13 votes

Why eigen values and poles of a system are equivalent?

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]&=\...
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13 votes
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Why is an RC circuit a first order system?

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 ...
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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 ...
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8 votes
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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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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 ...
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7 votes
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Improving Velocity Estimation Using Multiple Sensors in a Dynamic System

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 ...
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7 votes
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Kalman Filter: How to Define Inputs and Outputs of a Model

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 ...
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6 votes
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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 ...
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6 votes
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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, ...
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6 votes

Make a signal that fits another the best possible with a limitation in the 2nd derivative

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 ...
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  • 6,903
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 ...
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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 (...
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  • 73
6 votes
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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:...
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5 votes
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What is the physical interpretation of the dB scale on a bode plot and what is a negative dB?

Decibels (dB) are used to represent a power ratio with a logarithmic scale. Specifically, a power ratio can be expressed in dB as follows: $$ R|_{dB} = 10 \log_{10}R = 10 \ \log_{10}\frac{P_1}{P_2} $$...
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5 votes
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What is the Reference in Control Theory?

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 ...
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5 votes

What are the advantages of LTI ( Linear Time Invariant ) systems over other systems?

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 ...
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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 $t<0$:...
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5 votes
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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 = ...
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5 votes
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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
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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 ...
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5 votes
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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 -...
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  • 37.7k
5 votes
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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,...
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  • 8,638
4 votes

Do FIR filter have any application in control theory?

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 ...
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  • 945
4 votes

Do we use closed loop or open loop information in Bode plot, Nyquist plot and Root Locus?

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 ...
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4 votes
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Do we use closed loop or open loop information in Bode plot, Nyquist plot and Root Locus?

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(...
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4 votes

Are there theories to manage states of signal volatility around a limit

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 ...
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4 votes
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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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  • 3,272
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 ...
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