LPV H∞ Control with an Augmented Nonlinear Observer for Sawyer Motors

Khac Huan Su,Youngwoo Lee,Kwankyun Byeon,Wonhee Kim

doi:10.3390/math10010018

Khac Huan Su, Youngwoo Lee + Show 2 more

Open Access

https://doi.org/10.3390/math10010018

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Journal: Mathematics	Publication Date: Dec 21, 2021
Citations: 1	License type: CC BY 4.0

Affiliation: Chonnam National University, Chung-Ang University

Abstract

This study presents LPV H∞ control with an augmented nonlinear observer (ANOB) to improve both the position and yaw tracking errors for Sawyer motors. The proposed control method consists of the forces and torque modulation scheme, an ANOB, and a Lyapunov-based current controller with the LPV H∞ state feedback controller to guarantee the stability of tracking error dynamics. The ANOB is designed to estimate all the state variables including the position, velocity, current, and disturbance using only position feedback. We propose a vertex expansion technique to solve the influence of the convex interpolation parameters in the LPV system on the tracking error performance. To be robust against disturbance, a state feedback controller with the LPV gain scheduling is determined by applying the H∞ control in the linear-matrix-inequality (LMI) technique. The closed-loop stability is proved through the Lyapunov theory. The effectiveness of the proposed control method is evaluated through simulation results and compared with the conventional proportional-integral-derivative (PID) control method to verify both the improved tracking error performance and a suitable disturbance rejection.

Highlights

In high-precision motion control, Sawyer motors have been widely used to achieve the strict requirements in position ControlThese motors play an extremely important role in automated assembly lines, precision machining tools, and semiconductor wafer stage systems
The proposed control method consists of the forces and torque modulation scheme, an augmented nonlinear observer (ANOB), and a Lyapunov-based current controller with the linear parameter varying (LPV) H∞ state feedback controller
The forces and torque modulation scheme is developed to guarantee the stability of the position and yaw tracking errors for the mechanical tracking error dynamics and to generate the desired phase currents

Summary

Introduction

In high-precision motion control, Sawyer motors have been widely used to achieve the strict requirements in position ControlThese motors play an extremely important role in automated assembly lines, precision machining tools, and semiconductor wafer stage systems. The motor has high position resolution and speed motion in the open-loop microstepping ControlHowever, it can have step-out, a long settling time, and especially low disturbance compensation These problems are closely related to the yaw motion control that degrades the position tracking performance. In the context of the previous studies mentioned above, the augmented nonlinear observer design is essential for the Sawyer motors to improve the transient response in position control in the presence of disturbance. The main contribution of this study was to design the LPV H∞ control with an ANOB to reduce both the position and yaw tracking errors for the Sawyer motors in the presence of disturbance. The proposed control method consists of the forces and torque modulation scheme, an ANOB, and a Lyapunov-based current controller with the LPV H∞ state feedback controller.

Mathematical Model of Sawyer Motor

Forces and Torque Modulation Scheme

Lyapunov-Based Current Controller

Vertex Expansion Technique

Augmented Nonlinear Observer

Simulation Results

Conclusions