scholarly journals Selection of Control Vector Switching Points for Circuit Optimization

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Lyapunov Function ◽  
Dynamic System ◽  
Design Process ◽  
Time Derivative ◽  
Computational Cost ◽  
Optimal Structure ◽  
Control Vector ◽  
Processor Time ◽  
Design Algorithm ◽  
Cpu Time

The process of optimizing the circuit is formulated as a controlled dynamic system. A special control vector has been defined to redistribute the computational cost between circuit analysis and parametric optimization. This redistribution will help solve the task of optimizing the circuit for minimum CPU time. In this case, the task of optimizing the circuit with minimal CPU time can be formulated as the classical optimal control problem for minimizing some functional. The concept of the Lyapunov function of a controlled dynamic system is used to analyze the main characteristics of the design process. An analysis of the Lyapunov function and its time derivative makes it possible to predict the optimal structure of the control vector for constructing an optimal or quasi-optimal circuit design algorithm. The results are based on the previously discovered effect of accelerating the design process. In this case, the optimal structure of the control vector is determined, which minimizes processor time.

Analysis of the structure of different optimization strategies

2020 ◽  
Vol 39 (3) ◽  
pp. 583-593
Author(s):  
Alexander Zemliak ◽  
Jorge Espinosa-Garcia
Keyword(s):  
Lyapunov Function ◽  
Dynamic System ◽  
Optimal Structure ◽  
Optimization Process ◽  
Main Element ◽  
Circuit Optimization ◽  
Control Vector ◽  
Processor Time ◽  
Content Type ◽  
Cpu Time

Purpose In this paper, on the basis of a previously developed approach to circuit optimization, the main element of which is the control vector that changes the form of the basic equations, the structure of the control vector is determined, which minimizes CPU time. Design/methodology/approach The circuit optimization process is defined as a controlled dynamic system with a special control vector. This vector serves as the main tool for generalizing the problem of circuit optimization and produces a huge number of different optimization strategies. The task of finding the best optimization strategy that minimizes processor time can be formulated. There is a need to find the optimal structure of the control vector that minimizes processor time. A special function, which is a combination of the Lyapunov function of the optimization process and its time derivative, was proposed to predict the optimal structure of the control vector. The found optimal positions of the switching points of the control vector give a large gain in CPU time in comparison with the traditional approach. Findings The optimal positions of the switching points of the components of the control vector were calculated. They minimize processor time. Numerical results are obtained for various circuits. Originality/value The Lyapunov function, which is one of the main characteristics of any dynamic system, is used to determine the optimal structure of the control vector, which minimizes the time of the circuit optimization process.

scholarly journals Study of the Dynamic Characteristics of Some Circuit Optimization Strategies

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Optimal Control ◽  
Lyapunov Function ◽  
Design Process ◽  
Analog Circuits ◽  
Analog Circuit ◽  
Time Derivative ◽  
Computational Cost ◽  
Design Strategies ◽  
Processor Time ◽  
Cpu Time

The work explores the possibility of a significant reduction in processor time required to optimize analog circuits. For this, we can reformulate and generalize the problem of chain optimization based on the approaches of optimal control theory. The analog circuit design process is formulated as a dynamic controlled system. A special control vector has been defined to redistribute the computational cost between circuit analysis and parametric optimization. This redistribution significantly reduces CPU time. The task of designing a circuit for the minimum processor time can be formulated as a classical optimal control problem while minimizing some functional. The introduction of the concept of the Lyapunov function of a controlled dynamic system made it possible to use it to analyse the main characteristics of the design process. An analysis of the behaviour of a special function, which is a combination of the Lyapunov function and its time derivative, made it possible to compare various design strategies and select the best ones that are executed in minimal CPU time.

scholarly journals Computer Time Minimizing for the Circuit Optimization

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Maximum Principle ◽  
Dynamic System ◽  
Traditional Approach ◽  
Optimization Procedure ◽  
Computer Time ◽  
Circuit Optimization ◽  
Control Vector ◽  
Processor Time ◽  
The Maximum Principle ◽  
Cpu Time

