Explicit Constructions of Global Stabilization Control Laws for a Class of Nonminimum Phase Nonlinear Systems

2006 ◽  
Author(s):  
Weiyao Lan ◽  
Ben M. Chen
Keyword(s):  
Nonlinear Systems ◽  
Global Stabilization ◽  
Control Laws ◽  
Nonminimum Phase ◽  
Stabilization Control ◽  
Explicit Constructions

CONTROLLERS FOR NONLINEAR SYSTEMS USING NORMAL FORMS

2003 ◽  
Vol 13 (02) ◽  
pp. 459-465 ◽  
Author(s):  
DAVID M. WALKER ◽  
GARY FROYLAND ◽  
KEVIN JUDD ◽  
ALISTAIR I. MEES
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Normal Forms ◽  
Feedback Stabilization ◽  
Control Laws ◽  
Stabilization Control ◽  
Region Of Stability ◽  
Linear Controllers

We describe a method for the design of feedback stabilization control laws for nonlinear systems using the theory of normal forms and the results from optimal control theory. We show that the resulting controllers can provide a larger region of stability than local linear controllers designed to perform the same task.

scholarly journals Nonlinear Global Stabilization Control for the Underactuated WAcrobot System

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Shuli Gong ◽  
Ancai Zhang ◽  
Zhi Liu ◽  
Zhenxing Li ◽  
Chengdong Yang ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Reduced Order Model ◽  
Underactuated System ◽  
Global Stabilization ◽  
Order Model ◽  
Control Laws ◽  
Reduced Order ◽  
Stabilization Control ◽  
Stabilizing Control ◽  
Control Objective

A WAcrobot is an underactuated nonlinear system that has three degrees of freedom (DOF) and two inputs. This paper discusses the global stabilization control problem for this 3-DOF underactuated system. A new control strategy is developed to solve this problem. The strategy first changes the 3-DOF WAcrobot system to be a 2-DOF reduced-order model in finite time. This transforms the stabilizing control of the WAcrobot system into that of the reduced-order model. After that, nonsingular control laws that globally stabilize the reduced-order model at the origin are designed. It guarantees the stabilizing control objective of the WAcrobot to be achieved. Finally, a simulation experimental example demonstrates the validity of the presented theoretical results. Simulation results show the advantage of our strategy over others.

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