Robust, near time-optimal control of nonlinear second order systems with model uncertainty

2002 ◽  
Author(s):  
K.H. You ◽  
E.B. Lee
Keyword(s):  
Optimal Control ◽  
Model Uncertainty ◽  
Second Order ◽  
Time Optimal Control ◽  
Time Optimal ◽  
Second Order Systems

Robust, Near Time-Optimal Control of Nonlinear Second-Order Systems: Theory and Experiments

1991 ◽  
Vol 113 (3) ◽  
pp. 363-370 ◽  
Author(s):  
W. S. Newman ◽  
K. Souccar
Keyword(s):  
Optimal Control ◽  
Feedback Linearization ◽  
Sliding Mode ◽  
Industrial Robot ◽  
Second Order ◽  
Time Optimal Control ◽  
Modeling Uncertainties ◽  
Time Optimal ◽  
Second Order Systems ◽  
Bang Bang Control

A technique is presented for controlling second-order, nonlinear systems using a combination of bang-bang time-optimal control, sliding-mode control, and feedback linearization. Within the control loop, a state space evaluation of the system classifies the instantaneous dynamics into one of three regions, and one of three corresponding control algorithms is invoked. Using a prescribed generation of desirable sliding surfaces, the resulting combined controller produces nearly time-optimal performance. The combination controller is provably stable in the presence of model uncertainty. Experimental data are presented for the control of a General Electric GP132 industrial robot. The method is shown to achieve nearly time-optimal motion that is robust to modeling uncertainties. Representative transients compare favorably to bang-bang control and PD control.

Augmented Controllable Region of Unstable Second Order Systems With Impulsive Actions

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Wookjin Sung ◽  
Jiecai Luo ◽  
Kwanho You
Keyword(s):  
Optimal Control ◽  
Model Uncertainty ◽  
Second Order ◽  
Control Input ◽  
Impulsive Action ◽  
Mixed Control ◽  
Collaborative Control ◽  
Control Actions ◽  
Simulation Results ◽  
Second Order Systems

In this paper, we suggest how to enlarge the maximum controllable region for unstable linear systems with mixed control actions. Using the impulsive action as an alternating control input, it is shown how the collaborative control inputs (bang-bang and impulsive action) work to augment the controllable region of unstable second order systems. However, the weakness resides in the sensitivity to model uncertainty and the time-consuming work to construct the switch curves (bang-bang switch curve and impulse firing curve). We suggest an efficient way to approximate the switch curves. It overcomes the shortcomings from the use of original switch curves, which are constructed through time backward computation. Simulation results show how the approximate switch curves can be used to determine the optimal control values for an augmented maximum controllable region.

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