Definition of a Complex Domain Adjoint for Use in Optimal Control Problems

1978 ◽  
Vol 11 (1) ◽  
pp. 33-35
Author(s):  
M. J. Grimble
Keyword(s):  
Linear Time ◽  
Adjoint Operator ◽  
Adjoint System ◽  
Simple Relationship ◽  
Complex Frequency ◽  
Simple Method ◽  
Linear Time Invariant ◽  
Definition Of ◽  
The Time Domain ◽  
Linear Time Invariant System

A complex frequency version of the time domain adjoint operator for a linear time-invariant system is obtained. A very simple relationship is shown to exist between this operator and the system transfer function matrix. A simple method of simulating the adjoint system is described.

A Generalized Form of ToMFIR Approach to Fault Detection in Dynamic Systems

2011 ◽  
Author(s):  
Chun-Mei Liu ◽  
Wen Chen
Keyword(s):  
Fault Detection ◽  
Dynamic Systems ◽  
Linear Time ◽  
Control Input ◽  
Linear Time Invariant ◽  
Definition Of ◽  
Linear Time Invariant System ◽  
Time Invariant ◽  
Fault Information ◽  
Special Case

This paper is to develop a general form for Total Measurable Fault Information-based Residual (ToMFIR) approach to fault detection in dynamic systems. The ToMFIR is initially established for systems with a constant control input signal and a fault approaching to a constant. Practical systems satisfying the aforementioned conditions is few. That is why a generalized form is developed in this work. The definition of the ToMFIR is first introduced and the special case is also presented for the continuity of the statement. Based on a stable and linear time-invariant system, the general form of the ToMFIR is derived, and a practical DC motor example, with a PID controller, is used to demonstrate the effectiveness and robustness of the ToMFIR-based fault detection.

scholarly journals Discrete-time modeling and input-output linearization of current-fed induction motors for torque and stator flux decoupled control

2014 ◽  
Vol 14 (1) ◽  
pp. 128-140 ◽  
Author(s):  
Stanislav Enev
Keyword(s):  
Discrete Time ◽  
Linear Time ◽  
Input Output ◽  
Time Model ◽  
Linear Time Invariant ◽  
Time Modeling ◽  
Applied Design ◽  
Stator Flux ◽  
Definition Of ◽  
Linear Time Invariant System

Abstract In this paper an exact discrete-time model of the induction motor in a current-fed mode, including stator flux components is derived and validated. The equations of the motor are written in a frame aligned with the rotor electrical position, which results in a linear, time-invariant system. Based on the derived exact discrete-time representation of the motor dynamics, an input-output linearizing control law is designed for decoupled torque and stator flux control. The applied design technique led to a non-trivial, still useful, definition of the electromagnetic output of the motor. Simulation results are presented showing that the aimed performance is obtained, that is, no coupling exists between the outputs, and the initial design problem of controlling a nonlinear interacting TITO system is reduced to a problem of controlling two linear and decoupled SISO systems with simple dynamics.

Evaluation of fractional order of the discrete integrator. Part II

2020 ◽  
Vol 23 (2) ◽  
pp. 408-426
Author(s):  
Piotr Ostalczyk ◽  
Marcin Bąkała ◽  
Jacek Nowakowski ◽  
Dominik Sankowski
Keyword(s):  
Fractional Order ◽  
Output Signal ◽  
Linear Time ◽  
Mathematical Problem ◽  
Simple Method ◽  
Linear Time Invariant ◽  
Input And Output ◽  
Order Difference Equation ◽  
Time Invariant ◽  
Discrete Integrator

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.

Deterministic Continuous-Time Signals and Systems

2021 ◽  
pp. 562-598
Author(s):  
Stevan Berber
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Linear Time ◽  
Continuous Variable ◽  
Linear Time Invariant ◽  
Time Signals ◽  
Analysis And Synthesis ◽  
Linear Time Invariant Systems ◽  
Definition Of ◽  
Time Invariant

Due to the importance of the concept of independent variable modification, the definition of linear-time-invariant system, and their implications for discrete-time signal processing, Chapter 11 presents basic deterministic continuous-time signals and systems. These signals, expressed in the form of functions and functionals such as the Dirac delta function, are used throughout the book for deterministic and stochastic signal analysis, in both the continuous-time and the discrete-time domains. The definition of the autocorrelation function, and an explanation of the convolution procedure in linear-time-invariant systems, are presented in detail, due to their importance in communication systems analysis and synthesis. A linear modification of the independent continuous variable is presented for specific cases, like time shift, time reversal, and time and amplitude scaling.

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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