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.

Passive optimal feedback control of an articulated flexible arm

2020 ◽  
pp. 107754632095676
Author(s):  
Raja Tebbikh ◽  
Hicham Tebbikh ◽  
Sihem Kechida
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Closed Loop ◽  
Open Loop ◽  
Optimal Feedback Control ◽  
Convolution Operators ◽  
High Frequencies ◽  
Zero Initial Condition ◽  
Flexible Arm ◽  
Euler Bernoulli Beam

This article deals with stabilization and optimal control of an articulated flexible arm by a passive approach. This approach is based on the boundary control of the Euler–Bernoulli beam by means of wave-absorbing feedback. Due to the specific propagative properties of the beam, such controls involve long-memory, non-rational convolution operators. Diffusive realizations of these operators are introduced and used for elaborating an original and efficient wave-absorbing feedback control. The globally passive nature of the closed-loop system gives it the unconditional robustness property, even with the parameters uncertainties of the system. This is not the case in active control, where the system is unstable, because the energy of high frequencies is practically uncontrollable. Our contribution comes in the achievement of optimal control by the diffusion equation. The proposed approach is original in considering a non-zero initial condition of the diffusion as an optimization variable. The optimal arm evolution, in a closed loop, is fixed in an open loop by optimizing a criterion whose variable is the initial diffusion condition. The obtained simulation results clearly illustrate the effectiveness and robustness of the optimal diffusive control.

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 feedback control of stochastic McShane differential systems

1974 ◽  
Vol 11 (2) ◽  
pp. 302-309 ◽  
Author(s):  
N. U. Ahmed ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Necessary Conditions ◽  
Parabolic Type ◽  
Optimal Feedback Control ◽  
Distributed Parameter ◽  
Optimal Controls ◽  
Necessary Conditions For Optimality ◽  
Reduced Problem

In this paper, the optimal control problem of system described by stochastic McShane differential equations is considered. It is shown that this problem can be reduced to an equivalent optimal control problem of distributed parameter systems of parabolic type with controls appearing in the coefficients of the differential operator. Further, to this reduced problem, necessary conditions for optimality and an existence theorem for optimal controls are given.

Optimal feedback control of stochastic McShane differential systems

1974 ◽  
Vol 11 (02) ◽  
pp. 302-309
Author(s):  
N. U. Ahmed ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Necessary Conditions ◽  
Parabolic Type ◽  
Optimal Feedback Control ◽  
Distributed Parameter ◽  
Optimal Controls ◽  
Necessary Conditions For Optimality ◽  
Reduced Problem

In this paper, the optimal control problem of system described by stochastic McShane differential equations is considered. It is shown that this problem can be reduced to an equivalent optimal control problem of distributed parameter systems of parabolic type with controls appearing in the coefficients of the differential operator. Further, to this reduced problem, necessary conditions for optimality and an existence theorem for optimal controls are given.

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