# Design of Adaptive-RST Controller for Nonlinear Magnetic Levitation System Using Multiple Zone-Model Approach in Real-Time Experimentation

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## Abstract

**:**

## 1. Introduction

## 2. Magnetic Levitation System (Maglev)

#### 2.1. Magnetic Levitation System Overview

#### 2.2. The (Maglev) System Dynamics

#### 2.3. Description of the Mechanical Model of the Maglev System

#### 2.4. The System Identification Modeling Using Multi Zone-Model Approach

#### 2.5. System Identification Process

## 3. Control System Design

#### 3.1. RST Controller Design

#### 3.2. RST Controller Parameters Calculation

#### 3.3. Adaptive Supervisor and Switching

- (1)
- When is it appropriate to make the transfer from one model to another? We need to decide which model to use;
- (2)
- When is a switching scheme stable? Will switching stop after a finite time? Will the switching scheme improve performance?

## 4. Real-Time Implementation and Results

## 5. Conclusions

- This paper deals with a magnetic-levitation (maglev) system. Real-time experimentation and simulations both confirmed the effectiveness of the maglev transportation system’s control strategy by using multi-model and multi-control approaches;
- The maglev system is nonlinear and very sensitive to disturbances, which is why the set point is divided into three zones to obtain three models;
- The three models were computed using the least-squares identification approach and the generation of pseudo-random signals (PRBS). LabVIEW and WinPIM were utilized in real-time to locate all models;
- The method’s applicability was demonstrated by utilizing a real-time structure with an RST control mechanism, and all parameters of the RST controller were computed by using the WinREG platform;
- Supervisor switching was implemented with two main criteria. The first one is the set point, and the second one is the level of the error;
- On the LabVIEW platform, experimental results are tested by conducting regulation and tracking experiments. The results of the experiments show that this method is very good, with strong response and stability. Smooth and exponential convergence of system variables to their desired levels with three zones;
- The experimental results also showed that the multi-zone model with multi-controller approaches is better with rising time, overshoot, settling time, rejecting the disturbances, and total response;
- The proposed real-time-platform presents an economical solution, not expensive (hardware and software), and more stable when compared with our previous paper [13];
- The obtained results sustain proposed solutions and suggest future steps, such as robustness conditions designed for bumpless switching in multiple model control structures [24];

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 12.**Performances for Z2 operating point with $\left({R}_{1},{S}_{1},{T}_{1}\right)$ algorithm *.

**Figure 13.**Performances for Z2 operating point with $\left({R}_{3},{S}_{3},{T}_{3}\right)$ algorithm *.

**Figure 14.**Multi-model controller real-time with Maglev system application and performances for Z2 operating point with $\left({R}_{2},{S}_{2},{T}_{2}\right)$ algorithm *.

**Figure 16.**The response of PID controller using fuzzy-tuning approach [13].

**Table 1.**Shows a comparison of the proposed solution (multi-model and multi-controller) (Zone 2 as a case study) versus a single controller (C1 with M2 and C3 with M2).

Controller Types | Overshoot | Settling Time | Rise Time | Disturbances |
---|---|---|---|---|

${\mathrm{RST}}_{1}\text{}\mathrm{with}\text{}\mathrm{M}2$ | 8.33% | 1.1 | 0.36 | Not good |

${\mathrm{RST}}_{3}\text{}\mathrm{with}\text{}\mathrm{M}2$ | 16.4% | 1.4 | 0.373 | Not good |

$\mathrm{Multi}\text{}\left(\mathrm{Model},\text{}\mathrm{Controller}\right)\text{}$ $\left(\mathrm{propused}\text{}\mathrm{solution}\right)$ | 1.1% | 0.81 | 0.312 | Good |

Controller Types | Overshoot | Settling Time | Rise Time | Oscillations |
---|---|---|---|---|

$\mathrm{Switching}\text{}\mathrm{from}\text{}\mathrm{Z}1\text{}\mathrm{to}\text{}\mathrm{Z}2$ | 7.78% | 0.94 | 0.32 | Very small |

$\mathrm{Switching}\text{}\mathrm{from}\text{}\mathrm{Z}2\text{}\mathrm{to}\text{}\mathrm{Z}3$ | 1.1% | 0.81 | 0.312 | No |

**Table 3.**Comparison between the proposed solution (multi-model and multi-controller) with the results obtained in our previous paper [13] under the title (design of PID controller for nonlinear magnetic levitation system using fuzzy-tuning approach).

Controller Types | Overshoot | Settling Time | Rise Time | Disturbances |
---|---|---|---|---|

$\mathrm{Fuzzy}-\mathrm{PID}$ | 5.72% | 0.85 | 0.68 | Good |

$\mathrm{Multi}\text{}\left(\mathrm{Model},\text{}\mathrm{Controller}\right)$ $\mathrm{with}\text{}\mathrm{RST}\text{}$ $\left(\mathrm{propused}\text{}\mathrm{solution}\right)$ | 1.1% | 0.81 | 0.312 | Good |

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**MDPI and ACS Style**

Ismail, L.S.; Lupu, C.; Alshareefi, H.
Design of Adaptive-RST Controller for Nonlinear Magnetic Levitation System Using Multiple Zone-Model Approach in Real-Time Experimentation. *Appl. Syst. Innov.* **2022**, *5*, 93.
https://doi.org/10.3390/asi5050093

**AMA Style**

Ismail LS, Lupu C, Alshareefi H.
Design of Adaptive-RST Controller for Nonlinear Magnetic Levitation System Using Multiple Zone-Model Approach in Real-Time Experimentation. *Applied System Innovation*. 2022; 5(5):93.
https://doi.org/10.3390/asi5050093

**Chicago/Turabian Style**

Ismail, Laith S., Ciprian Lupu, and Hamid Alshareefi.
2022. "Design of Adaptive-RST Controller for Nonlinear Magnetic Levitation System Using Multiple Zone-Model Approach in Real-Time Experimentation" *Applied System Innovation* 5, no. 5: 93.
https://doi.org/10.3390/asi5050093