UDC 681.5
LQR DESIGN FOR A CMG INVERTED PENDULUM WITH NON-CONSTANT EQUILIBRIUM POSITION
I. V. Ryadchikov, Ph.D. (Phys. and Math.), Head of the Laboratory of Robotics and Mechatronics, Kuban State University, Krasnodar, Russia; This email address is being protected from spambots. You need JavaScript enabled to view it.
S. I. Sechenev, post-graduate student, Kuban State University, Krasnodar; This email address is being protected from spambots. You need JavaScript enabled to view it.
N. V. Mikhalkov, engineer of the Laboratory of Robotics and Mechatronics, Kuban State University, Krasnodar, Russia; This email address is being protected from spambots. You need JavaScript enabled to view it.
A. E. Biryuk, Ph.D. (Phys. and Math.), assistant professor of the Chair of Function Theory, Kuban State University, Krasnodar, Russia; This email address is being protected from spambots. You need JavaScript enabled to view it.
A. A. Svidlov, Ph.D. (Phys. and Math.), researcher, Department of Arid Zones, Laboratory of Problems of Distribution of Stable Isotopes in Living Systems, SSC RAS, Moscow, Russia; This email address is being protected from spambots. You need JavaScript enabled to view it.
A. A. Gusev, post-graduate student, Kuban State University, Krasnodar, Russia; This email address is being protected from spambots. You need JavaScript enabled to view it.
D. V. Sokolov, assistant professor of the University of Lorraine, Nancy, France; dmitry.sokolov@univlorraine.fr
E. V. Nikulchev, Ph.D. (Tech.), professor of the Chair of Systems Control and Modelling, MIREA – Russian Technological University, Moscow, Russia; This email address is being protected from spambots. You need JavaScript enabled to view it.
The task of developing a feedback control system for an inverted pendulum controlled by a control moment gyroscope (CMG) with a real-time revision of equilibrium position after the displacement of mass center is considered. The aim is to study and synthesize a linear-quadratic regulator capable of stabilizing the inverted pendulum with a CMG in a new equilibrium position. To build up a mathematical model of the control object, the Lagrangian of the inverted pendulum with a CMG and Euler-Lagrange equations are derived. The linearization of the model obtained is carried out near unbiased equilibrium position. It is shown that the problem of linear control synthesis has a solution in this case. Then the model is equipped with parametric quantity of instrumental error in determining the direction to the vertical, caused by the displacement of mass center. It is shown that in this case the system of linear equations will have an asymptotically stable stationary solution, while in the new equilibrium position the center of gravity of the inverted pendulum will be above the pivot point. The robustness check of the obtained control was implemented in a computer model built using MATLAB / Simulink and on an experimental plant. The characteristics of transient processes confirm the reliability of synthesized linear-quadratic control with the stabilization of the inverted pendulum with CMG in a new equilibrium position.
Key words: inverted pendulum, CMG, gyroscope, automatic control system, feedback, linear quadratic regulator, error in determining the position of the center of mass, robust control, simulation, MATLAB/Simulink.