Investigation into capabilities of a numerical method in designing automatic control systems for objects with a long time delay

• Main Authors: Pantiukhin, A., Sidorova, A., Emelyanova, T., Goncharov, V.
• Format: Conference Proceeding
• Language: English
• Subjects: Automatic control systems; Coefficients; Complexity; Control systems design; Controllers; Ill-conditioned problems (mathematics); Numerical analysis; Numerical methods; Regularization; Time lag; Transcendental functions; Transfer functions
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0071307

The paper addresses the problem of designing automatic control systems (ACS) for objects with transport delay. The mathematical description of such controlled objects and systems in general via Laplace images has a characteristic feature – the presence of a delay component model in the form of a transcendental expression. It prevents applying classical methods for the controller design that are successfully used in calculations of non-delay systems. Therefore, approximating the transcendental transfer function with a rational fraction is taken, but this approach introduces an error in calculations. However, there exists a numerical method that does not require replacing the transcendental function with a fractional rational expression, which suggests its potentially increased precision compared to the traditional variant of controller design. Hence, the objective of this work is to test this assumption, as well as to identify the possibly associated limitations of the selected method. Here, the most important quality performance indicator is the speed under constraints imposed on overshoot. The study of the ACS precision depending on the controller complexity was envisaged in the work program. The first order controller was taken as the initial. A sequential increase in the number of variable coefficients confirmed the predicted conclusion about the increased ACS speed, but this is only valid for controllers up to the second order, inclusive. The problem cannot be solved for a third-order controller with five unknown coefficients, due to ill-conditioning of the matrices. As demonstrated, a further increase in speed from the increased complexity of controllers requires special measures. These can include: regularization of the design equation, reduction in the number of required coefficients by setting some coefficients from a priori data, or their determination by some methods.