Comparison of control methods for inverted 2-degree of freedom pendulum mounted on the cart

Abstract

The paper considers and analyzes the existing methods of controlling systems with a deficit of control actions. Based on the analysis, it was decided to use linear controllers with feedback on the state vector of the system and to compare these methods - modal and linearquadratic. For the study, a dynamic model was chosen, which is an inverted 2-degree of freedom (2DOF) pendulum mounted on a cart. By an iterative method, acceptable system of generalized coordinates that definitely describes the state of the model was selected. Kinematic relations that describe the position of the model in generalized coordinates were derived. Using the Lagrange procedure, a system of nonlinear differential equations describing the motion of a dynamic model was obtained. The procedure of model linearization about the upright equilibrium point was also carried out in order to synthesize control system. Based on the results of modeling, which was carried out by numerical integration method in the Matlab environment, conclusions were drawn on the applicability of these control methods and their effectiveness.