scholarly journals Finite-time stabilization of underactuated mechanical systems in the presence of uncertainties: application to the cart-pole system

2017 ◽  
pp. 165-190 ◽  
Keyword(s):  
Finite Time ◽  
Mechanical Systems ◽  
Underactuated Mechanical Systems ◽  
Finite Time Stabilization ◽  
Pole System

Robust Finite Time Controller Design for Second Order Underactuated Mechanical Systems

2013 ◽  
Vol 284-287 ◽  
pp. 2310-2314 ◽  
Author(s):  
Kuang Shine Yang ◽  
Chi Cheng Cheng ◽  
Jung Hua Yang
Keyword(s):  
Lyapunov Stability ◽  
Finite Time ◽  
Controller Design ◽  
Tracking Error ◽  
Mechanical Systems ◽  
Second Order ◽  
Underactuated Systems ◽  
Underactuated Mechanical Systems ◽  
Pendulum System ◽  
Finite Time Convergence

Stabilization and tracking control of nonlinear uncertain underactuated systems are always challenging problems because underacturated systems have fewer independent control actuators than degrees of freedom to be controlled. For a class of second order underactuated mechanical systems, a robust finite time control strategy is developed in this paper. The robust finite time controller is to drive the tracking error to be zero at the fixed final time. In fact, finite time convergence implies nonsmooth or non-Lipschitz continuous autonomous systems with nonuniqueness of solution. In order to prove the stability, we present a generalized Lyapunov stability proof for the second order underactuated mechanical system. By utilizing a Lyapunov stability theorem, we can achieve finite time tracking of desired reference signals for underactuated systems, which is subject to both external disturbances and system uncertainties. The proposed control scheme is demonstrated by actual experiments on a Furuta pendulum system. Based on the experiment results, the finite time convergence of system errors can be assured.

ROBUST FINITE TIME CONTROLLER DESIGN FOR SECOND ORDER NONLINEAR UNDERACTUATED MECHANICAL SYSTEMS

2013 ◽  
Vol 37 (3) ◽  
pp. 549-557 ◽  
Author(s):  
Chi-Cheng Cheng ◽  
Kuang-Shine Yang ◽  
Jung-Hua Yang
Keyword(s):  
Lyapunov Stability ◽  
Finite Time ◽  
Controller Design ◽  
Tracking Error ◽  
Mechanical Systems ◽  
Second Order ◽  
System Stability ◽  
Underactuated Mechanical Systems ◽  
Pendulum System ◽  
Time Control

For a class of second order underactuated mechanical systems, a robust finite time control strategy is developed in this paper. The robust finite time controller is to drive the tracking error to be zero at the fixed final time. In order to assure system stability, we present a generalized Lyapunov stability proof for the second order underactuated mechanical system. By utilizing a Lyapunov stability theorem, we can achieve finite time tracking of desired reference signals for underactuated systems, which are subject to both external disturbances and system uncertainties. The proposed control scheme is demonstrated by actual experiments on a Furuta pendulum system.

scholarly journals Prescribed finite time stabilization of linear systems with state constraints

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Tingting Yang ◽  
Yichao Ma ◽  
Pengfei Zhang ◽  
Jingyun Xu
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
State Constraints ◽  
Finite Time Stabilization

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

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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