# A Novel Fixed-Time Super-Twisting Control with I&I Disturbance Observer for Uncertain Manipulators

## TL;DR

This paper introduces a new control method for robotic arms that improves precision and reduces unwanted vibrations, ensuring fast and reliable performance even with uncertain conditions.

## Contribution

A novel fixed-time super-twisting control with an I&I disturbance observer is proposed to ensure bounded convergence time and suppress chattering in uncertain robotic systems.

## Key findings

- The proposed controller achieves fixed-time convergence of tracking errors regardless of initial conditions.
- Control torque chattering is effectively eliminated using the new control strategy.
- Tracking error accuracy reaches as low as 2 × 10−9 in simulations.

## Abstract

This paper proposes a novel fixed-time super-twisting sliding mode control (ST-SMC) strategy for uncertain robotic arm systems, aiming to address the issues of control chattering and the uncontrollable upper bound of convergence time in traditional sliding mode control algorithms. The proposed approach enhances system robustness, suppresses chattering, and ensures that the convergence time of the robotic arm can be explicitly bounded. First, a sliding surface with fixed-time convergence characteristics is constructed to guarantee that the tracking errors on this surface converge to the origin within a prescribed time. Then, an immersion and invariance (I&I) disturbance observer with exponential convergence properties is designed to estimate large, time-varying disturbances in real time, thereby compensating for system uncertainties. Based on this observer, a new super-twisting sliding mode controller is developed to drive the trajectory tracking errors toward the sliding surface within fixed time, achieving global fixed-time convergence of the tracking errors. Simulation results demonstrate that, regardless of the initial conditions, the proposed controller ensures fixed-time convergence of the tracking errors, effectively eliminates control torque chattering, and achieves a tracking error accuracy as low as 2 × 10−9. These results validate the proposed method’s applicability and robustness for high-precision robotic systems.