# A Nonlinear Magnetic Stabilization Control Design for an Externally Manipulated DC Motor: An Academic Low-Cost Experimental Platform

## Abstract

**:**

## 1. Introduction

- A contactless vibrational position control design to a DC-Motor.
- A controller realization by just using speed estimation of the DC-Motor.
- A controller based on analog electronics.
- An experimental platform with a moveable magnetic sensor.

## 2. Control Algorithm Design

**Remark**

**1.**

## 3. Control Realization: Materials and Methods

## 4. Discussion

## 5. Conclusions

- A mathematical design of a vibrational control based on a simple model of a DC-Motor.
- A control scheme that strategically incorporates a constant parameter to mitigate the actuator dead-zone nonlinearity.
- A low-cost realization of the resultant controller.
- A contribution of a low-priced experimental platform to vibrational control.
- A control method that uses a magnetic Hall-effect sensor.

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

DC | Direct current |

Opamp | Operational amplifier |

## Appendix A. Python Code

`import numpy as np`

`import matplotlib.pyplot as plt`

`t=[0]`

`v=[1.0]`

`uc=[0]`

`h=0.01`

`k=0`

`kg=1`

`while(True):`

`u=kg*np.sign(v[k]+0.1+np.random.normal(scale=1,loc=0.0))`

`v.append(v[k]+h*(-u-0.2*np.sign(v[k])))`

`t.append(h+k*h)`

`uc.append(u)`

`k=k+1`

`if t[k]>15-h:`

`break`

`plt.figure(1)`

`plt.plot(t,v,color=’red’)`

`plt.grid(True)`

`plt.xlabel(’t(s)’)`

`plt.ylabel(’v(t)’)`

`plt.figure(2)`

`plt.plot(t,uc,color=’red’)`

`plt.grid(True)`

`plt.xlabel(’t(s)’)`

`plt.ylabel(’u(t)’)`

`plt.show()`

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**Figure 1.**A schematic representation of a DC-Motor under control. The magnet, represented in the black drawing, follows the moveable Hall-effect sensor.

**Figure 9.**Electronic realization of the control scheme by employing opamps. Here, all electronic elements are in standard units. For instance, the resistor element 1 M represents a resistance of 1 M$\Omega $, and the capacitor 47 a capacitance of 47F, and so on.

**Figure 14.**Experimental results for both signals, ${v}_{a}$ and ${v}_{b}$: a zoom-in version of the previous picture.

**Figure 16.**Phase trajectories of the closed-loop system (3).

**Figure 17.**In a yellow line: A realistic trajectory of the closed-loop system (3) presenting chattering.

Element | Specification | Price |
---|---|---|

3 Operational amplifiers | LM741 | 3 |

2 Power transistors | MJE305T, MJE2955T | 4 |

2 Potentiometers | Mechanical | $1.5$ |

1 Permanent magnet | $0.50$ | |

1 DC-Motor | $12/24$ Volts | 15 |

1 Bread board | 4 | |

1 Dual power supply | 20 | |

1 Hall-Effect sensor | $0.50$ | |

Others | $0.50$ | |

Total | 50 |

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**MDPI and ACS Style**

Acho, L.
A Nonlinear Magnetic Stabilization Control Design for an Externally Manipulated DC Motor: An Academic Low-Cost Experimental Platform. *Machines* **2021**, *9*, 101.
https://doi.org/10.3390/machines9050101

**AMA Style**

Acho L.
A Nonlinear Magnetic Stabilization Control Design for an Externally Manipulated DC Motor: An Academic Low-Cost Experimental Platform. *Machines*. 2021; 9(5):101.
https://doi.org/10.3390/machines9050101

**Chicago/Turabian Style**

Acho, Leonardo.
2021. "A Nonlinear Magnetic Stabilization Control Design for an Externally Manipulated DC Motor: An Academic Low-Cost Experimental Platform" *Machines* 9, no. 5: 101.
https://doi.org/10.3390/machines9050101