# Full- and Reduced-order Model of Hydraulic Cylinder for Motion Control

## TL;DR

This paper develops and compares full- and reduced-order nonlinear models of hydraulic cylinders, enabling improved system analysis and motion control design by capturing key dynamics and simplifying for practical use.

## Contribution

It introduces a comprehensive fifth-order nonlinear model and a simplified second-order reduced model for hydraulic cylinders, facilitating analysis and control design.

## Key findings

- Full model captures valve spool dynamics and nonlinearities.
- Reduced model simplifies analysis by neglecting fast valve dynamics.
- Both models provide insights into frequency response and system damping.

## Abstract

This paper describes the full- and reduced-order models of an actuated hydraulic cylinder suitable for system dynamics analysis and motion control design. The full-order model incorporates the valve spool dynamics with combined dead-zone and saturation nonlinearities - inherent for the orifice flow. It includes the continuity equations of hydraulic circuits coupled with the dynamics of mechanical part of cylinder drive. The resulted model is the fifth-order and nonlinear in states. The reduced model neglects the fast valve spool dynamics, simplifies both the orifice and continuity equations through an aggregation, and considers the cylinder rod velocity as output of interest. The reduced model is second-order that facilitates studying the system behavior and allows for direct phase plane analysis. Dynamics properties are addressed in details, for both models, with focus on the frequency response, system damping, and state trajectories related to the load pressure and relative velocity.