Stable Linear Systems Simplification Via Pade´ Approximations to Hurwitz Polynomials

1981 ◽  
Vol 103 (3) ◽  
pp. 279-284 ◽  
Author(s):  
Y. Bistritz ◽  
U. Shaked
Keyword(s):  
Linear Time ◽  
Low Frequency ◽  
Order System ◽  
Padé Approximations ◽  
Approximate Design ◽  
Linear Time Invariant ◽  
Hurwitz Polynomials ◽  
Pade Approximations ◽  
Linear Time Invariant System ◽  
Time Invariant

In many problems of control and simulation of a high order system, it is often advantageous to have an appropriate lower order model for approximate design. Introducing the concept of (mixed) Pade´ approximations to Hurwitz polynomials, a novel method for linear time invariant system simplification is established. The method offers many models of the same order that are stable for a stable system, approximate a desired number of the system eigenvalues near to and far from the origin, and emphasize differently the approximation of the low frequency/steady-state and high frequency/transient responses of the system. The presented method is based entirely on a simple unified Pade´ technique.

Adaptive Cancellation of Matched Unknown Sinusoidal Disturbances for LTI Systems by State Derivative Feedback

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Halil İ. Baştürk ◽  
Miroslav Krstic
Keyword(s):  
Linear Time ◽  
Feedback System ◽  
Adaptive Controller ◽  
Order System ◽  
Output Vector ◽  
Linear Time Invariant ◽  
Exponentially Stable ◽  
Adaptive Cancellation ◽  
Linear Time Invariant System ◽  
Time Invariant

Solutions already exist for the problem of canceling sinusoidal disturbances by measurement of state or an output for linear and nonlinear systems. In this paper, we design an adaptive controller to cancel matched sinusoidal disturbances forcing a linear time-invariant system by using only measurement of state-derivatives. Our design is based on three steps; (1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector, (2) design of an adaptive disturbance observer and, (3) design of an adaptive controller. We prove that the equilibrium of the closed-loop adaptive system is globally uniformly asymptotically stable and locally exponentially stable. The effectiveness of the controller is illustrated with a simulation example of a second-order system.

Adaptive Cancelation of Matched Unknown Sinusoidal Disturbances for LTI Systems by State Derivative Feedback

2011 ◽  
Author(s):  
Halil I˙. Bas¸tu¨rk ◽  
Miroslav Krstic
Keyword(s):  
Linear Time ◽  
Feedback System ◽  
Adaptive Controller ◽  
Order System ◽  
Output Vector ◽  
Linear Time Invariant ◽  
Exponentially Stable ◽  
Linear Time Invariant System ◽  
Time Invariant ◽  
Linear And Nonlinear Systems

Solutions already exist for the problem of canceling sinusoidal disturbances by measurement of state or an output for linear and nonlinear systems. In this paper, we design an adaptive controller to cancel matched sinusoidal disturbances forcing a linear time-invariant system by using only measurement of state-derivatives. Our design is based on three steps; 1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector, 2) design of an adaptive disturbance observer and, 3) design of an adaptive controller. We prove that the equilibrium of the closed-loop adaptive system is globally uniformly asymptotically stable and locally exponentially stable. The effectiveness of the controller is illustrated with a simulation example of a second order system.

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 Temporal Variability in the Response of a Linear Time-Invariant Catchment System to a Non-Stationary Inflow Concentration Field

2020 ◽  
Vol 10 (15) ◽  
pp. 5356
Author(s):  
Ching-Min Chang ◽  
Kuo-Chen Ma ◽  
Mo-Hsiung Chuang
Keyword(s):  
Closed Form ◽  
Temporal Variability ◽  
Linear Time ◽  
Concentration Field ◽  
Surface Water Quality ◽  
Catchment Scale ◽  
Input Concentration ◽  
Linear Time Invariant ◽  
Linear Time Invariant System ◽  
Time Invariant

Predicting the effects of changes in dissolved input concentration on the variability of discharge concentration at the outlet of the catchment is essential to improve our ability to address the problem of surface water quality. The goal of this study is therefore dedicated to the stochastic quantification of temporal variability of concentration fields in outflow from a catchment system that exhibits linearity and time invariance. A convolution integral is used to determine the output of a linear time-invariant system from knowledge of the input and the transfer function. This work considers that the nonstationary input concentration time series of an inert solute to the catchment system can be characterized completely by the Langevin equation. The closed-form expressions for the variances of inflow and outflow concentrations at the catchment scale are derived using the Fourier–Stieltjes representation approach. The variance is viewed as an index of temporal variability. The closed-form expressions therefore allow to evaluate the impacts of the controlling parameters on the temporal variability of outflow concentration.

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