Synthesis of a robust positional electric drive control system based on h2-optimization
Keywords:
regulator, electric drive, control system, optimization, disturbance, robust controlAbstract
The synthesis of a robust control system for a DC positional electric drive with an H2-optimal position controller, operating under conditions of incomplete information about the object and taking into account its structural uncertainties is presented in the article. Its importance is due to the fact that in almost any engineering problem of designing of control system there is an uncertainty (or error) in the object model (the mathematical model of the object obtained on the basis of theory or as a result of identification differs from a real technical system) and in the knowledge of the class of input disturbances. In the work, a positional electric drive with a DC drive motor and a controlled transistor converter for powering the motor armature circuit was adopted as a control object. In the mathematical description of the object, the magnetic flux of the motor is assumed to be constant, the influence of the armature reaction and eddy currents is not taken into account (the motor is compensated). The authors proposed a block diagram of the power part of the control object, on which the direct current motor is presented in the form of aperiodic and integrating links connected in series, covered by a rigid negative feedback in the direction of the counter-EMF machine. The algorithm of the H2-optimal controller is considered. To solve the H2-optimization problem, two Hamilton matrices were introduced, corresponding to the algebraic Riccati equation for control and filtration. When synthesizing a robust H2-optimal position controller, the Robust Control Toolbox → Controller Synthesis package of the Matlab system was used, which made it possible to calculate the central controller that minimizes the H2-norm of the closed-loop system according to the presented algorithms. The obtained H2-optimal controller is a fourth-order controller. Using the «2 - Riccati approach» it was shown that under certain conditions the H2-theory of control (LQG-theory) is the limiting case of the H∞-theory. The synthesized H2-optimal controller provides the necessary accuracy of working out the specified displacements and the degree of sensitivity to parametric and coordinate disturbances that acting on the object.
References
1. Робастное управление синхронным электроприводом: Монография / Е.В. Полилов, Е.С. Руднев, С.П. Скорик. – Алчевск: ДонГТУ, 2012. – 253 с.
2. H∞ Robust Control of Permanent-Magnet Synchronous Motors: Performance Analysis / E. Rudnev, D. Morozov, V. Gritsyuk, R. Brozhko // 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering (UKRCON), 2019, pp. 596-600.
3. Полилов Е.В., Зеленов А.Б., Руднев Е.С. Синтез робастного H∞-субоптимального регулятора положения позиционного электропривода // Вісник Кременчуцького державного технічного університету ім. Михайла Остроградського. – Кременчук: КДПУ. – 2008. – Ч. 1; № 3 (50). – С.64-71.
4. Методы робастного, нейро-нечеткого и адаптивного управления: Учебник / Под ред. Н.Д. Егупова; издание 2-ое, стереотипное. – М.: МГТУ им. Н.Э. Баумана, 2002. – 744 с.
5. Grimble M.J., Biss D. Selection of Optimal Control Weighting Functions to Achieve Good H∞ Robust Designs // Proceedings of IEE International Conference Control 88, Conference Publication. – 1988. – № 285.
6. Doyle J.С, Glover К., Khargonekar P.P., Francis B.A. State-space solutions to standard H2 and H∞ control problems // IEEE Transactions on Automatic Control, AC-34. – 1989. – Vol. 34; №8. – pp.831-847.
