scholarly journals Discussion: “A Switching Criterion for Certain Time-Optimal Regulating Systems” (Rang, E. R., 1962, ASME J. Basic Eng., 84, pp. 30–32)

1962 ◽  
Vol 84 (1) ◽  
pp. 32-32
Author(s):  
J. P. LaSalle
Keyword(s):  
Time Optimal ◽  
Switching Criterion

A Switching Criterion for Certain Time-Optimal Regulating Systems

1962 ◽  
Vol 84 (1) ◽  
pp. 30-32
Author(s):  
E. R. Rang
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Surface Integral ◽  
Practical Solution ◽  
Characteristic Roots ◽  
Time Optimal ◽  
Constant Coefficients ◽  
Real Characteristic ◽  
Switching Criterion ◽  
Order Surface

A rule for computing the initial relay position for time-optimal regulation corresponding to any set of initial conditions without solving the transcendental switching equations is presented. The discussion is restricted to systems represented by ordinary differential equations with constant coefficients with real characteristic roots. The calculation requires the evaluation of an (n − 1)-order surface integral and cannot be considered a practical solution of the problem.

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