Polynomial-based Stability Analysis of Modified IMC-PID Controller for Piezoelectric Actuator System in Time Delay Environment

Piezoelectric actuators are widely used in several industrial applications requiring precision positioning. However, the positioning accuracy of this nonlinear actuator is severely limited by physical phenomenon such as hysteresis, uncertainties. Accordingly, to improve the performance of piezo micro-nano positioning system, appropriate control laws are designed to linearize the hysteresis through closed-loop approaches. A modified internal model controller (MIMC) is useful with regard to efficient computational hardware resource utilization when compared with the conventional approach provided the resulting controller is stable. This paper focuses on one such widely used and computationally inexpensive control framework in the form of PID-based MIMC to mitigate hysteretic nonlinearity in piezoelectric actuators with the aim to investigate the time delay uncertainty handling range of the controller. The system stability pertaining to time delay has been analyzed numerically and the maximum delay that the system can withstand without losing its stability, i.e. the delay margin has been determined using polynomial-based approach. It has been found that upon increasing the delay beyond a specific critical value, the controller performance is limited and the system turns unstable. Simulations carried out in time delay environment validate the theoretically achieved results.