Questions tagged [system-identification]
System identification means building a mathematical model of the input-output relationship of a system by observing its inputs and the subsequent outputs.
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Relative error between two transfer functions
I have a system whose transfer function is given by $\frac{\mathbf{b}_1}{\mathbf{a}_1}$. And I have an estimated transfer function model $\frac{\mathbf{b}_2}{\mathbf{a}_2}$. I want to find the ...
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Unique identification of poles and zeros of two LTI systems
I have two linear systems in cascade, whose individual orders are known. The input u to the first linear system and the output y at the end of the second linear system are available. The intermediate ...
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lsqcurvefit using dynamic input data
I have input vector $\boldsymbol{u}$ and output vector $\boldsymbol{y}$ of length $N$, and I use $u_k,y_k$ to denote the $k$-th elements of $\boldsymbol{u}$ & $\boldsymbol{y}$ and $u_{k-1}$ as the ...
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Unbalanced binary sequences for system identification?
I have a physical system that I'd like to obtain the frequency response for. I can only provide binary sequences as inputs to the system. Normally, I'd use a MLS (maximal length sequence) and ...
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Excitation signals for system identification - Applications
I have a practical question regarding the various applications of excitation signals in identifying Linear Time-Invariant (LTI) systems. Specifically, I am curious about the usage of the following ...
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Trying to replicate results from tfestimate function in Matlab
I have been trying to replicate the results from the tfestimate function in Matlab by performing, from my understanding, the corresponding signal processing steps in a separate Matlab script file. The ...
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Interpreting eigenvalues of non-normalized covariance matrix of time-series measurements
Cross-posted from physics stackexchange
Summary: Eigenvalues of a "non-normalized" covariance matrix of time-series measurements from a linear system have units of Action (energy * time). ...
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Generate a continuous time system with desired bode diagram
I have a fluid mechanics model that is heavy to simulate. Its main output is a scalar $q$ related to some energy transfer, and its input is a pressure $P$. This model, noted system 2, is coupled with ...
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How to represent nonuniform resampling of signal using math functions?
I am working on optical coherence tomography algorithm. In main pipeline I should use nonuniform resampling to eliminate transformation of optical signal in IR-spectrometer (that signal disperses by ...
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Get the inverse transfer function from the measured response
What is a numerically stable way to obtain the inverse transfer function from a measured response?
I have a system that shows a low-pass behavior. I would like to increase the bandwidth by some form ...
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Why time invariant system in order to know any output for any input using the impulse response?
Suppose we have a system $S$.We give it the input $\delta(t)$ and get a response $S(\delta(t))$.If the system is linear and time invariant we can calculate every output $y(t)$ from any input $x(t)$ by ...
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Modelling problem
Considering a finite-length impulse response $h[n]$ of length $M $ (which amounts to considering $h[n] = 0,$ for $n \geq M$). The data model, with additive disturbance, is then written as:
$$y[n] = ...
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Is it possible to use AMIGO tuning rules with relay control?
I am trying to control a plant with PID using tuning rules such as the Ziegler-Nichols rules. However, it is not always easy just to send a step to your plant
source of the image.
Another method to ...
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is this signal is perodic?
What is the time period of
$$ x(t) = 7 e^{\jmath(5t + \pi/2)} + 10^{\jmath(7t + \pi/5)}$$ ?
X(t) is the combination of two functions. one is the natural logarithm base, $e$, and the other is 10.
if ...
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Inferring a response from the Analytic Signal
I have a slowly varying sinusoidal system. The output is separated using methods that produce a real signal $x(t)$ and quadrature component $y(t)$ such that $x(t)$ represents the real physical value ...
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LMS Adaptive Filter for system identification
i am currently attempting system identification using the LMS algorithm. The input and the output data are available and are very noisy and consists of multiple frequencies. The input and the output ...
