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

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