Data-driven rational feedforward tuning: With application to an ultraprecision wafer stage

2019 ◽  
Vol 234 (6) ◽  
pp. 748-758 ◽  
Author(s):  
Weicai Huang ◽  
Kaiming Yang ◽  
Yu Zhu ◽  
Xin Li ◽  
Haihua Mu ◽  
...  
Keyword(s):  
High Performance ◽  
Optimal Parameter ◽  
Least Square Method ◽  
Parameter Tuning ◽  
Basis Functions ◽  
Least Square ◽  
Data Driven ◽  
Estimation Accuracy ◽  
Rational Basis ◽  
Noisy Condition

Rational basis functions are introduced into iterative learning control to enhance the flexibility towards nonrepeating tasks. At present, the application of rational basis functions either suffers from nonconvex optimization problem or requires the predefinition of poles, which restricts the achievable performance. In this article, a new data-driven rational feedforward tuning approach is developed, in which convex optimization is realized without predefining the poles. Specifically, the optimal parameter which eliminates the reference-induced error is directly solved using the least square method. No parametric model is involved in the parameter tuning process and the optimal parameter is estimated using the measured data. In the noisy condition, it is proved that the estimated optimal parameter is unbiased and the estimation accuracy in terms of variance is analysed. The performance of the proposed approach is tested on an ultraprecision wafer stage. The experimental results confirm that high performance is achieved using the proposed approach.

scholarly journals A Method for Reconstruction of Boiler Combustion Temperature Field Based on Acoustic Tomography

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yuhui Wu ◽  
Xinzhi Zhou ◽  
Li Zhao ◽  
Chenlong Dong ◽  
Hailin Wang
Keyword(s):  
Temperature Field ◽  
Temperature Distribution ◽  
Optimal Parameter ◽  
Interpolation Method ◽  
Least Square Method ◽  
Reconstruction Algorithm ◽  
Least Square ◽  
Temperature Fields ◽  
Acoustic Tomography ◽  
Measured Temperature

Acoustic tomography (AT), as a noninvasive temperature measurement method, can achieve temperature field measurement in harsh environments. In order to achieve the measurement of the temperature distribution in the furnace and improve the accuracy of AT reconstruction, a temperature field reconstruction algorithm based on the radial basis function (RBF) interpolation method optimized by the evaluation function (EF-RBFI for short) is proposed. Based on a small amount of temperature data obtained by the least square method (LSM), the RBF is used for interpolation. And, the functional relationship between the parameter of RBF and the root-mean-square (RMS) error of the reconstruction results is established in this paper, which serves as the objective function for the effect evaluation, so as to determine the optimal parameter of RBF. The detailed temperature description of the entire measured temperature field is finally established. Through the reconstruction of three different types of temperature fields provided by Dongfang Boiler Works, the results and error analysis show that the EF-RBFI algorithm can describe the temperature distribution information of the measured combustion area globally and is able to reconstruct the temperature field with high precision.

Using Integration of Thermal-Balance Based and Data-Driven Models to Determine Single Duct Variable Air Volume System Cooling Baseline

2013 ◽  
Author(s):  
Gyujin Shim ◽  
Li Song ◽  
Gang Wang
Keyword(s):  
Physical Model ◽  
Least Square Method ◽  
Energy Performance ◽  
Least Square ◽  
Physical Models ◽  
Data Driven ◽  
Lumped Model ◽  
Variable Air Volume ◽  
Data Driven Approach ◽  
Cooling Coil

In order to use real-time energy measurements to identify system operation faults and inefficiencies, a cooling coil energy baseline is studied in an air-handling unit (AHU) through an integration of physical models and a data driven approach in this paper. A physical model for an AHU cooling coil energy consumption is first built to understand equipment mechanism and to determine the variables impacting cooling coil energy performance, and then the physical model is simplified into a lumped model by reducing the number of independent variables needed. Regression coefficients in the lumped model are determined statistically through searching optimal fit using the least square method with short periods of measured data. Experimental results on an operational AHU (8 ton) are presented to validate the effectiveness of this approach with statistical analysis. As a result of this experiment, the proposed cooling energy baselines at the cooling coil have ±20% errors at 99.7% confidence. Six-day data for obtaining baseline is preferred since it shows similar results as 12-day.

Nonlinear Modeling and Experimental Validation of Uni-Axial Servo-Hydraulic Shaking Table

2016 ◽  
Author(s):  
Paolo Righettini ◽  
Roberto Strada ◽  
Shirin Valilou ◽  
Ehsan Khademolama
Keyword(s):  
High Performance ◽  
Nonlinear Modeling ◽  
Least Square Method ◽  
Hydraulic Cylinder ◽  
Difficult Problem ◽  
Least Square ◽  
Shaking Table ◽  
Lugre Model ◽  
Friction Forces ◽  
Friction Models

