Chemical and Petroleum Engineering

, Volume 55, Issue 7–8, pp 578–589

# Control Systems for Dynamic Processes with Single Degree of Freedom with Automatic Adaption of the Structure and Parameters of the System to an External Load

• N. I. Gdanskii
• A. É. Popovich
• A. V. Goncharov
• A. V. Karpov
AUTOMATION OF NUMERICAL ANALYSES AND DESIGN

An adaptive method of control of a system with single degree of freedom along a given trajectory of displacement under the conditions of unpredictable variation of a surmountable external load is set forth. Simulation of the load with the use of a special force vector that reflects the nature of its variation is proposed. The components of the force vector (averaged values of partial derivatives of the load with respect to time and spatial coordinate) are calculated from the working information which the control system receives at previous moments of displacement of the control object. The order of the model is the maximumorder of the derivatives included in the model. The general structure and derivation of formulas for models of zero, first and second order are given. The practical case of measurement of the angular displacement of a shaft using incremental encoders is given separately. Initially, direct load models are considered in which time is the independent variable. Then, for a drive with incremental encoders, inverse models are presented separately in which the angle of rotation of the output shaft is the independent coordinate. Conditions under which the adequacy of the parameters of the power vector and the redundancy and insufficiency of the order of the control model is estimated are considered separately. Based on these conditions, a general algorithm for the functioning of the control system by means of which both the parameters and the structure of the control system may be dynamically changed is given.

## Key words

adaptive control external load model direct model inverse model parameters and structure of the control system

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## Authors and Affiliations

• N. I. Gdanskii
• 1
Email author
• A. É. Popovich
• 1
• A. V. Goncharov
• 1
• A. V. Karpov
• 2
1. 1.Razumovskiy Moscow State University of Technologies and Control (First Cossack University)MoscowRussia
2. 2.Russian State Social UniversityMoscowRussia