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Grey Box system identification using LMS algorithm
The transfer function and the input output data of the system are known. The transfer function is given by $$G(s) = \frac{K}{(Js+b)(Ls+R)+K^2}$$
How are the parameters of the transfer function ...
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Transfer function and Laplace domain
If we give a input $x(t)=u(t)$ to a system $\mathcal{S}$ we get an output $y(t) = e^{-t} u(t)$.
After we Laplace-transform both the input and the output we get the transfer function
$$H(s) = 1-\frac{1}...
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Where to start in Nonlinear System Identification
Now that I have accomplished learning and applying various linear system identification techniques to simulated data sets.
I am looking now to dig deeper into the world of system identification by ...
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Request for publicly available datasets for linear system identification practice
Apologies if the question is not fit properly here.
Goal: I have a system identification project where I need a dataset to construct a dynamic model and perform correlation and/or predictions. The ...
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Is the system $y\left(t\right)=\int _{t^3-1}^{t^3}x\left(s\right)ds\:$ invertible? [duplicate]
I have the following system: $$y\left(t\right)=\int _{t^3-1}^{t^3}x\left(s\right)ds\:$$
I was told to determine if it's invertible system, casual system, memoryless system and linear system. I was ...
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The definition of Time Invariant systems
according to the wikipedia Time-invariant system article:
Mathematically speaking, "time-invariance" of a system is the following property:[4]: p. 50
Mathematically speaking, "time-...
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Does the error in the impulse response accumulate when applying a step-input?
Consider the model of the form $y[n]=0.9y[n-1]+x[n]+e[n]$, I forgot if this is called an ARX model but who cares, anyways assume $e[n]$ is a zero-mean white noise. I am applying a non-parametric ...
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Sufficient condition for a system to have memory
This is for a black box system which is not LTI and for which we have no input output expression, but we have some examples of sample inputs and corresponding outputs.
I believe in this situation, we ...
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IIR System Identification Difficult Problem
Identifying IIR systems is considered a difficult problem and different approaches have been proposed. Why is it considered difficult? I would like to find an accessible discussion of the problem (a ...
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How to design fir filter from transfer function
Transfer function is this equation in frequency domain:
$$G(f) = \frac{1}{4\pi d} e^{i2 \pi d f/c}$$
or Hankel function
d : constant (distance),
c : 340
We may think we know complex number of ...
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Best way convert transfer function to FIR filter without group delay if i have complex transfer function data
when i calculate acoustic transfer function, system identification using adaptive fir filtering is usually used and that have not tap/2 group delay maybe.
in simulation if i have complex number of ...
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Identifying system to represent output data as combination of 3 input data
I have some numerical data, which has 3 input vectors and 1 output vector. I have to use all the inputs to represent the output. I am new to dsp and struggling to understand how to do this.
X1: Mostly ...
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Check whether a system has memory or not
My question is whether the systems below are memoryless or not:
$1.) \ y(t)=K$ where $K$ is a constant
$2.) \ y(t) = x(t_0) $ where $t_0$ is a constant
So, from the definition I have been using so far ...
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What is the difference between a causal system and a system with memory?
As far as I know, memoryless systems are causal systems. But why aren't systems with memory necessarily causal?
Since the system with memory is affected by past input and current input, I think that ...
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Design of digital filter with desired phase response
I want to design a digital filter with the following phase response in MATLAB. i.e. at 1kHz, the phase response should be 9 degrees, at 2khz phase response should be 18 degrees ,at 3kHz phase response ...
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System identification for a single-input-single-output-system
Let $u(n)$ be the input and $v(n)$ the output of a single-input-single-output system described by the Auto-Regressive-Moving-Average equation $$v(n)=\sum_{k=0}^{m_{0}}b_ku(n-k)+\sum_{k=1}^{n_{0}}a_{k}...
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Transfer function estimation from frequency response
Let's assume that we know that we are dealing with a SISO second order system for which we have the frequency response (magnitude and phase for a known frequency range ω). What methods would people ...