The solution of a problem of analogue circuit optimization is mathematically defined as a controllable dynamic system. In this context the minimization of the processor time of designing can be formulated as a problem of time minimization for transitional process of dynamic system. A special control vector that changes the internal structure of the equations of optimization procedure serves as a principal tool for searching the best strategies with the minimal CPU time. In this case a well-known maximum principle of Pontryagin is the best theoretical approach for finding of the optimum structure of control vector. Practical approach for realization of the maximum principle is based on the analysis of behaviour of a Hamiltonian for various strategies of optimization. It is shown that in spite of the fact that the problem of optimization is formulated as a nonlinear task, and the maximum principle in this case isn't a sufficient condition for obtaining a minimum of the functional, it is possible to obtain the decision in the form of local minima. The relative acceleration of the CPU time for the best strategy found by means of maximum principle compared with the traditional approach is equal two to three orders of magnitude.

scholarly journals Circuit Optimization Study According to the Maximum Principle

2021 ◽  
Vol 20 ◽  
pp. 362-371
Author(s):  
Alexander Zemliak
Keyword(s):  
Maximum Principle ◽  
Traditional Approach ◽  
Optimization Procedure ◽  
Circuit Optimization ◽  
Control Vector ◽  
Processor Time ◽  
The Maximum Principle ◽  
Cpu Time ◽  
Optimization Study ◽  
Time Minimization

The minimization of the processor time of designing can be formulated as a problem of time minimization for transitional process of dynamic system. A special control vector that changes the internal structure of the equations of optimization procedure serves as a principal tool for searching the best strategies with the minimal CPU time. In this case a well-known maximum principle of Pontryagin is the best theoretical approach for finding of the optimum structure of control vector. Practical approach for realization of the maximum principle is based on the analysis of behavior of a Hamiltonian for various strategies of optimization. The possibility of applying the maximum principle to the problem of optimization of electronic circuits is analyzed. It is shown that in spite of the fact that the problem of optimization is formulated as a nonlinear task, and the maximum principle in this case isn't a sufficient condition for obtaining a minimum of the functional, it is possible to obtain the decision in the form of local minima. The relative acceleration of the CPU time for the best strategy found by means of maximum principle compared with the traditional approach is equal two to three orders of magnitude.

Fast Conjugate Heat Transfer Simulation of Long Transient Flexible Operations Using Adaptive Time Stepping

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
R. Maffulli ◽  
L. He ◽  
P. Stein ◽  
G. Marinescu
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Time Derivative ◽  
Computational Cost ◽  
Strong Impact ◽  
Time Step ◽  
Time Stepping ◽  
Adaptive Time ◽  
Fully Coupled ◽  
Adaptive Time Stepping

The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully coupled time-accurate unsteady conjugate heat transfer (CHT) results under these conditions would require to march in both domains using the time-step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that remove these requirements through a source-term based modeling (STM) approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time-step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs.

On the choice of CFD codes in the design process of planing sailing yachts

2009 ◽  
Author(s):  
Jérémie Raymond ◽  
Jean-Marie Finot ◽  
Jean-Michel Kobus ◽  
Gérard Delhommeau ◽  
Patrick Queutey ◽  
...  
Keyword(s):  
Free Surface ◽  
Design Process ◽  
Finite Differences ◽  
Potential Flow ◽  
Surface Condition ◽  
Cpu Time ◽  
Free Surface Condition ◽  
Finite Differences Method ◽  
Non Linear ◽  
Ranse Solver

