Frequency Domain Approach to Solve the Time-Optimal Control of a Distributed Parameter System

1995 ◽  
Author(s):  
Hasan Alli ◽  
Tarunraj Singh
Keyword(s):  
Optimal Control ◽  
Wave Equation ◽  
Time Optimal Control ◽  
Distributed Parameter ◽  
Dimensional System ◽  
Distributed Parameter System ◽  
Parameter System ◽  
Finite Dimensional ◽  
Time Optimal ◽  
Frequency Domain Approach

Abstract In this paper, the time-optimal control of the wave equation is derived in closed form. A frequency domain approach is used to obtain the time-optimal solution which is bang-off-bang. The system studied in this paper is a uniform flexible rod with a control input at each end, whose dynamics in axial vibration is represented by the wave equation. In order to verify the optimality of the control profile derived for the distributed parameter system, the system is discretized in space and a series of time-optimal control problems are solved for the finite dimensional model, with increasing number of flexible modes. In the limit, the controllers show the convergence of the first and final switch of the bang-bang controller of the finite dimensional system to the first and final switch of the bang-off-bang controller of the distributed parameter system, in addition to the convergence of the maneuver time. The number of switches in between the first and final switch is a function of the order of the finite dimensional system. The maneuver time of the distributed parameter system is compared to that of an equivalent rigid system and the coincidence of the time-optimal controller for the flexible and rigidized systems is illustrated for certain maneuvers.

Optimale Steuerung eines Systems mit verteilten Parametern am Beispiel eines Tiefofens / Optimal control of a distributed parameter system applied to a metallurgical Furnace

1974 ◽  
Vol 22 (11) ◽  
Author(s):  
D. Franke
Keyword(s):  
Optimal Control ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Wird Eine ◽  
Parameter System ◽  
Metallurgical Furnace ◽  
Mathematisches Modell

Der Beitrag behandelt am Beispiel eines Tiefofens die Anwendung der Optimierungstheorie für Systeme mit verteilten Parametern. Als mathematisches Modell wird die Wärmeleitungsdifferentialgleichung zugrunde gelegt.Die Minimierung eines quadratischen Güte-Index bei beschränkter Stellgröße führt nach A. G. Butkovskiy auf eine nichtlineare Integralgleichung für die optimale Steuerfunktion. Zur Lösung dieser Integralgleichung wird eine hybride Rechenschaltung vorgestellt. Anhand eines Zahlenbeispiels werden Rechnerergebnisse mitgeteilt und diskutiert.

Optimal Control of a Distributed Parameter, Time-Lagged River Aeration System

1975 ◽  
Vol 97 (2) ◽  
pp. 164-171 ◽  
Author(s):  
M. K. O¨zgo¨ren ◽  
R. W. Longman ◽  
C. A. Cooper
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Open Loop ◽  
Optimal Feedback Control ◽  
Distributed Parameter ◽  
Control Law ◽  
Optimal Controls ◽  
Distributed Parameter System ◽  
Parameter System ◽  
Characteristic Lines

The control of artificial in-stream aeration of polluted rivers with multiple waste effluent sources is treated. The optimal feedback control law for this distributed parameter system is determined by solving the partial differential equations along characteristic lines. In this process the double integral cost functional of the distributed parameter system is reduced to a single integral cost. Because certain measurements are time consuming, the feedback control law is obtained in the presence of observation delay in some but not all of the system variables. The open loop optimal control is then found, showing explicity the effect of changes in any of the effluent sources on the aeration strategy. It is shown that the optimal strategy for a distribution of sources can be written as an affine transformation upon the optimal controls for sources of unit strength.

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