10
votes
Relation between signal processing and control systems engineering?
I did my signal processing Ph.D. in a control systems department. My take is that signal processing is open loop; control systems close the loop.
Apart from that, the mathematics behind both are very ...
- 25.9k
8
votes
Relation between signal processing and control systems engineering?
Both draw on Linear System Theory (a.k.a. "Signals and Systems"). So also does Communications Systems and Linear Electric Circuits, Electronic Circuits,and Distributed Networks (a.k.a. Transmission ...
- 21.1k
7
votes
Accepted
In the context of transfer functions, what is the relationship between the terms "proper", "causal", and "realizable"?
Causality is a necessary condition for realizability. Stability (or, at least, marginal stability) is also important for a system to be useful in practice.
For linear time-invariant (LTI) systems, ...
- 91.4k
6
votes
Accepted
How can a system be unstable if $L(j\omega)$ is never exactly $-1$?
You cannot make conclusions about the stability of a system by only considering its transfer function evaluated on the imaginary axis $s=j\omega$. Replacing $s$ by $j\omega$ in the transfer function ...
- 91.4k
6
votes
What is the principle behind my voice echoing perpetually when 2 separate devices are used for playback and recording on video calls?
On each individual device, the speaker output can get subtracted from the microphone before it gets sent to other locations. This prevents others from hearing themselves through your microphone. When ...
- 261
6
votes
State space physical meaning
As you pointed out, there are many state-space realizations of one particular transfer function. The reason is that a transfer function only represents the input-output behavior of a system (...
- 75
6
votes
Accepted
How accurate is the dominant poles approximation in higher order control systems?
It depends entirely on how close the less dominant poles are to the dominant poles. A simple way to understand what is happening is consider poles on the real negative axis for continuous time systems:...
- 53.9k
5
votes
Accepted
Why oscillations in PI control?
Integration has memory. When the error becomes zero, there is no guarantee that the integrator has reached to zero sum of the previous errors.
So even when there is no error at a particular time the ...
- 522
5
votes
Why do these 2 methods give different solutions?
The problem is that you took the derivative of the function
$$\hat{x}_u(t)=2e^{-3t}-e^{-4t}\tag{1}$$
whereas using the Laplace transform you implicitly assumed that $x_u(t)$ equals zero for $t<0$:...
- 91.4k
5
votes
Accepted
How do I stabilize my oscillating system?
First, combine your two variable set of first order differential equations into a single variable second order one.
$$ \frac{d^2y}{dt^2} = c \frac{dx}{dt} = acy + bc $$
$$ \frac{d^2y}{dt^2} - acy = ...
- 7,590
5
votes
Accepted
State space equations
Two principles here:
When dealing with a differential equation, you define intermediate state variables so everything is in terms of first derivatives.
This system is nonlinear, so the state-space ...
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5
votes
Relation between signal processing and control systems engineering?
There's a fairly simple distinction.
Signal processing is a set of tools that can be used for control engineering.
Control engineering is about making something move how you want it to move. Some of ...
- 321
5
votes
Layman Description of the Kalman Filter
Simple Description
Imagine you're in a car that is traveling at 70MPH with cruise control. Because the cruise control isn't perfect, your actual speed might vary slightly. This imperfection is called ...
- 902
5
votes
Which step response matches the system transfer function
Open loop gain at DC is -3dB or .707 and 0 degrees. We don’t know the forward gain but assuming it is the open loop gain, the closed loop gain would be $.707/(1+.707)= .4148$, matching the first plot.
...
- 53.9k
5
votes
Accepted
Which step response matches the system transfer function
The final value of the step response is the DC gain of the closed-loop transfer function, which is generally different from the open-loop DC gain.
Assuming unity gain feedback, the feed-forward ...
- 91.4k
5
votes
How to set parameters of the PI controller inside the PLL?
Two suggestions to move forward:
Reduce $K_i$ to the point of an acceptable overshoot (this will provide the bottom line answer for comparison to the computations.
