Underactuated Mechanical Systems – A Review of Control Design

This paper presents a control design technique which enables approximate reference trajectory tracking for a class of underactuated mechanical systems. The control law comprises two terms. The first involves feedback of the trajectory tracking error in the actuated coordinates. Building on the concept of vibrational control, the second term imposes high-frequency periodic inputs that are modulated by the tracking error in the unactuated coordinates. Under appropriate conditions on the system structure and the commanded trajectory, and with sufficient separation between the time scales of the vibrational forcing and the commanded trajectory, the approach provides convergence in both the actuated and unactuated coordinates. The procedure is first described for a two degree-of-freedom (DOF) system with one input. Generalizing to higher-dimensional, underactuated systems, the approach is then applied to a 4DOF system with two inputs. A final example involves control of a rigid plate that is flapping in a uniform flow, a 3DOF system with one input. More general applications include biomimetic locomotion systems, such as underwater vehicles with articulating fins and flapping wing micro-air vehicles.

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Vibrational control of underactuated mechanical systems: control design through the averaging analysis

Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207) ◽

10.1109/acc.1998.703248 ◽

1998 ◽

Cited By ~ 1

Author(s):

Keum-Shik Hong ◽

Kang-Ryeol Lee ◽

Kyo-Il Lee

Keyword(s):

Mechanical Systems ◽

Control Design ◽

Underactuated Mechanical Systems ◽

Vibrational Control ◽

Averaging Analysis ◽

Systems Control

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Control Design Schemes for Underactuated Mechanical Systems

Analysis and Control of Underactuated Mechanical Systems ◽

10.1007/978-3-319-02636-7_5 ◽

2014 ◽

pp. 55-91

Author(s):

Amal Choukchou-Braham ◽

Brahim Cherki ◽

Mohamed Djemaï ◽

Krishna Busawon

Keyword(s):

Mechanical Systems ◽

Control Design ◽

Underactuated Mechanical Systems

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Observer-based robust integral of the sign of the error control of class I of underactuated mechanical systems: Theory and real-time experiments

Transactions of the Institute of Measurement and Control ◽

10.1177/01423312211031396 ◽

2021 ◽

pp. 014233122110313

Author(s):

Afef Hfaiedh ◽

Ahmed Chemori ◽

Afef Abdelkrim

Keyword(s):

Real Time ◽

Error Control ◽

Degrees Of Freedom ◽

Sliding Mode ◽

Mechanical Systems ◽

Class I ◽

Control Input ◽

Underactuated Mechanical Systems ◽

Control Scheme ◽

And Performance

In this paper, the control problem of a class I of underactuated mechanical systems (UMSs) is addressed. The considered class includes nonlinear UMSs with two degrees of freedom and one control input. Firstly, we propose the design of a robust integral of the sign of the error (RISE) control law, adequate for this special class. Based on a change of coordinates, the dynamics is transformed into a strict-feedback (SF) form. A Lyapunov-based technique is then employed to prove the asymptotic stability of the resulting closed-loop system. Numerical simulation results show the robustness and performance of the original RISE toward parametric uncertainties and disturbance rejection. A comparative study with a conventional sliding mode control reveals a significant robustness improvement with the proposed original RISE controller. However, in real-time experiments, the amplification of the measurement noise is a major problem. It has an impact on the behaviour of the motor and reduces the performance of the system. To deal with this issue, we propose to estimate the velocity using the robust Levant differentiator instead of the numerical derivative. Real-time experiments were performed on the testbed of the inertia wheel inverted pendulum to demonstrate the relevance of the proposed observer-based RISE control scheme. The obtained real-time experimental results and the obtained evaluation indices show clearly a better performance of the proposed observer-based RISE approach compared to the sliding mode and the original RISE controllers.

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