The task of modal control of a two-mass electromechanical system
DOI:
https://doi.org/10.34185/1562-9945-3-128-2020-01Keywords:
електромеханічна система, частота коливань, модальний регулятор, поліном, матриця, перехідний процес, перерегулюванняAbstract
In this paper, an example of a block diagram of a control system for an electromechanical two-mass object, taking into account the dynamics of the drive. The control of the system is based on such state variables as: angle of rotation; angular velocities of the first and second masses; elastic component of elastic moment. The system description is provided in the state space in vector-matrix form, which is suitable for further analysis and synthesis of the control system.
A mathematical model of the fourth-order electromechanical system was developed taking into account the availability of measurements of all state variables. The calculation of the values of the poles of the system with a modal controller is performed, and the transients are obtained and studied for the standard forms of the Butterworth polynomial and the Newton polynomial for the fourth order of the system.
Mathematically described control object in the form of a two-mass electromechanical system with adjustment of modal controller parameters in MATLAB program. Methods for obtaining linear feedback by state vector are investigated. Transitions were obtained and investigated when used for debugging a modal Newton polynomial controller and a Butterworth polynomial for a fourth-order system, with recommendations for future use in a Butterworth polynomial system that produces less static error.
In the case of the Butterworth polynomial, the static error is 6% and in the Newton polynomial the error is 12%. The overregulation of the system in the Butterworth polynomial is significantly greater than in the Newton polynomial, respectively, the pulsation is also larger. An overregulation of less than 15% is acceptable for a given system.
The model of the two-mass electromechanical system, obtained in the paper, provides for the availability of measurements of all state variables, which in some cases is not possible. The obtained model of the electromechanical system is ready for further use in systems with state observers, where it is possible to restore variables that are unavailable for measurement with the exception of the installation of additional measuring sensors.
References
Popovich M.G. The theory of automatic control / M.G. Popovich,
O.V. Kovalchuk. - K: Libid, 2007. - 656 p.
Meleshkin A. I. Modal synthesis of low-order regulators / A. I. Meleshkin. - Novosibirsk, 1999 . – 76 p.
Pankratov V.V. Special sections of the theory of automatic control. Part 1. Modal management and observers /V.V. Pankratov. -Novosibirsk, 2011.–187p.
Modal control of interconnected electric drives with elastic links and gaps in kinematic gears / V. A. Ivankov, S. V. Tararykin, V. V. Tyutikov, V. V. Krasilnikyanets. // Bulletin of the ISEU. - 2006. - №. 3. - Р. 6–12.
Kochnev N. V. Modal control of non-rigid electromechanical systems in metallurgy [Electronic resource] / N. V. Kochnev, T. N. Kochneva // Modern equipment and technologies. 2015. - 2015. – Access mode to the resource: http://technology.snauka.ru/2015/04/6296.
