'Constant in gain Lead in phase' element - Application in precision motion control

Abstract

This work presents a novel 'Constant in gain Lead in phase' (CgLp) element using nonlinear reset technique. PID is the industrial workhorse even to this day in high-tech precision positioning applications. However, Bode's gain phase relationship and waterbed effect fundamentally limit performance of PID and other linear controllers. This paper presents CgLp as a controlled nonlinear element which can be introduced within the framework of PID allowing for wide applicability and overcoming linear control limitations. Design of CgLp with generalized first order reset element (GFORE) and generalized second order reset element (GSORE) (introduced in this work) is presented using describing function analysis. A more detailed analysis of reset elements in frequency domain compared to existing literature is first carried out for this purpose. Finally, CgLp is integrated with PID and tested on one of the DOFs of a planar precision positioning stage. Performance improvement is shown in terms of tracking, steady-state precision and bandwidth.

References in corpus (2)

• Resetting Disturbance Observers with application in Compensation of bounded nonlinearities like Hysteresis in Piezo-Actuators
• No More Differentiator in PID:Development of Nonlinear Lead for Precision Mechatronics

Cited by in corpus (15)

• Loop-shaping for reset control systems -- A higher-order sinusoidal-input describing functions approach
• The optimal sequence for reset controllers
• Fractional-Order Single State Reset Element
• Continuous reset element: Transient and steady-state analysis for precision motion systems
• A Frequency-Domain Stability Method for Reset Systems
• Tuning of Constant in gain Lead in phase (CgLp) Reset Controller using higher-order sinusoidal input describing function (HOSIDF)
• Band-Passing Nonlinearity in Reset Elements
• Complex order control for improved loop-shaping in precision positioning
• Benefiting from Linear Behaviour of a Nonlinear Reset-based Element at Certain Frequencies
• Reset Control for Vibration Disturbance Rejection
• Frequency Response Analysis for Reset Control Systems: Application to Predict Precision of Motion Systems
• Complex-order Reset Control System
• Tuning of a Class of Reset Elements Using Pseudo-Sensitivities
• Stacking Integrators Without Sacrificing the Overshoot in Reset Control Systems
• Reset band for mitigatation of quantization induced performance degradation