# Posture Control of Hydraulic Flexible Second-Order Manipulators Based on Adaptive Integral Terminal Variable-Structure Predictive Method

## TL;DR

This paper introduces a new control method for hydraulic flexible manipulators to improve tracking accuracy and reduce torque fluctuations in complex industrial tasks.

## Contribution

The novel DITSMPC method integrates adaptive sliding mode control with predictive time domain functions to reduce system buffeting and improve precision.

## Key findings

- The DITSMPC method achieves smooth torque changes with an integral of torque variations of 5.22×10³.
- Trajectory tracking errors for each joint remain within ±0.0025 rad, outperforming classical methods.
- The proposed method effectively weakens the buffeting effect of sliding mode control.

## Abstract

As operational scenarios become more complex and task demands intensify, the requirements for the intelligence and automation of manipulators in industry are increasing. This work investigates the challenge of posture tracking control for hydraulic flexible manipulators by proposing a discrete-time integral terminal sliding mode predictive control (DITSMPC) method. First, the proposed method develops a second-order dynamic model of the manipulator using the Lagrangian dynamic strategy. Second, a discrete-time sliding mode control (SMC) law based on an adaptive switching term is designed to achieve high-precision tracking control of the system. Finally, to weaken the influence of SMC buffeting on the manipulator system, the predictive time domain function is integrated into the proposed SMC law, and the delay estimation of the unknown term in the manipulator system is carried out. The DITSMPC scheme is derived and its convergence is proven. Simulation experiments comparing the DITSMPC scheme with the classical discrete-time SMC method demonstrate that the proposed scheme results in smooth torque changes in each joint of the manipulator, with the integral of torque variations being 5.22×103. The trajectory tracking errors for each joint remain within ±0.0025 rad, all of which are smaller than those of the classical scheme.