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 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.

Study on Electromagnetic Heating Process of Wind Power Gear: Temperature Morphology and Evolution

2020 ◽  
Vol 13 (3) ◽  
Author(s):  
Huaiyu Wen ◽  
Yi Han ◽  
Xiaobo Zhang ◽  
Feng Liu ◽  
Hongwang Zhang
Keyword(s):  
Temperature Field ◽  
Temperature Distribution ◽  
Wind Turbine ◽  
Tooth Profile ◽  
Maximum Temperature ◽  
Heating Process ◽  
Central Section ◽  
Maximum Temperature Difference ◽  
Constant Change ◽  
Boltzmann Function

Abstract As a key component of wind turbine, the surface strengthening treatment of wind turbine gear is crucial to enhance its performance and service life. In the process of tooth-by-tooth induction heating, clear temperature distribution and process evolution could realize the lean control of heating effect and quality. In this article, the tooth-by-tooth heating process under the v-shaped inductor was studied to analyze the temperature field morphology and its evolution process. The results show that in the tooth profile region, the boundary morphology of the temperature field near the central section of the heating region conforms to the Boltzmann function, while the far sections conform to the normal distribution. At the end of heating, from the surface to the depth of the heating layer and from the heating center to both sides, both the maximum temperature difference and the distribution temperature are reduced. Meanwhile, the maximum temperature point near the central section is offset during the evolution of the temperature field morphology. The change of physical properties of materials and induced eddy distribution caused by involute structure and the constant change of temperature gradient are the fundamental reasons for the appearance of nonuniform temperature field and temperature excursion. The spatiotemporal variation of the hottest point was found, and the temperature morphology and evolution were revealed, which would provide a theoretical basis for adjusting the temperature distribution of tooth profile according to the requirements of different heating layers.

Discrete Adjoint Sensitivities for the Real-Time Optimal Control of Large District Heating Networks During Failure Events

2016 ◽  
Author(s):  
Alberto Pizzolato ◽  
Adriano Sciacovelli ◽  
Vittorio Verda
Keyword(s):  
Optimal Control ◽  
Temperature Field ◽  
Real Time ◽  
Control Strategy ◽  
District Heating ◽  
Time Optimal Control ◽  
The Real ◽  
Discrete Adjoint ◽  
Time Optimal ◽  
Heating Networks

In this paper, we propose an innovative approach for the real-time optimal control of district heating networks during anomalous conditions. We aim at minimizing the maximum thermal discomfort of the connected users after a pipe breakage by an integrated and centralized management of the user control-valves. Our control strategy uses a gradient-based optimizer driven by discrete adjoint sensitivities, which makes it fast and nearly insensitive to the problem dimensions. We tested the proposed approach by simulating a set of different malfunctions in the Turin District heating network and by analyzing the building temperature field during the optimizer convergence history. Compared to the control strategy in use today, we observe that our approach flattens the temperature field and eliminates discomfort peaks, bringing a considerable increase of the minimum user temperature which ranges from a minimum of 1.8 °C to a maximum of 15.4 °C. Furthermore, our optimization strategy allows for superior results to what is achievable conventionally with an 85 % increase of the pumping head, making back-up pumping devices a non-necessary investment.

scholarly journals Time-optimal control of fractional-order linear systems

2015 ◽  
Vol 18 (3) ◽  
Author(s):  
Ivan Matychyn ◽  
Viktoriia Onyshchenko
Keyword(s):  
Optimal Control ◽  
Linear Systems ◽  
Control Function ◽  
Terminal State ◽  
Time Optimal Control ◽  
Fractional Dynamics ◽  
Support Functions ◽  
Problem Of Time ◽  
Time Optimal ◽  
Control Of Linear Systems

AbstractThe problem of time-optimal control of linear systems with fractional dynamics is treated in the paper from the convex-analytic standpoint. A linear system of fractional differential equations involving Riemann- Liouville derivatives is considered. A method to construct a control function that brings trajectory of the system to the terminal state in the shortest time is proposed in terms of attainability sets and their support functions

Time Optimal Control of Balanced Manipulators

1989 ◽  
Vol 111 (2) ◽  
pp. 187-193 ◽  
Author(s):  
W. S. Newman ◽  
N. Hogan
Keyword(s):  
Optimal Control ◽  
Efficient Algorithm ◽  
Difficult Problem ◽  
Time Optimal Control ◽  
Restricted Class ◽  
Moving Targets ◽  
Problem Of Time ◽  
Time Optimal ◽  
On Line ◽  
Point To Point

An efficient algorithm is presented for solving time-optimal control for a restricted class of manipulators: balanced, decoupled manipulators. It is shown how the dynamics of such manipulators are sufficiently simple that optimal control solutions for point-to-point moves can be found analytically. A change of coordinates is proposed in which the more difficult problem of time-optimal interception of moving targets can be solved efficiently. A fast algorithm is described for computing and updating optimal interception solutions on line.

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