Extending interconnection and damping assignment passivity-based control (IDA-PBC) to underactuated mechanical systems with nonholonomic Pfaffian constraints: The mobile inverted pendulum robot

2009 ◽  
Author(s):  
Vijay Muralidharan ◽  
Maruthi T. Ravichandran ◽  
Arun D. Mahindrakar
Keyword(s):  
Inverted Pendulum ◽  
Mechanical Systems ◽  
Underactuated Mechanical Systems ◽  
Passivity Based Control

Synchronization Control for a Class of Underactuated Mechanical Systems via Energy Shaping

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Dongfang Zhu ◽  
Di Zhou ◽  
Jingyang Zhou ◽  
Kok Lay Teo
Keyword(s):  
Control System ◽  
Mechanical Systems ◽  
Synchronization Control ◽  
Underactuated Mechanical Systems ◽  
Tracking Errors ◽  
Energy Shaping ◽  
Synchronization Errors ◽  
Shaping Technique ◽  
Passivity Based Control ◽  
Control Methodology

A synchronization control strategy for a class of underactuated mechanical systems is proposed by using the energy shaping technique, aiming to achieve the required performance of the synchronization motion. A synchronization controller is designed based on the interconnection and damping assignment passivity-based control methodology. It will guarantee that the position tracking errors and the synchronization errors of the underactuated mechanical systems are to converge to zero asymptotically. Experiments on a synchronization control system with two single-inverted pendulums as well as simulations of a synchronization control system consisting of four ball-beam devices are presented to demonstrate the effectiveness of the proposed method.

Damping-Induced Self Recovery Phenomenon in Mechanical Systems With an Unactuated Cyclic Variable

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
Dong Eui Chang ◽  
Soo Jeon
Keyword(s):  
Inverted Pendulum ◽  
Mechanical Systems ◽  
Conserved Quantity ◽  
The Self ◽  
Underactuated Mechanical Systems ◽  
Damping Force ◽  
Momentum Map ◽  
Time Integral ◽  
Conservation Of Momentum ◽  
Globally Attractive

Conservation of momentum is often used in controlling underactuated mechanical systems with symmetry. If a symmetry-breaking force is applied to the system, then the momentum is not conserved any longer in general. However, there exist forces linear in velocity such as the damping force that break the symmetry but induce a new conserved quantity in place of the original momentum map. This paper formalizes a new conserved quantity which can be constructed by combining the time integral of a general damping force and the original momentum map associated with the symmetry. From the perspective of stability theories, the new conserved quantity implies the corresponding variable possesses the self recovery phenomenon, i.e., it will be globally attractive to the initial condition of the variable. We discover that what is fundamental in the damping-induced self recovery is not the positivity of the damping coefficient but certain properties of the time integral of the damping force. The self recovery effect and theoretical findings are demonstrated by simulation results using the two-link planar manipulator and the torque-controlled inverted pendulum on a passive cart. The results in this paper will be useful in designing and controlling mechanical systems with underactuation.

scholarly journals Global stabilisation of underactuated mechanical systems via PID passivity-based control

Automatica ◽  
2018 ◽  
Vol 96 ◽  
pp. 178-185 ◽  
Author(s):  
Jose Guadalupe Romero ◽  
Alejandro Donaire ◽  
Romeo Ortega ◽  
Pablo Borja
Keyword(s):  
Mechanical Systems ◽  
Underactuated Mechanical Systems ◽  
Passivity Based Control

scholarly journals Global Stabilisation of Underactuated Mechanical Systems via PID Passivity-Based Control

2017 ◽  
Vol 50 (1) ◽  
pp. 9577-9582 ◽  
Author(s):  
Jose Guadalupe Romero ◽  
Alejandro Donaire ◽  
Romeo Ortega ◽  
Pablo Borja
Keyword(s):  
Mechanical Systems ◽  
Underactuated Mechanical Systems ◽  
Passivity Based Control
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