Solution and Parameter Estimation in Linear Time-Invariant Delayed Systems Using Laguerre Polynomial Expansion

1983 ◽  
Vol 105 (4) ◽  
pp. 297-301 ◽  
Author(s):  
Fan-Chu Kung ◽  
Hua Lee
Keyword(s):  
Time Delay ◽  
Large Scale ◽  
Laguerre Polynomial ◽  
Linear Time ◽  
Small Time ◽  
Polynomial Expansion ◽  
Feedback Systems ◽  
Linear Time Invariant ◽  
Small Time Delay ◽  
Time Invariant

Finite dimensional Laguerre polynomial expansion can be applied to approximate the solution of linear time-invariant systems. Here, we extend this approach to systems with small time delay by introducing a delay matrix operator to the system equations. In addition, parameters of linear unity-feedback systems with small time delay can also be estimated by using the Laguerre expansion. In this paper we provide algorithms for large scale systems to avoid direct matrix inversion and give examples to demonstrate the approximation.

Complementary Sensitivity Design of PID Controllers for Arbitrary-Order Transfer Functions With Time Delay

2008 ◽  
Author(s):  
Tooran Emami ◽  
John M. Watkins
Keyword(s):  
Time Delay ◽  
Transfer Functions ◽  
Linear Time ◽  
Order System ◽  
Pid Controllers ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Plant Transfer ◽  
Time Invariant

A graphical technique for finding all proportional integral derivative (PID) controllers that stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) system of any order system with time delay has been solved. In this paper a method is introduced that finds all PID controllers that also satisfy an H∞ complementary sensitivity constraint. This problem can be solved by finding all PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. A key advantage of this procedure is the fact that it does not require the plant transfer function, only its frequency response.

scholarly journals Identification of LTI Time-Delay Systems with Missing Output Data Using GEM Algorithm

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xianqiang Yang ◽  
Hamid Reza Karimi
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Irregular Sampling ◽  
Delay Systems ◽  
Model Parameters ◽  
Delay Model ◽  
Sensor Failure ◽  
Linear Time Invariant ◽  
Failure Data ◽  
Time Invariant

This paper considers the parameter estimation for linear time-invariant (LTI) systems in an input-output setting with output error (OE) time-delay model structure. The problem of missing data is commonly experienced in industry due to irregular sampling, sensor failure, data deletion in data preprocessing, network transmission fault, and so forth; to deal with the identification of LTI systems with time-delay in incomplete-data problem, the generalized expectation-maximization (GEM) algorithm is adopted to estimate the model parameters and the time-delay simultaneously. Numerical examples are provided to demonstrate the effectiveness of the proposed method.

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