ON THE LINEAR COMBINATION OF SAMPLE VARIANCE, RATIO AND PRODUCT ESTIMATORS OF FINITE POPULATION VARIANCE UNDER TWO STAGE SAMPLING

2020 ◽  
Vol 20 (3) ◽  
pp. 307
Author(s):  
Ishaq Olawoyin ◽  
Ahmed Audu ◽  
Auwalu Ibrahim ◽  
Hassan Abdulkadir ◽  
Tukur Kabiru
Keyword(s):  
Linear Combination ◽  
Finite Population ◽  
Sample Variance ◽  
Variance Ratio ◽  
Population Variance ◽  
Two Stage

Two-Stage Robust Tracking Controller for Linear Systems With Known Uncertainty Using Filtered Basis Functions

2020 ◽  
Author(s):  
Keval S. Ramani ◽  
Chinedum E. Okwudire
Keyword(s):  
Linear Combination ◽  
Linear Systems ◽  
Tracking Error ◽  
Basis Functions ◽  
Frobenius Norm ◽  
Control Input ◽  
Two Stage ◽  
Nominal Model ◽  
Control Of Linear Systems ◽  
Optimal Set

Abstract There is growing interest in the use of the filtered basis functions (FBF) approach to track linear systems, especially nonminimum phase (NMP) plants, because of the distinct advantages it presents as compared to other popular methods in the literature. The FBF approach expresses the control input to the plant as a linear combination of basis functions. The basis functions are forward filtered through the plant dynamics and the coefficients of the linear combination are selected such that the tracking error is minimized. This paper proposes a two-stage robust filtered basis functions approach for tracking control of linear systems in the presence of known uncertainty. In the first stage, the nominal model for filtering the basis functions is selected such that a Frobenius norm metric which considers the known uncertainty is minimized. In the second stage, an optimal set of basis functions is selected such that the effect of uncertainty is minimized for the nominal model selected in the first stage. Experiments on a 3D printer, demonstrate up to 7 times improvement in tracking performance using the proposed method as compared to the standard FBF approach.

scholarly journals A Study on the Chain Ratio-Type Estimator of Finite Population Variance

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yunusa Olufadi ◽  
Cem Kadilar
Keyword(s):  
Finite Population ◽  
Numerical Comparison ◽  
Mean Square ◽  
Auxiliary Variables ◽  
Population Variance ◽  
Two Phase ◽  
First Order ◽  
Phase Sampling ◽  
The Mean ◽  
Two Phase Sampling

We suggest an estimator using two auxiliary variables for the estimation of the unknown population variance. The bias and the mean square error of the proposed estimator are obtained to the first order of approximations. In addition, the problem is extended to two-phase sampling scheme. After theoretical comparisons, as an illustration, a numerical comparison is carried out to examine the performance of the suggested estimator with several estimators.

Sign in / Sign up

Export Citation Format

Share Document