# Tag Info

### $\mathcal H_2$ norm for LTV system

LTV systems don't have a transfer function associated with them, so the integral of the squared 2-norm of the transfer function does not exist. However, according to Parseval's theorem in the ...
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### MATLAB allmargin() function return multiple GainMargin, but how to identify them on the Bode plot?

Try right clicking and there should be a menu item along the lines of show->all margins as opposed to show->minimum margin....
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### why Type III systems has at least two gain margins?

Consider a plant with a transfer function equal to $$H(s) = \frac{250000}{s^2 \left(s^2 + 1000 s + 250000 \right)} \tag 1$$ For some good reason (when I've done this it's for low-frequency disturbance ...

### controls - how to measure phase margin for low gain system

I have a closed loop system with the corresponding gain and phase plots... Gain and pase margins of a system are identified from the gain and phase versus frequency plots for the corresponding open ...
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### What is the physical intuition behind an "integrator" in control theory

An integrator is something that "remembers" how long a steady-state error has persisted and ramps the gain in proportion to how long the error has existed. So, imagine that we have a chart ...
1 vote
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### Partial derivative of change in state with respect to multiplicative faults

I agree with you, and I think this is simply an inconsequential mistake from the book, since in the proof, this result is only an intermediate step, and it is later evaluated at $\theta_{A_i} = 0$.
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### What is the physical intuition behind an "integrator" in control theory

Hopefully it will help – the integrator performs mathematical integration (value accumulation). Similarly, the derivative performs derivation (direction and steepness of the change in the accumulated ...
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### What is the physical intuition behind an "integrator" in control theory

I'm an electronic engineer, so to me, an integrator is a capacitor. Capacitors integrate charge current to get Q, total charge, and capacitor voltage is proportional to total charge. The most obvious ...
1 vote
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### State space representation of a 2 tank system

They got cancelled. At equilibrium when $dh₂/dt = 0$, the equation for the second tank is $0 = k√ħ₁ - k√ħ₂$.
1 vote
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### What is the Z transform of the Discreate PI control model？

Your model is already in discrete form but you need to introduce the $z$-operator to your equation. I perceive a missconception about the z-Transform. I hope the following lines will clarify that... ...
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### Multiloop feedback control system find closed loop gain

I've redrawn your diagram below and added some of my own labels: We can then find an expression for $Y(s)/U(s)$ as follows: \begin{align} Y(s) &= X_1(s) - X_2(s) \\ &= H_1(s)X_3(s) - H_2(s)Y(...
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### Different kinds of control loops

The categorization you have mentioned is one common way to categorize control loops based on their inputs. However, there are other ways to categorize control loops as well, such as based on their ...
1 vote

### Why are the phase indicators different between the open loop bode plot and the closed loop bode plot?

A Bode plot is sufficient to tell you how much margin there is (both phase and gain) before a pole or pole pair in a system crosses the stability boundary -- but it does not, by itself, tell you if ...
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### Why are the phase indicators different between the open loop bode plot and the closed loop bode plot?

So in this case, does the phase margin indicator fail? Yes; due to the peculiarity of the system being considered. I couldn't locate a straight text book reference. This is close enough. From ...
1 vote
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### What is the effect of the resonant frequency of the system function Porter diagram on the stability of the system and how to analyze it?

"Actual" Gain Margin Let the phase at 10 rad/s to 60 rad/s be -165 deg. i.e, 20 deg away from 180 deg. At those frequencies, this 20 deg distance from -180 deg will vanish if the system (for ...
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### $\mathcal H_2$ norm for LTV system

Thank you @fibonatic for your answer. After a comprehensive study of the literature, I would like to add these explanations to @fibonatic's in case someone has the same question in the future. The H2 ...
1 vote

### What causes an EUC to propel forwards when leaned forwards?

Think of it like this. When the user leans forward their weight will no longer be directly over the point where the wheel touches the ground, this offset force creates a torque which can be easily ...
1 vote

### Real-life examples of linear dynamical systems with nonzero D matrix

An example of a system in which D is non-zero is a (point) mass on a flat surface, if we have a horizontal force F on mass M as input u, and as output both an accelerometer measurement and the ...
1 vote

### Significance of asymptotes in root locus

The poles of your root locus plot will move in the direction of those asymptotes when you increase your open-loop gain. The asymptotes can (e.g.) help you understand if increasing (or decreasing) your ...

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