# Adaptive Internal Model Backstepping Control for a Class of Second-Order Electromagnetic Micromirror with Output Performance Constraints and Anomaly Control

## TL;DR

This paper proposes a new control method for electromagnetic micromirrors to ensure accurate tracking and performance under uncertain conditions.

## Contribution

A novel internal model backstepping controller is introduced to handle output constraints and anomalies in micromirror systems.

## Key findings

- The controller satisfies output performance constraints of the micromirror.
- It maintains performance in anomalous control situations.
- Simulations confirm the effectiveness of the proposed method.

## Abstract

This paper investigates the asymptotic tracking problem for a class of second-order electromagnetic micromirror model with output performance constraints and anomaly control, which is subject to model parameter uncertainties and external disturbances. Specifically, this paper formulates the trajectory tracking control problem of an electromagnetic micromirror as a closed-loop control trajectory tracking problem based on the general solution framework of output regulation. Moreover, the extended internal model is introduced to reformulate the closed-loop control problem into a state stabilization problem of the augmented system. Based on the augmented system, an internal model backstepping controller is proposed by integrating the barrier Lyapunov Functions (BLF) and the Nussbaum gain function with the backstepping structure.This controller not only satisfies the output performance constraints of the micromirror, but also maintains the control performance in anomalous control situations. The final performance simulation demonstrates the efficacy of the proposed controller.