Characterizing and correcting gradient errors in non-cartesian imaging: Are gradient errors linear time-invariant (LTI)?

AbstractThis is a continuation (Part II) of our previous paper [19]. In this paper we present a simple method of the fractional-order value calculation of the fractional-order discrete integration element. We assume that the input and output signals are known. The linear time-invariant fractional-order difference equation is reduced to the polynomial in a variable ν with coefficients depending on the measured input and output signal values. One should solve linear algebraic equation or find roots of a polynomial. This simple mathematical problem complicates when the measured output signal contains a noise. Then, the polynomial roots are unsettled because they are very sensitive to coefficients variability. In the paper we show that the discrete integrator fractional-order is very stiff due to the degree of the polynomial. The minimal number of samples guaranteeing the correct order is evaluated. The investigations are supported by a numerical example.

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

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1177/09596518211022897 ◽

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.

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Differential-algebraic systems are generically controllable and stabilizable

Mathematics of Control Signals and Systems ◽

10.1007/s00498-021-00287-x ◽

2021 ◽

Author(s):

Achim Ilchmann ◽

Jonas Kirchhoff

Keyword(s):

Algebraic Geometry ◽

Linear Time ◽

Differential Algebraic Equations ◽

Algebraic Equations ◽

Algebraic Systems ◽

Linear Time Invariant ◽

Survey Article ◽

Link Type ◽

Invariant Differential ◽

Time Invariant

AbstractWe investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.

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Linear Time Invariant Homogeneous Matrix Descriptor (Singular) Discrete-Time Systems with Non Consistent Initial Conditions

2010 Sixth International Conference on Networking and Services ◽

10.1109/icns.2010.60 ◽

2010 ◽

Cited By ~ 1

Author(s):

Athanasios A. Pantelous ◽

Athanasios D. Karageorgos ◽

Grigoris I. Kalogeropoulos

Keyword(s):

Discrete Time ◽

Initial Conditions ◽

Linear Time ◽

Linear Time Invariant ◽

Discrete Time Systems ◽

Homogeneous Matrix ◽

Time Invariant ◽

Time Systems

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Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

Applied Sciences ◽

10.3390/app11041717 ◽

2021 ◽

Vol 11 (4) ◽

pp. 1717

Author(s):

Gilberto Gonzalez Avalos ◽

Noe Barrera Gallegos ◽

Gerardo Ayala-Jaimes ◽

Aaron Padilla Garcia

Keyword(s):

Steady State ◽

Linear Time ◽

Direct Determination ◽

The State ◽

Steady State Response ◽

State Variables ◽

Linear Time Invariant ◽

State Response ◽

Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

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