Adaptation of the control synthesized by the ACAR method to the control based on the implementation of the maximum principle

A special case of synthesizing the electromechanical control system by the maximum method and using the Analytical Construction method of Aggregate Regulators (ACAR) is considered in the article. For the basis the task of synthesizing the optimal for speed electromechanical positioning system was chosen, while the moment of resistance to movement linearly depended on the output coordinate of the system, that is, on the angle of the engine rotor rotation. Synthesis of the optimal system for speed makes it possible to increase the efficiency of the entire production process in many production tasks, and the synthesis of the optimal linear control system based on the maximum principle is a fairly well-formalized problem. Here it should be noted that the procedure for synergistic synthesis of the optimal control system has no such formalization. An approach that brings together the solutions obtained by these two methods, which makes it possible to increase the efficiency of the ACAR method by adding some features of the methodology for synthesizing optimal systems by introducing nonlinearity of the “saturation” type is proposed in the article. The results obtained made it possible to formulate the following basic scientific proposition: the synthesis of a control system based on the synergetic approach makes it possible to obtain a system close to optimal (quasi-optimal, but after the modification of the synergetic synthesis method itself.) Here we also formulate the hypothesis of a connection between the time constants, using the ACAR method, with the optimal control switching time determined in the maximum method.

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Estimation of proximity of controls synthesized on basis of maximum principle and ADAR method

Vestnik of Don State Technical University ◽

10.23947/1992-5980-2018-18-4-438-448 ◽

2019 ◽

Vol 18 (4) ◽

pp. 438-448

Author(s):

V. P. Lapshin ◽

I. A. Turkin ◽

V. V. Khristoforova

Keyword(s):

Control System ◽

Maximum Principle ◽

Position Control ◽

Synthesis Method ◽

Synthesis Problem ◽

Control Technique ◽

The Maximum Principle ◽

Synergistic Approach ◽

Time Optimal ◽

Synthesis Methodology

Introduction.A special case of synthesizing the same electromechanical control system by the Pontryagin maximum principle and by the synergetic synthesis method is considered. The task was to solve the synthesis problem of the time optimal electromechanical position control system; herewith the travel resistance modulus linearly depended on the output coordinate of the system. This approach to the selection of the synthesis problem was because the synthesis of time optimal systems is one of the most widespread problems, and it is solved by increasing the efficiency of the existing control systems.Materials and Methods.Synthesis of the time optimal linear control system based on the maximum principle is a widely accepted problem in the modern control theory. However, the procedure of synergistic synthesis does not have such formalization. This being the case, the paper suggests an approach that brings together these two methods, which, in our opinion, will increase the efficiency of the synergistic synthesis method through adding some features of the synthesis methodology for optimal systems.Research Results.The paper formulates two key concepts. The first one is as follows: the application of the maximum principle for an object of the DC motor class when synthesizing the positioning algorithm under the conditions of linear loading functionally dependent on the engine rotation angle allows the time optimal system to be optimized. The second concept states that synthesis of a control system based on the synergistic approach enables to obtain a system close to optimal (quasioptimal), but after modifying the synergetic synthesis method itself. A hypothesis is formulated on the possible connection between the introduced (when implementing the procedure of state space extension in the synergetic synthesis method) time constants with the optimal switching time of control defined in the maximum method.Discussion and Conclusions.The synthesis through the maximum control technique and the ADAR method is performed. In virtue of the comparison of efficiency of these methods, a hypothesis is put forward on the possible compatibility of the studied methods.

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Optimal Control of a General Environmental Space

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3143803 ◽

1986 ◽

Vol 108 (4) ◽

pp. 330-339 ◽

Cited By ~ 7

Author(s):

M. A. Townsend ◽

D. B. Cherchas ◽

A. Abdelmessih

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

Moisture Content ◽

Control Strategies ◽

Switching Control ◽

The Maximum Principle ◽

Environmental Space ◽

And Performance

This study considers the optimal control of dry bulb temperature and moisture content in a single zone, to be accomplished in such a way as to be implementable in any zone of a multi-zone system. Optimality is determined in terms of appropriate cost and performance functions and subject to practical limits using the maximum principle. Several candidate optimal control strategies are investigated. It is shown that a bang-bang switching control which is theoretically periodic is a least cost practical control. In addition, specific attributes of this class of problem are explored.

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