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System identification from Bode plot
Please can anyone address me to routines (possibly for MATLAB/Octave) to identify system poles and zeros from its Bode plot (magnitude+phase)? I am aware there are functions for system identification ...
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Transfer Function to go from a Step Input to a Linear Ramp between the two step values
I want a very basic simulation of a linear axis that can be given a position demand, and it will move to that position at a constant speed. At this point, I do not care about acceleration, but if I ...
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How to estimate the system characteristic function given experimental input and output
I have experimental signals $y_i(t)$ for $i = 1,\ldots,n$ that correspond to different excitation inputs to a system $x_i(t)$ for $i = 1,\ldots,n$. The goal is to find the system characteristic ...
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Difference equation system identification
Suppose I have a difference equation modeling a vehicle like this:
$$d[k+1]=d[k]+a\cdot u[k]+b,\tag1\label{eq}$$
where $d[k]$ is total distance traveled at time $k$, $u[k]$ is engine input at time $k$ ...
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Region of root locus not inside the feasible region for a given performance specification
I wanted to plot the root locus for a system, whose plant transfer function is
$$
P(s)= \frac{k}{Ts+1}e^{-ts}.
$$
A PI controller was suggested for this system, and the task is to find $K_p$ and $K_i$...
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Bode plot from from step response data
For quality control, I want to measure the frequency response of hardware I built. What I can easily generate on the hardware is a step response. Thus, I want to derive the magnitude and phase from ...
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Transfer function estimation using system identification
I am posting a control system problem here because of this post reference.
Question:
I have input and output datasets. These are graphically shown below.
The blue line is output and the pink line is ...
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Given a system with Transfer Function and its desired output. Is it possible to find the required Input?
I'm currently working on an DC servomotor. I managed to find it transfer function using System Identification theory and Matlab.
The transfer function is given as
$$H(Z) = \frac{1 - 0.4952z^{-1} + 0....
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Estimation of Group Delay from Noisy Frequency Response Measurements
Consider a linear, time-invariant system. Noisy measurements of the magnitude and phase associated with the frequency response of the system are available over some dense generally non-uniform grid ...
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How to find the perfect regularization number?
I have an issue!
Assume that we are going to solve $Ax=b$ but $x$ contains noise.To minimize that noise we can use regularization:
$$x = (A^TA + \lambda I)^{-1}A^Tb$$
Where $\lambda$ is a small ...
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Why does this transfer function estimation not work? System identification
Goal:
I have an unknow dynmical system $G(s)$ and I want to find it from measurement data, output $y(t)$ and input $u(t)$. The data is frequency responses.
Method:
I begun first with creating the ...
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Confusion regarding application of time invariance to flip system?
I am reading book signal processing first
Chapter 5
I am reading article of time invariance
Where author mentions example of a flip system as shown in attached photo ,i have drawn a red curve above ...
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Characterizing an unknown LTI system
What are the best approaches to characterize an unknown discrete time LTI system? I believe one of the approaches is to input a known input and measure the output to find a transfer function. What are ...
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Why is the error between the desired signal and estimated signal in the case of LMS filter remaining constant even after n number of iterations
I am giving white noise as input to an adaptive filter which is initialized to zero (value of filter coefficients of adaptive filter is 0). I am getting a desired response $d(n)$ by passing white ...
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Stabilizing the inverse transform of a system
Currently I am trying to understand an unknown mechatronic system. I used white noise as an input signal and measured the output of the system. Then I estimated a second order SISO transfer function (...
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Confusion about systems involving integrals
$$y_1(t)=\int_a^tx(τ)dτ$$
$$y_2(t)=\int_a^bx(t)dt$$
I'm confused about what are the input signals in each of these systems.
To my understanding, in the second case the input signal is $x$ since both ...
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Unstable plant transfer function identification
I would like to find the transfer function of an unknown unstable SISO plant.
If it was a stable plant, I would input a sine sweep and measure the frequency response at the output; but I cannot do ...
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