Questions tagged [differential-equation]
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24
questions
1
vote
1answer
76 views
Why does Simulink generate this code for a PID controller?
For the Simulink PID Controller model
The Simulink generated code (rewrite for better understanding) is:
...
2
votes
1answer
67 views
Why is particular solution zero for an impulse excitation signal?
We were being taught the impulse response for a series RC Circuit- consisting of simply one resistance, one capacitor, and an impulse excitation all in series.
I get that the homogeneous part of the ...
0
votes
0answers
6 views
Adding noise in frequency domain while solving an SPDE
I’m implementing a numerical solver to a certain kind of a 2D stochastic PDE using Fourier Transforms.
So, this solver is a Galerkin type method, which means that choosing the right basis functions I ...
0
votes
0answers
15 views
Square pulse test of Upwind Finite Differences
I`m analyzing the numerical methods for the 1D convection equation for stability, consistency, and accuracy. I want to see How does this square pulse move in domain and time?
Here is my code
% ...
0
votes
1answer
252 views
RC high pass filter differential equation
I have the question to derive:
$$RC \frac{dy(t)}{dt} + y(t) = RC \frac{dx(t)}{dt}$$
which describes a high pass filter or $CR$ circuit with $x(t)$ the input and $y(t)$ the output.
I am really ...
3
votes
0answers
50 views
Causal and Non-memoryless LTI sytems described by LCCDE
I was wondering about the nature of stable systems (in the BIBO sense) that are causal with memory for which we wish to represent them by LCCDE (if they may exist). How frequent do LCCDE exist such ...
0
votes
2answers
169 views
From transfer function to differential equation
I have the below detailed solution (boxed in blue) that I don't understand completely:
I can reconstitute the differential equation from:
$$ (1+Ts) X(s) = K_v U(s) $$
$$ x(t) + T\dot x(t) = K_v u(t) $...
1
vote
0answers
39 views
Augment State Space Model with Derivative of State
Problem
How do you augment a state space model with the derivative of a state? I know how to augment a state space model with the integral of a state by doing the following. Given a linear system
$$ \...
0
votes
0answers
21 views
Parameter tracking using Augmented state vector approach and unscented Kalman filter
I'm trying to reproduce and extend figure 9 results in
Nonlinear dynamical system identification from uncertain and indirect measurements"HU Voss, J Timmer, J Kurths - International Journal of ...
1
vote
1answer
141 views
Stability of a system in time-domain
Consider a system for which the input $x(t)$ and output $y(t)$ are related by the differential equation $$\frac{d^2y(t)}{dt^2} + \frac{3}{2}\frac{dy(t)}{dt} - y(t) = x(t) \tag{1}$$Determine $h(t)$ for ...
0
votes
1answer
51 views
How does the intuitive notion of causality fit in with control systems?
Edit: By causality, in this question, I do not mean the traditional mathematical definition in the theory o signals and systems; I mean causality as in an intuitive 'what's moving/pushing what notion'....
0
votes
0answers
35 views
How to I get transfer function?
there is a ODE
$dx/dt-ax(t)=u(t)$
Firstly, I have to find the transfer function $u$ to $x$ using exponential input. So I put $u(t)=e^{st}$ to the ODE, and I got $x(t)=x(0)e^{at}+1/(s-a)e^{st}$. In ...
1
vote
1answer
150 views
Confusion in initial condition of differential equation using Laplace transform transform
I'm confused in solving linear constant coefficients differential equations (LCCDEs) by Laplace transform if initial conditions are given at time
just before $t=0$
just after $t=0$
exactly at $t=0$
...
3
votes
1answer
425 views
Impulse response if initial conditions are given
In most books, impulse response of LTI systems are calculated by assuming initial rest condition, but how to calculate response of an impulse input if there are some initial conditions present ?
My ...
1
vote
1answer
90 views
Finding the system output by convolution
pretty new to this concept, so do bear with me.
A linear dynamic system is described by the following differential equation:
Transfer function H(s) is calculated to be =
I've already found the ...
0
votes
0answers
101 views
Output Noise Power for ODE
My system is described by the following ODE:
$$
\frac{\mathrm{d}y(t)}{\mathrm{d}t} = a-y(t)x(t)
$$
Where $a$ is a constant and x(t) is a poisson process so that:
$$
E[x(t)x(s)] = qI\delta(t-s)
$$
...
0
votes
0answers
45 views
Is a LTI system with dead-time equivalent with a LTI system with no dead-time but delayed input signal?
I wonder if the system parameters would remain the same after all.
According to the definitions, the gain is the change of the output induced by the change of the input if we assume that the gain is ...
1
vote
0answers
63 views
Is non-causal, non-LTI solution to difference equation correct?
Find a solution to the difference equation $y[n]-\frac{5}{6}y[n-1]+\frac{1}{6}y[n-2]=\frac{1}{3}x[n-1]$ that is neither casual nor LTI, where $y[0]=y[1]=1$ and $x[n]=\delta[n]$
The homogenous ...
3
votes
1answer
48 views
Proof for the solution of homogenous difference equation
Suppose the output $y_h[n]$ of a linear, time-invariant system is described by by the following equation for input $x[n]=0$,
$$\sum_{k=0}^{N}a_k y_h[n-k] = 0$$
My book states the $y_h[n]$ is in fact ...
0
votes
1answer
41 views
Difference equation with variable coefficients in MATLAB
Given the following difference equation
$$y[n]-\left(\dfrac{n}{n+1}\right)y[n-1] = n\cdot x[n]$$
How can we use MATLAB to solve it?
I know if the coefficients are constant we can simply use ...
1
vote
1answer
482 views
Determine the system function H(s) of a system and find out the differential equation
I have created the following system for practice purposes. From this system I want to determine the system function H(s).
In the picture I have worked with auxiliary (dummy) variables, which should ...
2
votes
2answers
2k views
LCCDE in simple words?
What is LCCDE?I only know its abbreviation/full form :linear constant-coefficient difference equation
I know that in s domain we have differential equations and in z domain we have difference ...
4
votes
1answer
66 views
Damped spring mass system - parameter estimation
I've tried to calculate the parameters of a damped spring mass system of the form
$m~ y''(t)+d~y'(t)+c~y(t)=F(t)$
but I have some problems determining the mass m of the system.
The damped ...
2
votes
1answer
313 views
Transform a Continuous Time Differential Equation of a Low Pass Filter to Discrete Time
Assuming I have a linear differential equation of first order low pass filter:
$$RC*y(t)'+y(t) = x(t) $$
And Assuming i know now that the input x(t) is being sampled at a rate of $T_s$
how can now ...
