### Abstract

Mechanical models of balancing a ball rolling on a see-saw (“ball and beam” system) and balancing an inverted pendulum attached to a cart rolling on a see-saw (“pendulum-cart and beam” system) are analyzed. A delayed proportional-derivative controller is modeled with four different actuation schemes. The angular position, the angular velocity, the angular acceleration of the see-saw and the torque acting on the see-saw are considered to be the variables manipulated by the control system. The corresponding mathematical models take the form of retarded, neutral and advanced functional differential equations. Stabilizability analysis shows that the ball and beam system can only be stabilized in the presence of feedback delay if the manipulated variable is the angular position of the see-saw or the torque acting on the see-saw. The pendulum-cart and beam system can only be stabilized in the presence of feedback delay if the manipulated variable is the torque acting on the see-saw.

Original language | English |
---|---|

Pages (from-to) | 288-293 |

Number of pages | 6 |

Journal | IFAC-PapersOnLine |

Volume | 51 |

Issue number | 14 |

DOIs | |

Publication status | Published - Jan 1 2018 |

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### Keywords

- ball
- beam
- feedback delay
- inverted pendulum
- stability
- stabilizability

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

**Mathematical models for balancing tasks on a see-saw with reaction time delay.** / Buza, Gergely; Insperger, Tamas.

Research output: Contribution to journal › Article

*IFAC-PapersOnLine*, vol. 51, no. 14, pp. 288-293. https://doi.org/10.1016/j.ifacol.2018.07.238

}

TY - JOUR

T1 - Mathematical models for balancing tasks on a see-saw with reaction time delay

AU - Buza, Gergely

AU - Insperger, Tamas

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Mechanical models of balancing a ball rolling on a see-saw (“ball and beam” system) and balancing an inverted pendulum attached to a cart rolling on a see-saw (“pendulum-cart and beam” system) are analyzed. A delayed proportional-derivative controller is modeled with four different actuation schemes. The angular position, the angular velocity, the angular acceleration of the see-saw and the torque acting on the see-saw are considered to be the variables manipulated by the control system. The corresponding mathematical models take the form of retarded, neutral and advanced functional differential equations. Stabilizability analysis shows that the ball and beam system can only be stabilized in the presence of feedback delay if the manipulated variable is the angular position of the see-saw or the torque acting on the see-saw. The pendulum-cart and beam system can only be stabilized in the presence of feedback delay if the manipulated variable is the torque acting on the see-saw.

AB - Mechanical models of balancing a ball rolling on a see-saw (“ball and beam” system) and balancing an inverted pendulum attached to a cart rolling on a see-saw (“pendulum-cart and beam” system) are analyzed. A delayed proportional-derivative controller is modeled with four different actuation schemes. The angular position, the angular velocity, the angular acceleration of the see-saw and the torque acting on the see-saw are considered to be the variables manipulated by the control system. The corresponding mathematical models take the form of retarded, neutral and advanced functional differential equations. Stabilizability analysis shows that the ball and beam system can only be stabilized in the presence of feedback delay if the manipulated variable is the angular position of the see-saw or the torque acting on the see-saw. The pendulum-cart and beam system can only be stabilized in the presence of feedback delay if the manipulated variable is the torque acting on the see-saw.

KW - ball

KW - beam

KW - feedback delay

KW - inverted pendulum

KW - stability

KW - stabilizability

UR - http://www.scopus.com/inward/record.url?scp=85052485278&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052485278&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2018.07.238

DO - 10.1016/j.ifacol.2018.07.238

M3 - Article

AN - SCOPUS:85052485278

VL - 51

SP - 288

EP - 293

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 14

ER -