Modeling and Control of Dynamical Systems in Presence of Actuator and Sensor Based on Singular Perturbations Systems Approach

In this paper, the performance of a closed-loop dynamical system is investigated in the presence of controller, actuator and sensor. Usually, in analysis, the dynamics of sensor and actuator are assumed to be ideal and they are ignored however these components have dynamic practically. Since, the function speed of the sensor and the actuator must be more than the speed of dynamic system, it is reasonable to separate the equations of the closed-loop system, in the presence of the actuator and sensor, into slow equations (the dynamical system’s equations) and fast equations (equations of actuator and sensor). This paper focuses on this issue and the modeling of the closed-loop system in the structure of singular perturbation systems with the breakdown of fast and slow operating modes. Some theorems in the area of stability analysis and stabilization of the closed-loop system are given. Finally, simulations have been carried out for a mechanical example and it has been shown that the dynamics of the actuator and sensor should be faster than the dynamic system to achieve the desired results.