scholarly journals Two-channel time-optimal control of nonstationary heat conductive process with account for response time of boundary control actions

2021 ◽  
Vol 29 (2) ◽  
pp. 47-60
Author(s):  
Natalya A. Il’ina
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Parabolic Type ◽  
Time Optimal Control ◽  
Optimal Time ◽  
Time Control ◽  
Distributed Parameters ◽  
Control Actions ◽  
Optimal Controllers ◽  
Time Optimal

The task of organization a closed time-optimal control system of linear object with distributed parameters of parabolic type is considered. The object has two lumped internal controls for the power of heat sources excited in the electromagnetic field of an inductor. The proposed method for the synthesis of optimal controllers uses an alternance method for calculating the optimal program controls for each of the control actions. An example of the construction of a quasi-optimal time control system for the process of periodic induction heating of a metal workpiece with constant values of the feedback coefficients calculated for the most characteristic initial spatial distribution is given.

scholarly journals Two-channel time-optimal control of induction heating process with maximum temperature constraint

2020 ◽  
Vol 28 (2) ◽  
pp. 41-58
Author(s):  
Natalya A. Il`ina
Keyword(s):  
Optimal Control ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Induction Heating ◽  
Time Optimal Control ◽  
Maximum Temperature ◽  
Heating Process ◽  
Problem Of Time ◽  
Control Actions ◽  
Time Optimal

The formulation and method of solution of the problem of time-optimal control of induction heating process of an unlimited plate with two control actions on the value of internal heat sources with technological constraint in relation to a one-dimensional model of the temperature field are proposed. The problem is solved under the conditions of a given accuracy of uniform approximation of the final temperature distribution over the thickness of the plate to the required. The method of finite integral transformations is used to search for the input-output characteristics of an object with distributed parameters with two control actions. The preliminary parameterization of control actions based on analytical optimality conditions in the form of the Pontryagin maximum principle is used. At the next stage reduction is performed to the problem of semi-infinite optimization, the solution of which is found using the alternance method. The alternance properties of the final resulting temperature state at the end of the optimal process lead to a basic system of relations, which, if there is additional information about the shape of the temperature distribution curve, is reduced to a system of equations that can be solved. An example of solving the problem of time-optimal control of temperature field of an unlimited plate with two offices is carried out in two stages. At first stage the case of induction heating without maximum temperature constraints is considered, at the second stage is carried out on the basis of the results of the first stage to obtain the solution subject to the limitation on the maximum temperature of the heated billet.

scholarly journals Single-Switching Reachable Operation Points in a DC-DC Buck Converter: An Approximation from Time Optimal Control

Micromachines ◽  
2020 ◽  
Vol 11 (9) ◽  
pp. 834
Author(s):  
Ilya Dikariev ◽  
Fabiola Angulo ◽  
David Angulo-Garcia
Keyword(s):  
Optimal Control ◽  
Load Resistance ◽  
Buck Converter ◽  
Time Optimal Control ◽  
Optimal Time ◽  
Oscillatory Regime ◽  
Analytic Expressions ◽  
Time Optimal ◽  
Switching Action ◽  
Time Optimal Control Problem

In this paper, we study the time optimal control problem in a DC-DC buck converter in the underdamped oscillatory regime. In particular, we derive analytic expressions for the admissible regions in the state space, satisfying the condition that every point within the region is reachable in optimal time with a single switching action. We then make use of the general result to establish the minimum and maximum variation allowed to the load in two predefined design set-ups that fulfills the time optimal single switching criteria. Finally, we make use of numerical simulations to show the performance of the proposed control under changes in the reference voltage and load resistance.

Applying bilinear time‐optimal control system in boost converters

2014 ◽  
Vol 7 (4) ◽  
pp. 850-860 ◽  
Author(s):  
Jalal Nazarzadeh ◽  
Mohammad Javad Jafarian
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Time Optimal Control ◽  
Boost Converters ◽  
Optimal Control System ◽  
Time Optimal

A time-optimal boundary controllability problem for the heat equation in a ball

2014 ◽  
Vol 144 (6) ◽  
pp. 1171-1189 ◽  
Author(s):  
Sorin Micu ◽  
Laurenţiu Emanuel Temereancă
Keyword(s):  
Optimal Control ◽  
Heat Equation ◽  
Parabolic Type ◽  
Time Optimal Control ◽  
Main Ingredient ◽  
Controllability Problem ◽  
Boundary Controllability ◽  
Müntz Polynomials ◽  
Time Optimal ◽  
Dimensional Ball

The aim of this paper is to study a boundary time-optimal control problem for the heat equation in a two-dimensional ball. The main ingredient is the extension of a result concerning Müntz polynomials due to Borwein and Erdélyi that allows us to prove an observability inequality for the dynamical system's truncation to a finite number of modes. This result, combined with a well-known Lebeau–Robbiano argument used to show the null-controllability of parabolic type equations, enables us to deduce the existence, uniqueness and bang-bang properties for the boundary time-optimal control.

Time Optimal Swing-Up Control of Single Pendulum1

2000 ◽  
Vol 123 (3) ◽  
pp. 518-527 ◽  
Author(s):  
Yongcai Xu ◽  
Masami Iwase ◽  
Katsuhisa Furuta
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Auxiliary Problem ◽  
Terminal State ◽  
Time Optimal Control ◽  
Necessary Condition ◽  
Optimal Time ◽  
Input Amplitude ◽  
Time Optimal ◽  
Bounded Input

Swing-up of a rotating type pendulum from the pendant to the inverted state is known to be one of most difficult control problems, since the system is nonlinear, underactuated, and has uncontrollable states. This paper studies a time optimal swing-up control of the pendulum using bounded input. Time optimal control of a nonlinear system can be formulated by Pontryagin’s Maximum Principle, which is, however, hard to compute practically. In this paper, a new computational approach is presented to attain a numerical solution of the time optimal swing-up problem. Time optimal control problem is described as minimization of the achievable time to attain the terminal state under the bounded input amplitude, although algorithms to solve this problem are known to be complicated. Therefore, in this paper, it is shown how the optimal time swing-up control is formulated as an auxiliary problem in that the minimal input amplitude is searched so that the terminal state satisfies a specification at a given time. Through the proposed approach, time optimal control can be solved by nonlinear optimization. Its approach is evaluated by numerical simulations of a simplified pendulum model, is checked satisfying the necessary condition of Maximum Principle, and is experimentally verified using the rotating type pendulum.

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