18
There are a lot of books out there, but if you are interested in Control and Signal Processing, I strongly suggest you take a look a Stephen Boyd Lectures from standford:
http://www.youtube.com/watch?v=bf1264iFr-w
There's the first one, the entire course is really valuable and he is a great Teacher.
Appart from That here's a good list of my preferred ...
13
The order of system gives the number of memory storing elements in the circuit.
What you have written above is a KVL equation of the circuit. But when you determine the order of the system you need to find the transfer function of the system. Laplace domain is normally used. The highest power of $s$ in the denominator in a strictly proper transfer function ...
12
Let's consider a discrete-time state space model (the derivation for a coninuous-time system is completely analogous):
$$\begin{align}\mathbf{q}[n+1]&=\mathbf{Aq}[n]+\mathbf{b}x[n]\\
y[n]&=\mathbf{c}^T\mathbf{q}[n]+dx[n]\tag{1}
\end{align}$$
where $x[n]$ is the input, $y[n]$ is the output, and $\mathbf{q}[n]$ is the state vector. Taking the $\...
10
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 similar. It's the applications that are generally very different.
8
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 Lines).
Both worry about system stability. Poles have to be inside the unit circle. DSP is actually broader than either Controls or Communications.
Control ...
answered Sep 30 '19 at 16:01
robert bristow-johnson
15.8k3 gold badges28 silver badges66 bronze badges
6
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 only makes sense for a stable system, otherwise you get a function of $\omega$ that does not describe the system, but another (stable) system.
Let me explain ...
6
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, which are fully characterized by their transfer function, we get realizability constraints on the transfer function. For continuous-time LTI systems, if we work ...
6
Hmmmmmmmmm, interesting question.
Since you want to use the second derivative as your criteria, it would seem that you would want to have the maximum second derivative absolutie value for as short of a duration as possible. This would suggest piecing together parabolas, matching the first derivatives at the joints.
How to do this algorithmically will take ...
6
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" if you're given only the image?
In the case above we use Finite Differences to approximate the continuous derivative.
So what actually is approximating $ \dot{...
6
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 using two devices in within audible range of each other, the devices cannot subtract the speaker audio from the microphone audio because the information path ...
6
The Kalman Filter is basically a framework to fuse 2 things:
Measurement.
Dynamic Model (Dynamic in the sense we can predict next value from a current value).
In your case the model is composed of two things:
Model which connects $ {T}_{ext} $ and $ {W}_{fuel} $ to $ {T}_{in} $.
Measurement of $ {T}_{ext} $.
Now, the reason you estimate $ {T}_{ext} $ is ...
5
Decibels (dB) are used to represent a power ratio with a logarithmic scale. Specifically, a power ratio can be expressed in dB as follows:
$$
R|_{dB} = 10 \log_{10}R = 10 \ \log_{10}\frac{P_1}{P_2}
$$
What does a negative number of dB mean? Manipulate the above equation a bit:
$$
R|_{dB} = 10 \log_{10}R
$$
$$
\frac{R|_{dB}}{10} = \log_{10}R
$$
$$
10^{\...
5
$$R\frac{di}{dt}-\frac1Ci=\frac{de_i}{dt}.$$
Isn't that a nice first order differential equation ?
5
Imagine that you're heating (or cooling) a home with a modern furnace (or air conditioner).
the reference or set point is the temperature that you set your thermostat to be. the feedback signal is the actual temperature that is measured with some kinda thermometer.
the actual value that you are trying to control, whether it's temperature or the position ...
answered Apr 22 '16 at 21:39
robert bristow-johnson
15.8k3 gold badges28 silver badges66 bronze badges
5
It's important to realize that in practice many types of systems are used, and only some of them can be regarded as (approximately) LTI. The (didactical) advantage of treating LTI systems in a basic signals and systems course is the elegance and relative simplicity of the underlying theory. Stability and causality are easily checked, and the input-output ...
5
The problem is that you took the derivative of the function
$$\hat{x}_u(t)=2e^{-3t}-e^{-4t}\tag{1}$$
whereas using the Laplace transform you implicitly assumed that $x_u(t)$ equals zero for $t<0$:
$$x_u(t)=\hat{x}_u(t)u(t)=(2e^{-3t}-e^{-4t})u(t)\tag{2}$$
where $u(t)$ is the unit step function.
If you take the derivative of $(2)$ then you'll get the ...
5
First, combine your two variable set of first order differential equations into a single variable second order one.
$$ \frac{d^2y}{dt^2} = c \frac{dx}{dt} = acy + bc $$
$$ \frac{d^2y}{dt^2} - acy = bc $$
Solve:
$$ y(t) = C_1 e^{\sqrt{ac} \cdot t} + C_2 e^{-\sqrt{ac} \cdot t} - \frac{b}{a} $$
$$ x(t) = \int{ ( ay(t) + b ) dt } $$
$$ x(t) = C_1 \frac{a}{...
5
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 equations won't be in terms of matrices.
Applying these principles, we define a state vector:
$$
\mathbf x = [x_1, x_2]^T,
$$
where:
$$
x_1 = y \\
x_2 = \dot y
$$...
5
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 (observable and controllable dynamics) and not the internal states.
That being said, you can directly write state-space realizations from a transfer function with the so-...
5
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 transfer function $G(s)$ equals the open-loop transfer function, and the closed-loop transfer function is given by
$$C(s)=\frac{G(s)}{1+G(s)}\tag{1}$$
The final value ...
4
If you know the exact response of the camera, you can convert the brightness samples of each pixel to a linear intensity scale and perform the averaging there. That will make your whole problem intensity linear and should solve all your problems.
However, I would strongly recommend using a more advanced exposure algorithm. For example you could introduce a ...
4
FIR filters are fairly common in some areas of control theory. As they usually incur a lot of added phase/time-delay, they are not really usable in the feedback path of regular control systems, but they are useful when the added phase/time-delay is not affecting the system in an adverse way, or when the particular phase response and time-delay is desired.
...
4
You can do that if you have new data to merge in.
For instance if you have a sensor for Velocity 1 and a sensor for Velocity 2 and in addition a connection between Velocity 1 and Velocity 2 you can use Kalman.
Yet if you have only one sensor for Velocity 1 which with the transfer system you estimate the Velocity 2 there is no additional info to fuse in.
...
4
The bode plot is just a plot showing the frequency representation of your system. Any transfer function has one, hence you can use it to see the response of both closed or open loop. Nyquist and the root locus are mainly used to see the properties of the closed loop system. The root locus shows the position of the poles of the c.l. system as the gain of your ...
4
The root locus is a way to see how the poles of your system vary from their open loop locations to their closed loop locations.
If the closed loop system is
$$
C(s) = \frac{O(s)}{1+KO(s)}
$$
where $O(s)$ is your open loop system and $K$ is the constant gain in the feedback path around the open loop system, then the root locus looks at how the poles of $C(s)$...
4
In electronics, a Schmitt trigger converts an analog signal to a digital signal by using two different thresholds (limits as you call them), one for an output state change from 0 to 1 and another for a change from 1 to 0. The first is somewhat higher so that if the input fluctuates between those two thresholds, then there will be no change in the output. The ...
4
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 variable.
In the diagram above $\epsilon(t)$ is a mathematical modeling (i.e. function) that characterizes the set of inputs (i.e. scalers) going into the controller....
4
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 system by making $y$ to converge to some fixed set point $\bar y$. Then necessarely there must be a point $(\bar x,\bar u)$ such that
\begin{align*}
0 &= a\...
4
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 integrator could still be under the influence of the errors from the history. That's why it continues to correct for a while more until it over/undershoots and ...
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