The discussion is based on results gathered during the first two years of a 3 years research program for the benefits of Groupe Finot-Conq, Naval Architects. The introduction presents the objectives of the program: Setting up a practical method using numerical and experimental available tools to design fast planing sailing yachts. The aim of this paper is to compare advantages and disadvantages of four different kinds of CFD codes which are linear and non-linear potential flow approach, RANSE solver using finite differences method and RANSE solver using volume of fluid method. The Fluid Mechanics Laboratory of the Ecole Centrale de Nantes (France) has developed those three approaches so those homemade codes will be used for this study. The first one is REVA, a potential flow code with a linearised free surface condition. ICARE is a RANSE solver using finite differences method with a non linear free surface condition. It is extensively used for industrial projects as for sailing yachts projects (ACC for example). ISIS-CFD is a RANSE solver using finite volume method to build the spatial discretization of the transport equations with unstructured mesh. The latter is able to compute sprays for fast planing ships but is also the slower in terms of CPU time. In addition, we had the opportunity to test FS-FLOW which is a potential flow code with a non linear free surface condition distributed by FRIENDSHIP CONSULTING. Numerical results for the four codes are compared with the other codes' results as with tank tests data. Those tank tests were made using captive model test technique on two Open60' models. Reasons of the choice of the captive model technique are explained and experimental procedures are briefly described. Comparisons between codes are mainly based on the easiness of use, the cost in CPU time and the confidence we can have in the results as a function of the boat speed. Flow visualizations, pressure maps, free surface deformation are shown and compared. Analysis of local quantities integrated or by zone is also presented. Results are analyzed focusing on the ability of each code to represent flow dynamics for every speed with a special attention to high speeds. The practical question raised is to know which kind of answers each code can bring in terms of tendencies evaluation or sensitivity to hull geometry modifications. The main goal is to be able to judge if those codes are able to make reliable and consistent comparisons of different designs. Conclusion is that none of the codes is perfect and gather all the advantages. It is still difficult to propose a definitive methodology to estimate hydrodynamic performances at every speed and at every stage of the design process. Knowing each code limitations, it appears more coherent to use each of them at different stages of the design process: the quickest and less reliable to understand the main tendencies and the longest and more precise to validate the final options.

scholarly journals Study of the Start Point of Optimization Trajectories for Complex Strategies of the Circuit Design Process

2021 ◽  
Vol 20 ◽  
pp. 133-139
Author(s):  
Alexander Zemliak
Keyword(s):  
System Design ◽  
Design Process ◽  
Circuit Design ◽  
Initial Point ◽  
Point Selection ◽  
Design Algorithm ◽  
Optimal Position ◽  
Starting Point ◽  
Dividing Surface ◽  
Selection Of

The different design trajectories have been analyzed in the design space on the basis of the new system design methodology. Optimal position of the design algorithm start point was analyzed to minimize the CPU time. The initial point selection has been done on the basis of the before discovered acceleration effect of the system design process. The geometrical dividing surface was defined and analyzed to obtain the optimal position of the algorithm start point. The numerical results of the design of passive and active nonlinear electronic circuits confirm the possibility of the optimal selection of the starting point of the design algorithm.

Designing a Pumping System of Gear Pumps Featuring the Involute Internal Gearing

2011 ◽  
Vol 490 ◽  
pp. 64-75
Author(s):  
Damian Słodczyk ◽  
Jarosław Stryczek
Keyword(s):  
Computer Program ◽  
Design Process ◽  
Design Algorithm ◽  
Pumping System ◽  
Hydraulic Machines ◽  
Gear Pumps ◽  
Engineering Drawings

On the basis of the analysed references it has been shown that an important problem in designing hydraulic machines is to develop a method of designing a pumping system of pumps with the internal gearing, which would integrate designing gears and compenstion elements. The authors of the paper has defined a design algorithm that consists of three basic stages: designing a concept of the system, designing the gear subsystem, and designing the compensation subsystem. The design process at particular stages have been described, and the results have been presented in engineering drawings. An original computer program 'Internal Pumping Set' which enhances the process of designing the pumping system has been created. An application of the program has been presented, and a design of an exemplary pumping system made.

Design of Dynamical Controllers for Linear Hamiltonian Systems

1999 ◽  
Author(s):  
Werner Haas ◽  
Michael Krommer ◽  
Hans Irschik
Keyword(s):  
Hamiltonian Systems ◽  
Controller Design ◽  
Time Derivative ◽  
Design Parameters ◽  
Internal Dynamics ◽  
Design Algorithm ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Linear Hamiltonian Systems ◽  
Frequency Domain Approach

Abstract Linear Hamiltonian control systems with collocation of sensor and actuator are considered. Based on a frequency domain approach a controller design algorithm is stated. The design leads to a controller with internal dynamics which uses the output of the system and its first time derivative. The presence of internal dynamics in the controller is an extension of the usual PD–control law and a main result of the work. The design is based on the special properties of the proposed class of systems. In particular, these Hamiltonian systems are passive. It is shown that the design leads to strictly passive controllers for a certain choice of the design parameters. This is another significant result and offers a way for robust ℒ2–stabilization even in the case of infinite dimensional systems. Some features of the controller design are discussed with respect to an application, the control of a composite circular plate.

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