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**Stabilizing control of an underactuated 2-dimensional TORA with only rotor angle measurement.**
*(English)*
Zbl 1286.93182

Summary: One dimensional Translational Oscillation with a Rotational Actuator (TORA) system has been used as a benchmark for motivating the study of nonlinear control techniques. In this paper, a novel underactuated 2-dimensional TORA (2DTORA), which has one actuated rotor and two underactuated translational carts, is presented. The analysis of controllability around the system’s equilibriums yielded the controllable equilibriums and constraints on physical parameters. To stabilize the system to its controllable equilibriums from any initial conditions, we propose a simple linear controller containing the rotor angle and angular velocity. The controller is derived from a proper Lyapunov function, including the system’s total energy, that is used to show the passivity property of the system. In addition, a high pass filter is adopted to approximately differentiate the rotor angle so that an estimated angular velocity was used in the controller rather than measuring the actual rotor angular velocity. As a result, only the angle measurement is required for the designed feedback controller to stabilize the underactuated system. Finally, simulation results verify our control design and analysis.

### MSC:

93E12 | Identification in stochastic control theory |

93D30 | Lyapunov and storage functions |

93C05 | Linear systems in control theory |

93C10 | Nonlinear systems in control theory |

### Keywords:

2-dimensional translational oscillation with a rotational actuator (2DTORA); underactuated system; passivity; Lyapunov function; high pass filter
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\textit{B. Gao} et al., Asian J. Control 15, No. 5, 1477--1488 (2013; Zbl 1286.93182)

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