is the base of the analysis and control for MLS, therefore, modeling of the magnetic flux density accurately plays a key role in the MLS, especially in case of applying model-based control [7]-[9]....

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##### References

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123,310 citations

### "Fuzzy sliding control with non-line..." refers methods in this paper

...Experimental results of Maglev (VAWT) in [1] show that system vibration can be reduced by 37....

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### "Fuzzy sliding control with non-line..." refers background in this paper

...e σ̇ = 0” [5], while the natural control unis discontinuous control law to be designed to account for nonzero uncertainties [6]....

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1,821 citations

### "Fuzzy sliding control with non-line..." refers background in this paper

...e σ̇ = 0” [5], while the natural control unis discontinuous control law to be designed to account for nonzero uncertainties [6]....

[...]

148 citations

### "Fuzzy sliding control with non-line..." refers methods in this paper

...A modified dynamic sliding-mode control has been reported in [4] to overcome the chattering problem of SMC, where the proposed controller is used to stabilize the dynamic of Maglev system in the new coordinates using feedback linearisation control....

[...]

75 citations

### "Fuzzy sliding control with non-line..." refers methods in this paper

...Sliding-mode control is used in [3] to control the linearised magnetic ball levitation system over a fixed set of operating points using singular perturbation method....

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##### Frequently Asked Questions (2)

###### Q2. What future works have the authors mentioned in the paper "Fuzzy sliding control with non-linear observer for magnetic levitation systems" ?

Future work will address experimental implementation using the proposed control schemes.