# Modelling and Fast Terminal Sliding Mode Control for Mirror-based Pointing Systems

## TL;DR

This paper introduces a novel discrete-time Fast Terminal Sliding Mode controller for mirror-based pointing systems, demonstrating improved transient response and stability through simulations and real-time experiments.

## Contribution

The paper develops a new discrete-time FTSM controller with a decoupled system model, parameter estimation, and stability proof, outperforming existing TSM and MPC methods.

## Key findings

- Enhanced transient dynamics with added linear term
- Superior performance over TSM and MPC in simulations
- Validated effectiveness through real-time experiments

## Abstract

In this paper, we present a new discrete-time Fast Terminal Sliding Mode (FTSM) controller for mirror-based pointing systems. We first derive the decoupled model of those systems and then estimate the parameters using a nonlinear least-square identification method. Based on the derived model, we design a FTSM sliding manifold in the continuous domain. We then exploit the Euler discretization on the designed FTSM sliding surfaces to synthesize a discrete-time controller. Furthermore, we improve the transient dynamics of the sliding surface by adding a linear term. Finally, we prove the stability of the proposed controller based on the Sarpturk reaching condition. Extensive simulations, followed by comparisons with the Terminal Sliding Mode (TSM) and Model Predictive Control (MPC) have been carried out to evaluate the effectiveness of the proposed approach. A comparative study with data obtained from a real-time experiment was also conducted. The results indicate the advantage of the proposed method over the other techniques.