Optimal Control of Technological Processes

The paper formulates conditions under which the roots closest to the imaginary axis (critical roots) of the characteristic equation of a linearized system are real for the maximum possible degree of stability of the closed-loop control system of a technological process with pure delay. For the param...

Full description

Saved in:
Bibliographic Details
Published inProcesses Vol. 11; no. 6; p. 1835
Main Authors Tsirlin, Anatoliy M., Balunov, Alexander I.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.06.2023
Subjects
Closed loops
Control stability
Control systems
Control theory
Controllers
Dynamic characteristics
Dynamic stability
Eigenvalues
Eigenvectors
Feedback control
Injection molding
Laws, regulations and rules
Mathematical analysis
Optimal control
Optimization
Parameter modification
Robust control
Stability analysis
Systems stability
Transfer functions
Russia
Online AccessGet full text

Cover

More Information
Summary:The paper formulates conditions under which the roots closest to the imaginary axis (critical roots) of the characteristic equation of a linearized system are real for the maximum possible degree of stability of the closed-loop control system of a technological process with pure delay. For the parameters of the controllers corresponding to the maximum degree of stability, these roots are multiples. Their multiplicity order is one more than the number of coefficients in the transfer function of the controller. It is demonstrated that for a typical technological control object, these conditions are satisfied for all “serial” control laws. This allowed for obtaining analytical expressions for optimal settings and limiting degrees of stability as functions of object parameters for typical dynamic characteristics of technological processes. The paper considers the problem of robust stability for control systems with an object containing pure delay. It has been proven that in the maximum stability problem, the operations of maximizing over controller parameters and minimizing over the set of possible object parameters can be interchanged. Therefore, selecting robust settings amounts to determining the minimum of the maximum stability over the set of possible object parameter values. Controllers with such settings are suitable, without modification, for a whole class of technological processes.
ISSN:2227-9717
2227-9717
DOI:10.3390/pr11061835