Do system identification (Bode ...
- 53.9k
5
votes
Accepted
How do you design using bode plots?
The Bode Plot is typically used to display the open loop magnitude and phase response, for which we can assess stability in many cases (not all). The stability criteria that the phase is less than -...
- 53.9k
5
votes
Accepted
Intuition for $\mathbf{P} = \mathbf{0}$ in steady-state when $\mathbf{Q} = \mathbf{0}$ (Kalman filter)
We each have different life experiences to fuel our intuition, but try this one out:
Let $\mathbf A = 1$ and $\mathbf Q = 0$, and $\mathbf C = 1$ -- i.e., the actual state variable just doesn't change,...
- 12.9k
4
votes
When can the $\mathcal Z$-transform be inverted? When not?
If I understand your question correctly then you're asking under which conditions the inverse $\mathcal{Z}$-transform of a given function $F(z)$ exists. Since the inverse $\mathcal{Z}$-transform is ...
- 91.4k
4
votes
Why oscillations in PI control?
For symplicity, consider the SISO linear system
\begin{align*}
\dot x &= ax +bu\\
y &= cx
\end{align*}
with $x$,$u$ and $y$ taking values in $\mathbb R$. Assume that you want to stabilize the ...
- 768
4
votes
Accepted
Mathematically speaking, is a "signal" a function or the set of outputs from a function
A signal is a physical quantity (e.g. voltage) carrying information, or a set of values (e.g. samples in discrete case) of the given function for different values of the underlying independent ...
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4
votes
Accepted
What is the difference between a lag compensation and PI control?
Well, the two systems differ only at low frequencies. In fact, if you define
$$
R_L = \dfrac{\tau_zs+1}{\tau_ps+1},\qquad R_I = \dfrac{\tau_zs+1}{\tau_ps}
$$
you have that $R_I(j\omega)\underset{\...
- 768
4
votes
Accepted
Step response of a differentiating system
If your system is an ideal differentiator with input-output relation
$$y(t)=\frac{dx(t)}{dt}\tag{1}$$
then its transfer function is
$$H(s)=\frac{Y(s)}{X(s)}=s\tag{2}$$
From the equation in your ...
- 91.4k
4
votes
Accepted
Discrete State Space Model - Why Are We Calculating $ x \left[ k + 1 \right] $ Instead of $ \dot{\boldsymbol{x}} \left( t \right) $?
I will ask you something that will give you intuition.
How would you calculate the Gradient of an image?
Image is a discretization of reality, so how would you estimate the gradient of the "Reality" ...
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4
votes
Discrete State Space Model - Why Are We Calculating $ x \left[ k + 1 \right] $ Instead of $ \dot{\boldsymbol{x}} \left( t \right) $?
Hi: I've been wondering about the same exact thing myself and the light bulb finally turned on a few days ago when I went back to Kalman's 1960 paper. ( I've read it many times but not recently ). ...
- 1,117
4
votes
Layman Description of the Kalman Filter
KF is actually a mixture of a deterministic state propagator and a statistical estimator.
Despite it's name including the term filter, Kalman filter is not a simple frequency selective one. It's ...
- 28.4k
4
votes
Stabilizing the inverse transform of a system
Like you mentionned, you cannot cancel a right-half-plane zero (or a zero outside the unit circle) by placing a pole on it. A unstable pole in your compensator will make the command of your controller ...
- 3,797
4
votes
Accepted
How do I get a faster system response?
The transfer function is $H(s) = \frac{16.94s + 579.5}{s^2 + 507.2s + 1224}$
This transfer function has 2 poles, one slow pole at -2.4248 and a fast pole at -504.7752. The function has a slowish zero ...
- 3,797
4
votes
Designing a Transfer Function with given requirements
Since the Asymptotes of the Root Locus tends to infinity through angles $(2r-1)\pi/n, r=1..n$, with $n+z$ poles and $z$ zeros, independently if they lie or not at the LHP, if you place the zeros ...
- 1,440
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