## Abstract

In this paper, a new method for model based optimal tracking control is presented.

The special composition of the cost functional leads to design parameters for constraining the

solution so as to ensure that machine limitations are not violated. By minimizing the cost

functional with the calculus of variations, or more precisely the Euler-Lagrange equations, the

state space representation of the system dynamics is transformed into an augmented state

space representation describing the optimal tracking dynamics. The optimal control input is

numerically calculated by solving the set of dierential equations, given by the augmented state

space system, globally with a specialized least-squares solver. The general control approach is

demonstrated on an underactuated crane-like system with xed load hoisting length operating

in the horizontal plane. In this case the introduced design parameters determine the tradeo

between the cost of tracking accuracy and the cost of using large values of crane speed

and acceleration. The potential of the proposed control scheme is proven by both simulation

and experimental tests. The multibody simulation is carried out with the software Simscape

MultibodyTM. For the experimental verication an industrial robot is used whose end eector

only moves in a horizontal plane to imitate the trolley of an overhead crane.

The special composition of the cost functional leads to design parameters for constraining the

solution so as to ensure that machine limitations are not violated. By minimizing the cost

functional with the calculus of variations, or more precisely the Euler-Lagrange equations, the

state space representation of the system dynamics is transformed into an augmented state

space representation describing the optimal tracking dynamics. The optimal control input is

numerically calculated by solving the set of dierential equations, given by the augmented state

space system, globally with a specialized least-squares solver. The general control approach is

demonstrated on an underactuated crane-like system with xed load hoisting length operating

in the horizontal plane. In this case the introduced design parameters determine the tradeo

between the cost of tracking accuracy and the cost of using large values of crane speed

and acceleration. The potential of the proposed control scheme is proven by both simulation

and experimental tests. The multibody simulation is carried out with the software Simscape

MultibodyTM. For the experimental verication an industrial robot is used whose end eector

only moves in a horizontal plane to imitate the trolley of an overhead crane.

Original language | English |
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Pages | 6267-6272 |

Number of pages | 6 |

Publication status | Published - 2020 |

Event | 21st IFAC World Congress (Virtual) - Berlin, Berlin, Germany Duration: 12 Jul 2020 → 17 Jul 2020 |

### Conference

Conference | 21st IFAC World Congress (Virtual) |
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Country/Territory | Germany |

City | Berlin |

Period | 12/07/20 → 17/07/20 |