An effective way for the testing of a large number of systems is using single and multi-axis shaking tables. Among the possible applications, the civil engineering field stands out for the testing of structures, or part of them, both on a reduced and on a full scale. However, design a high performance controller for a servo-hydraulic shaking table is a difficult problem due to its non-linarites and large friction forces. The goal of this paper is to develop and experimentally validate a robust numerical model that simulates the acceleration behavior of a uni-axial servo-hydraulic shaking table system with considering three friction models, the LuGre model, the modified LuGre model and the new modified LuGre model. First, a full system model of servo-hydraulic system is developed based on fluid mechanical expressions and then the friction force of hydraulic cylinder is modeled and validated on the real shaking table. Data of the experiment are gathered from input command valve, and the output acceleration and position of the table. All models are simulated by using MATLAB and SIMULINK computer program. The parameters of the system and the friction models are estimated by using least square method (LSM). Finally, the comparisons of simulated results with experimental ones show that the model of the system with considering third model of the friction can predict accurately the shaking table’s behaviors.

scholarly journals Geometric Interpretation of Errors in Multi-Parametrical Fitting Methods Based on Non-Euclidean Norms

Stats ◽  
2019 ◽  
Vol 2 (4) ◽  
pp. 426-438 ◽  
Author(s):  
Livadiotis
Keyword(s):  
Optimal Parameter ◽  
Least Square Method ◽  
Geometric Interpretation ◽  
Least Square ◽  
Geometric Representation ◽  
Geometric Meaning ◽  
Normal Equations ◽  
Optimal Values ◽  
Parameter Values ◽  
Fitting Parameters

The paper completes the multi-parametrical fitting methods, which are based on metrics induced by the non-Euclidean Lq-norms, by deriving the errors of the optimal parameter values. This was achieved using the geometric representation of the residuals sum expanded near its minimum, and the geometric interpretation of the errors. Typical fitting methods are mostly developed based on Euclidean norms, leading to the traditional least–square method. On the other hand, the theory of general fitting methods based on non-Euclidean norms is still under development; the normal equations provide implicitly the optimal values of the fitting parameters, while this paper completes the puzzle by improving understanding the derivations and geometric meaning of the optimal errors.

scholarly journals Terrain Feature Estimation Method for a Lower Limb Exoskeleton Using Kinematic Analysis and Center of Pressure

Sensors ◽  
2019 ◽  
Vol 19 (20) ◽  
pp. 4418 ◽  
Author(s):  
Myounghoon Shim ◽  
Jong In Han ◽  
Ho Seon Choi ◽  
Seong Min Ha ◽  
Jung-Hoon Kim ◽  
...  
Keyword(s):  
Lower Limb ◽  
Kinematic Analysis ◽  
Center Of Pressure ◽  
Contact Point ◽  
Estimation Method ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Accuracy ◽  
Lower Limb Exoskeleton ◽  
Contact Points

While controlling a lower limb exoskeleton providing walking assistance to wearers, the walking terrain is an important factor that should be considered for meeting performance and safety requirements. Therefore, we developed a method to estimate the slope and elevation using the contact points between the limb exoskeleton and ground. We used the center of pressure as a contact point on the ground and calculated the location of the contact points on the walking terrain based on kinematic analysis of the exoskeleton. Then, a set of contact points collected from each step during walking was modeled as the plane that represents the surface of the walking terrain through the least-square method. Finally, by comparing the normal vectors of the modeled planes for each step, features of the walking terrain were estimated. We analyzed the estimation accuracy of the proposed method through experiments on level ground, stairs, and a ramp. Classification using the estimated features showed recognition accuracy higher than 95% for all experimental motions. The proposed method approximately analyzed the movement of the exoskeleton on various terrains even though no prior information on the walking terrain was provided. The method can enable exoskeleton systems to actively assist walking in various environments.

Pose Estimation of Cooperative Targets for Space Exploration Task Based on Binocular Visual Measurement

2013 ◽  
Vol 333-335 ◽  
pp. 268-274
Author(s):  
Jing Jing Wang ◽  
Jian Yu Huang ◽  
Shi Yin Qin
Keyword(s):  
Pose Estimation ◽  
Three Dimensional ◽  
Least Square Method ◽  
Estimation Algorithm ◽  
High Accuracy ◽  
Least Square ◽  
Estimation Accuracy ◽  
Feature Points ◽  
Well Performance ◽  
Visual Measurement

In this paper, a high accuracy and efficiency pose estimation algorithm is proposed for space cooperative targets in RVD based on binocular visual measurement. At first, the scheme of visual measurement toward RVD is presented and the environment conditions and performance requirement are analysed and discussed. Then the relationship of pose estimation with detection and tracking is studied to give an implementing strategy of pose estimation with high accuracy and efficiency. Moreover, the key point is focused on the pose estimation of cooperative targets, in which a stereo vision mapping relation between three dimensionl coordinates of spacial feature points of cooperative targets and their corresponding image coordinates is established, then the least square method is employed to estimate the three-dimensional coordinates of feature points so as to calculate the relative position and attitude between tracking spacecraft and target spacecraft with high precision, finally a series of experimental resluts indicate that the proposed pose estimation algorithm under binocular visual measurement demonstrates well performance in the estimation accuracy, anti-noise and real-time thus can achieve the application requriements of RVD under binocular visual measurement.

Sign in / Sign up

Export Citation Format

Share Document