On σ-entropy Analysis of Linear Stochastic Systems in State Space

2021 ◽  
Vol 1 (1) ◽  
pp. 30-35
Author(s):  
Victor Boichenko ◽  
Alexey Belov
Keyword(s):  
Stochastic Systems ◽  
Linear Time ◽  
Continuous System ◽  
Disturbance Attenuation ◽  
Algebraic Riccati Equation ◽  
Continuous Systems ◽  
Random Disturbance ◽  
Linear Time Invariant ◽  
Random Disturbances ◽  
Linear Time Invariant System

In this paper the problem of random disturbance attenuation capabilities in linear continuous systems is studied. It is supposed  that the system operates under random disturbances with bounded σ-entropy level. σ-entropy norm indicates a performance index of the continuous system on the set of the random signals with bounded σ-entropy. This paper presents a time-domain solution to the calculation of σ-entropy norm of the continuous linear time-invariant system. σ-entropy norm is defined after solving coupled matrix equations: one algebraic Riccati equation, one nonlinear equation over log determinant function, and two Lyapunov equations.

Design and implementation of decoupled periodic control scheme for a laboratory-based quadruple-tank process

2021 ◽  
pp. 095965182110228
Author(s):  
Jatin K Pradhan ◽  
Arun Ghosh
Keyword(s):  
Real Time ◽  
High Frequency ◽  
Linear Time ◽  
Disturbance Attenuation ◽  
Minimum Phase ◽  
Periodic Control ◽  
Linear Time Invariant ◽  
Control Scheme ◽  
Gain Margin ◽  
Time Invariant

It is well known that linear time-invariant controllers fail to provide desired robustness margins (e.g. gain margin, phase margin) for plants with non-minimum phase zeros. Attempts have been made in literature to alleviate this problem using high-frequency periodic controllers. But because of high frequency in nature, real-time implementation of these controllers is very challenging. In fact, no practical applications of such controllers for multivariable plants have been reported in literature till date. This article considers a laboratory-based, two-input–two-output, quadruple-tank process with a non-minimum phase zero for real-time implementation of the above periodic controller. To design the controller, first, a minimal pre-compensator is used to decouple the plant in open loop. Then the resulting single-input–single-output units are compensated using periodic controllers. It is shown through simulations and real-time experiments that owing to arbitrary loop-zero placement capability of periodic controllers, the above decoupled periodic control scheme provides much improved robustness against multi-channel output gain variations as compared to its linear time-invariant counterpart. It is also shown that in spite of this improved robustness, the nominal performances such as tracking and disturbance attenuation remain almost the same. A comparison with [Formula: see text]-linear time-invariant controllers is also carried out to show superiority of the proposed scheme.

Optimal Nonlinear Estimation of Linear Stochastic Systems: The Multivariable Extension

1996 ◽  
Vol 118 (2) ◽  
pp. 350-353 ◽  
Author(s):  
M. A. Hopkins ◽  
H. F. VanLandingham
Keyword(s):  
Stochastic Systems ◽  
Transfer Functions ◽  
Mimo Systems ◽  
Linear Time ◽  
Nonlinear Method ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Time Invariant ◽  
Time Systems

This paper extends to multi-input multi-output (MIMO) systems a nonlinear method of simultaneous parameter and state estimation that appeared in the ASME JDSM&C (September, 1994), for single-input single-output (SISO) systems. The method is called pseudo-linear identification (PLID), and applies to stochastic linear time-invariant discrete-time systems. No assumptions are required about pole or zero locations; nor about relative degree, except that the system transfer functions must be strictly proper. In the earlier paper, proofs of optimality and convergence were given. Extensions of those proofs to the MIMO case are also given here.

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.

Nonfragile H∞ Output Feedback Controller Design for Linear Systems*

2003 ◽  
Vol 125 (1) ◽  
pp. 117-123 ◽  
Author(s):  
Guang-Hong Yang ◽  
Jian Liang Wang
Keyword(s):  
Output Feedback ◽  
Controller Design ◽  
Linear Time ◽  
Output Feedback Control ◽  
Disturbance Attenuation ◽  
Output Measurement ◽  
Linear Time Invariant ◽  
Measurement Feedback ◽  
Linear Time Invariant Systems ◽  
Time Invariant

This paper is concerned with the nonfragile H∞ controller design problem for linear time-invariant systems. The controller to be designed is assumed to have norm-bounded uncertainties. Design methods are presented for dynamic output (measurement) feedback. The designed controllers with uncertainty (i.e. nonfragile controllers) are such that the closed-loop system is quadratically stable and has an H∞ disturbance attenuation bound. Furthermore, these robust controllers degenerate to the standard H∞ output feedback control designs, when the controller uncertainties are set to zero.

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