Questions tagged [differential-equation]
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18
questions
0
votes
2answers
58 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:
$$ (1+Ts) X(s) = K_v U(s) $$
$$ x(t) + T\dot x(t) = K_v u(t) $...
1
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0answers
34 views
Augment State Space Model with Derivative of State
Problem
How do you augment a state space model with the derivative of a state? I know how to augment a state space model with the integral of a state by doing the following. Given a linear system
$$ \...
0
votes
0answers
17 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
122 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
42 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'....
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0answers
34 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
97 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
256 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
64 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
99 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
38 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
45 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
47 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
325 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 ...
1
vote
2answers
1k 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
62 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 ...
1
vote
1answer
280 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 ...
