Stabilizing control for linear systems with low resolution sensors

Discretization and Control of Rotating Pendulum under Lebesgue Sampling

“…Thus the system states are estimated with regard to quantization using the ILO [6,8]. In the ILO, the estimated statex at quanti-…”

“…In fact, this assumption is valid only if the pendulum is provided with a sensor to measure its angular velocity. To solve this problem, we will later use numerical integration in combination with ILO [8].…”

“…In this paper, we consider a cart and pendulum as an example of a nonlinear system, and extend the previous study [8] by proposing a control system design ( Fig. 1) to update the control input synchronously with quantization of the pendulum angle.…”

“…Therefore, updating a control input when new system information arrives via a network seems a natural approach, which can be interpreted as event-based control. Montestruque and Antsaklis investigated this issue and proposed an interesting method of model-based control for networked systems [7] that has much in common with our previous study of Lebesgue sampling [8].…”

“…In this method, however, one must estimate states that cannot be directly observed in the real system. For this purpose, we numerically discretize of motion of the cart-pendulum system by the Runge-Kutta method, then apply an impulsive Luenberger observer (ILO) [8]. We show that by such coupling of servo control with an observer, a control system can be designed with regard to the quantization width of the pendulum angle and corresponding intervals of Lebesgue sampling.…”