Nonlinear robust control of a hydraulic elevator: experiment-based modeling and two-stage Lyapunov redesign

In this paper, a robust velocity control problem for hydraulic elevators is investigated. The analysis is divided into two parts, mechanical and hydraulic. A detailed mathematical model for the mechanics is established for the purpose of simulation, but the control system design is carried out with a simplified model reduced from the detailed one. The three important characteristics of a hydraulic elevator, including cylinder friction, pump friction, and pump leakage, are modeled through experiments. The leakage property is characterized as a function of temperature and pressure. A two-stage nonlinear robust controller using the Lyapunov redesign method is established for velocity tracking control. At the first stage, a robust controller for the mechanical part is designed to yield the desired cylinder pressure for reference velocity tracking. At the second stage, a robust controller for the hydraulic part is designed to track the reference pressure generated from the first controller. Simulation results validate that the proposed method is robust in the presence of nonlinearities and uncertainties.