#
Control of Rotary Inverted Pendulum by Using On–Off Type of Cold Gas Thrusters^{ †}

^{1}

^{2}

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^{†}

## Abstract

**:**

## 1. Introduction

- Inverted pendulums have not been actuated by on–off-type thrusters before in the literature. This is the first study employing such actuators with the conventional control approach for rotary inverted pendulums. Nonlinearity of the system becomes higher compared to the other types of actuators.
- The system has high similarities with the thruster actuated spacecrafts having slosh dynamics. The approach used in this study can improve spacecraft control.

## 2. Background

#### 2.1. Cold Gas Thrusters

#### 2.2. Inverted Pendulum Control

## 3. Dynamics of the Rotary Inverted Pendulum

## 4. Controller Design

#### 4.1. Swing-Up Controller

#### 4.2. Balancing Controller

#### 4.2.1. State Space Model of the Rotary Inverted Pendulum

#### 4.2.2. State Space Model and Controllability in Discrete Domain

#### 4.2.3. Full State Feedback Controller

**K**is the state feedback gain matrix. The mathematical expression of the overall closed loop system is

**K**matrix to satisfy the requirements of the eigenvalues is done by Ackermann’s formula, which is given in Equations (49) and (50).

**A**) is given below. In the below equation ${\alpha}_{1}$, ${\alpha}_{2}$, ${\alpha}_{3}$ and ${\alpha}_{4}$ are the coefficients of the desired characteristic equations.

#### 4.3. Switching Controller

#### 4.4. Simulation Results

## 5. Results of the Experiments

#### 5.1. Experimental Test Setup

#### 5.2. Single Axis Experiment Results

#### 5.3. Inverted Pendulum Experiment Results

## 6. Discussions

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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Parameters | |
---|---|

${J}_{AO}$ | 0.2 kgm^{2} |

T | 1.25 Nm |

${r}_{rod}$ | 0.25 m |

${m}_{pen}$ | 25 g |

L | 0.135 m |

${J}_{B}$ | 0.0012 kgm^{2} |

Device | Model |
---|---|

Pressure Regulator | Norgren Olympian Plus |

Solenoid Valve | MHJ10-S-2,5-QS-6-hf |

Rotating Pneumatic Fitting | QSML-G1/8-4 |

Real Time Target Machine | Speedgoat Performance |

FPGA | IO331 FPGA Module |

Rotary Incremental Encoder | Yumo-E6B2-CWZ3E-1024 |

Slip Ring | 22 mm 240 [email protected] |

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**MDPI and ACS Style**

Silik, Y.; Yaman, U. Control of Rotary Inverted Pendulum by Using On–Off Type of Cold Gas Thrusters. *Actuators* **2020**, *9*, 95.
https://doi.org/10.3390/act9040095

**AMA Style**

Silik Y, Yaman U. Control of Rotary Inverted Pendulum by Using On–Off Type of Cold Gas Thrusters. *Actuators*. 2020; 9(4):95.
https://doi.org/10.3390/act9040095

**Chicago/Turabian Style**

Silik, Yusuf, and Ulas Yaman. 2020. "Control of Rotary Inverted Pendulum by Using On–Off Type of Cold Gas Thrusters" *Actuators* 9, no. 4: 95.
https://doi.org/10.3390/act9040095