Rotational motion control design for cart-pendulum system with Lebesgue sampling

This study addresses a discretization method with Lebesgue sampling for a type of nonlinear system, and proposes a control method based on the discrete system model. A cart pendulum system is used as this example. Applying this control method to some real system, how to implement the controller is a crucial problem. To overcome the problem, an impulsive Luenberger observer is introduced with a numerical forward mapping from the current system state to the one-step ahead state by well-known Runge-Kutta method. As the result, a cart pendulum system with a quantizer, whose quantization interval is relatively large, can be controlled effectively. Numerical simulations are performed to verify the effectiveness of the proposed method.