Adaptive Parameter Estimation With Convergence Analysis for the Prandtl–Ishlinskii Hysteresis Operator

2021 ◽  
Vol 1 (4) ◽  
Author(s):  
Rui Xu ◽  
Miaolei Zhou ◽  
Xiaobo Tan
Keyword(s):  
Parameter Estimation ◽  
Adaptive Estimation ◽  
Smart Material ◽  
Least Square ◽  
Recursive Least Square ◽  
Sensors And Actuators ◽  
Persistent Excitation ◽  
Adaptive Parameter ◽  
Adaptive Weight ◽  
Smart Material Systems

Abstract Hysteresis is a nonlinear characteristic ubiquitously exhibited by smart material sensors and actuators, such as piezoelectric actuators and shape memory alloys. The Prandtl–Ishlinskii (PI) operator is widely used to describe hysteresis of smart material systems due to its simple structure and the existence of analytical inverse. A PI operator consists of a weighted superposition of play (backlash) operators. While adaptive estimation of the weights for PI operators has been reported in the literature, rigorous analysis of parameter convergence is lacking. In this article, we establish persistent excitation and thus parameter convergence for adaptive weight estimation under a rather modest condition on the input to the PI operator. The analysis is further supported via simulation, where a recursive least square (RLS) method is adopted for parameter estimation.

scholarly journals Online Adaptive Parameter Estimation for Quadrotors

Algorithms ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 167 ◽  
Author(s):  
Jun Zhao ◽  
Xian Wang ◽  
Guanbin Gao ◽  
Jing Na ◽  
Hongping Liu ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Exponential Convergence ◽  
Estimation Error ◽  
Persistent Excitation ◽  
System Parameters ◽  
Adaptive Parameter ◽  
Adaptive Laws ◽  
Accuracy Parameter ◽  
The Stability ◽  
Quadrotor System

The stability and robustness of quadrotors are always influenced by unknown or immeasurable system parameters. This paper proposes a novel adaptive parameter estimation technology to obtain high-accuracy parameter estimation for quadrotors. A typical mathematical model of quadrotors is first obtained, which can be used for parameter estimation. Then, an expression of the parameter estimation error is derived by introducing a set of auxiliary filtered variables. Moreover, an augmented matrix is constructed based on the obtained auxiliary filtered variables, which is then used to design new adaptive laws to achieve exponential convergence under the standard persistent excitation (PE) condition. Finally, a simulation and an experimental verification for a typical quadrotor system are shown to illustrate the effectiveness of the proposed method.

scholarly journals Development of A Modified Extended Model-Based Fault Detection And Diagnosis Approach

2021 ◽  
Author(s):  
Alireza Alikhani ◽  
Ghasem Sharifi
Keyword(s):  
Fault Detection ◽  
Adaptive Estimation ◽  
Response Speed ◽  
Previous Method ◽  
Fault Detection And Diagnosis ◽  
Least Square ◽  
Extended Model ◽  
Multiple Model ◽  
Recursive Least Square ◽  
Model Based

Abstract A supervisory system for space missions is critical due to the high risk of missions, the costs, and the impossibility of adding redundancy. The model-based fault detection approaches are of interest due to their highly responsive speed, robustness against disturbances and uncertainties, and accuracy. Conventional model-based methods have some drawbacks such as feasibility and applicability. In this paper, a modified extended multiple models adaptive estimation (MEMMAE) method is developed which keep both the advantages of the previous model-based methods and take into account some limitations of that. This approach can be performed on various systems to detect and diagnose faults, with appropriate response speed and resistance to uncertainty and disturbances. By combining the recursive least-square algorithm with the extended multiple model adaptive estimation (EMMAE) method, the limitations of this method including simultaneous fault detection, diagnostics of failure cause, and high processing volume are eliminated. The method is implemented on a spacecraft as a case study using the MATLAB/SIMULINK software and demonstrates that the responsive speed and accuracy of the proposed method is significantly much more effective and accurate than the previous method.

Application of an Adaptive Forecast Algorithm to the River Västerdalälven

1988 ◽  
Vol 19 (5) ◽  
pp. 293-302 ◽  
Author(s):  
László Iritz
Keyword(s):  
Parameter Estimation ◽  
Systems Theory ◽  
Least Square ◽  
The Self ◽  
Type Model ◽  
Recursive Least Square ◽  
Electronic Engineering ◽  
Self Tuning ◽  
Recursive Least Square Algorithm ◽  
Hydrological Forecast

During the last two decades, advances in electronic engineering, hydrological modelling and systems theory have given considerable benefits to the hydrological forecast developments. Today several powerful adaptive techniques are available, which can improve the reliability of hydrological forecasting. One of these techniques is the self-tuning predictor based on an ARMA type model using direct parameter estimation by recursive least square algorithm. The selftuning predictor has been tested on the River Västerdalälven in Sweden.

scholarly journals Real-Time Calibration of Magnetometers Using the RLS/ML Algorithm

Sensors ◽  
2020 ◽  
Vol 20 (2) ◽  
pp. 535
Author(s):  
Guocan Cao ◽  
Xiang Xu ◽  
Dacheng Xu
Keyword(s):  
Parameter Estimation ◽  
Real Time ◽  
Calibration Method ◽  
Least Square ◽  
Estimation Methods ◽  
Recursive Least Square ◽  
Ml Estimation ◽  
Time Calibration ◽  
Complete Measurement ◽  
Calibration Algorithm

This study presents a new real-time calibration algorithm for three-axis magnetometers by combining the recursive least square (RLS) estimation and maximum likelihood (ML) estimation methods. Magnetometers are widely employed to determine the heading information by sensing the magnetic field of earth; however, they are vulnerable to ambient magnetic disturbances. This makes the calibration of a magnetometer inevitable before it is employed. In this paper, first, a complete measurement error model of the magnetometer is studied, and a simplified model is developed. Then, the real-time RLS algorithm is introduced and discussed in detail, and the unbiased optimal ML is utilized to improve the accuracy of the parameter estimation. The proposed algorithm is advantageous in correcting the parameters in real time and simultaneously obtaining unbiased parameter estimation. Finally, the simulation and experimental results demonstrate that both the accuracy and computational speed of the proposed algorithm is better than those of the widely used bath-processing method. Moreover, the proposed calibration method can be adopted for calibrating other three-axis sensors.

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