Questions tagged [differential-equation]

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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 ...
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108 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 ...
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1answer
41 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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31 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 ...
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67 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 $t=0$ ...
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127 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 ...
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1answer
52 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 ...
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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: $$ E[x(t)x(s)] = qI\delta(t-s) $$ ...
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33 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 ...
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37 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 ...
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46 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 ...
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40 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 ...
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1answer
204 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 ...
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721 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 ...
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56 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 ...
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256 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 ...