# Internal iteration gradient estimator based parameter identification for nonlinear sandwich system subject to quantized sensor and friction nonlinearity

## TL;DR

This paper introduces a new gradient estimation method for nonlinear systems affected by sensor quantization and friction.

## Contribution

The novel method uses internal iteration and adaptive filtering to improve parameter identification in nonlinear sandwich systems.

## Key findings

- The proposed method avoids redundant parameter estimation by using a decomposing approach.
- Internal iteration and adaptive filtering improve estimation performance and convergence rate.
- The method was successfully tested on both numerical and practical electromechanical systems.

## Abstract

This study proposes an internal iteration scalar-innovation gradient estimation method based on multi-innovation theory for a nonlinear sandwich system subject to a quantized sensor and friction nonlinearity. Different from the existing multi-innovation gradient method (MISG ), the proposed method is designed to resolve the existing shortages of the conventional MISG. First, the decomposing method is applied to derive the identification model, and the redundant parameter estimation problem is avoided. Then, an adaptive filter based on the prior knowledge of the system is proposed to obtain the helpful identification data. Second, to solve the multi-innovation length problem in MISG, the internal iteration principle is presented to convert the multi-innovation updating to scalar-innovation updating under a given innovation length, where the positive estimation performance can be achieved. Subsequently, the trigger mechanism is used to produce the suboptimal initial estimate value when the next parameter adaptive law is updated. Then, the fast convergence rate is obtained. Finally, the proposed estimation strategy is verified by conducting a numerical example and an experiment on a practical electromechanical system test bench.