## Control Systems and Computers, N5, 2018, Article 8

##### DOI: https://doi.org/10.15407/usim.2018.05.079

Upr. sist. maš., 2018, Issue 5 (277), pp. 79-92.

UDC 681.5

Klavdiya Yu. Solovchuk, PhD Student, International Research and Training Centre of Information Technologies and Systems of the NAS and MES of Ukraine, Glushkov ave., 40, Kyiv, 03680, Ukraine, solovchuk_ok@ukr.net

### Mathematical models for typical continued computer-oriented process control

Introduction. The modern stage of technical progress is characterized by the emergence of new highly effective automatic systems for various process control based on software and hardware of digital computers. The requirements to performance indexes of these systems increase all time. To design modern process control, some description of the corresponding class of processes in the form of a certain mathematical model is necessary.

Purpose of this paper is to conduct the system analysis of existing mathematical models for different multivariable process control found in literature and to order these models leading they to a unified but simple enough form to be convenient for the computer-aided control.

Methods. To give an appropriate description of typical processes in the mathematical form, both the fundamental balances of momentum, energy and material for the process and the experimental data are employed. Novel and traditional techniques are needed for deriving of the process models in the discrete-time form.

Results. The mathematical models for typical interconnected mechanical, hydromechanical, heat and mass transfer processes are presented. They may be described by the linear (linearized) differential equations to be suitable for their implementation in digital computer-oriented process control systems after transforming to the discrete-time form. Some specific features intrinsic to certain classes of these processes are established.

Conclusion. A unification of the mathematical models for different interconnected processes makes it possible to design the modern computer process control based on a uniform point of view. Again, the facts that the gain matrices which may appear in the equations describing their models may be ill-conditioned or even singular, should be taken into account.

Keywords: typical process, mathematical model, interconnected plant, discrete time.

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