Calculating switching times for the time-optimal control of single-input, single-output second-order systems

Automatica ◽  
2013 ◽  
Vol 49 (5) ◽  
pp. 1340-1347 ◽  
Author(s):  
Zhaolong Shen ◽  
Peng Huang ◽  
Sean B. Andersson
Keyword(s):  
Optimal Control ◽  
Second Order ◽  
Time Optimal Control ◽  
Single Input Single Output ◽  
Switching Times ◽  
Single Output ◽  
Time Optimal ◽  
Single Input ◽  
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.

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