Control Vector Parametrization with Karhunen−Loéve Expansion

2004 ◽  
Vol 43 (1) ◽  
pp. 127-135 ◽  
Author(s):  
Xing-Gui Zhou ◽  
Wei-Kang Yuan
Keyword(s):  
Control Vector ◽  
Vector Parametrization

Optimal control of a two-stage reactor system

2006 ◽  
Vol 60 (5) ◽  
Author(s):  
T. Hirmajer ◽  
M. Fikar
Keyword(s):  
Optimal Control ◽  
Dynamic Optimization ◽  
Adjoint Method ◽  
Batch Reactor ◽  
Optimal Operation ◽  
Reactor System ◽  
Control Vector ◽  
Maximum Conversion ◽  
Vector Parametrization ◽  
Operating Constraints

AbstractOptimal operation policies were investigated for a batch reactor system with two different operation stages. At the end of the first nonisothermal stage one of the reactants was added. Since that moment the reactor was operated isothermally. In each stage behavior of the reactor was described by a set of differential equations. The maximum conversion problem was investigated subject to various operating constraints. Dynamic optimization based on the control vector parametrization was used to find the optimal control profile. Gradients of the resulting nonlinear programming problem were obtained by adjoint method based on the optimal control theory.

scholarly journals Improved model predictive load frequency control of interconnected power system with synchronized automatic generation control loops

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Abdullahi Bala Kunya ◽  
Mehmet Argin ◽  
Yusuf Jibril ◽  
Yusuf Abubakar Shaaban
Keyword(s):  
Frequency Control ◽  
Cross Coupling ◽  
Absolute Error ◽  
Automatic Generation ◽  
Load Frequency Control ◽  
Automatic Generation Control ◽  
Control Vector ◽  
Interconnected Power System ◽  
Control Scheme ◽  
Generation Control

Abstract Background Automatic generation control (AGC) of multi-area interconnected power system (IPS) is often designed with negligible cross-coupling between the load frequency control (LFC) and automatic voltage regulation (AVR) loops. This is because the AVR loop is considerably faster than that of LFC. However, with the introduction of slow optimal control action on the AVR, positive damping effect can be achieved on the LFC loop thereby improving the frequency control. In this paper, LFC synchronized with AVR in three-area IPS is proposed. Model predictive controller (MPC) configured in a dense distributed pattern, due to its online set-point tacking is used as the supplementary controller. The dynamics of the IPS subjected to multi-area step and random load disturbances are studied. The efficacy of the developed scheme is ascertained by simulating the disturbed system in MATLAB/Simulink. Results Based on the comparative analysis on the system responses, it is established that by cross-coupling the LFC loop with AVR, reductions of 66.45% and 59.09% in the frequency and tie-line power maximum deviations respectively are observed, while the respective settling times are found to be reduced by 29.68% and 22.77% when compared with the uncoordinated control scheme. In addition, the standard deviation and variance of the integral time absolute error of the system’s responses have reduced by 23.21% and 20.83% respectively compared to those obtained in a similar study. Conclusions The reduction in the maximum deviations and settling times in the system states indicates that introducing the voltage control via AVR loop has improved the frequency control significantly. While the lower standard deviation and variance of the integral time absolute error signify improvement in the robustness of the developed algorithm. However, this improvement is at the detriment of the controller size and computational complexity. In the uncoordinated control scheme, the control vector is one-dimensional, while in the coordinated scheme, the control vector is two-dimensional for each CA.

scholarly journals Optimization of two opposing neutron beams parameters in dynamical (B/Gd) neutron cancer therapy

2019 ◽  
Vol 5 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Nassar H. S. Haidar
Keyword(s):  
Optimal Control ◽  
Cancer Therapy ◽  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Pareto Optimal ◽  
Control Vector ◽  
Relative Time ◽  
Neutron Beams ◽  
Utility Index ◽  
First Time

We demonstrate how the therapeutic utility index and the ballistic index for dynamical neutron cancer therapy (NCT) with two opposing neutron beams form a nonlinear optimization problem. In this problem, the modulation frequencies ω and ϖ of the beams and the relative time advance ε are the control variables. A Pareto optimal control vector ω* = (ω*, ϖ*, ε*) for this problem is identified and reported for the first time. The utility index is shown to be remarkably periodically discontinuous in ε, even in the neighborhood of ε*.

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