3
votes
$\mathcal H_2$ 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 ...
- 1,653
2
votes
Accepted
Controlling a system in a particular direction
I'll try to explain using examples.
Basic setup
Discrete time system in state space.
$$
\begin{align}
x_{n+1} &= A x_n + B u_n\\
x_1 &= A x_0 + B u_0\\
x_2 &= A^2 x_0 + AB u_0 + Bu_1\\
x_3 ...
- 951
2
votes
How to re-write systems of two linear second order ODEs in a state space form
State Space form:
Assuming the double dots are a mistake, and they're supposed to be single dots (please clarify):
$$
\begin{bmatrix}
\dot{z_1}\\
\dot{z_2}
\end{bmatrix}
=
\begin{bmatrix}
-1 & a \...
- 757
2
votes
Accepted
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....
- 951
2
votes
Accepted
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 ...
- 2,472
2
votes
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 ...
- 951
2
votes
Accepted
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 ...
- 14.3k
1
vote
Accepted
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 $\theta_{A_i} = 0$.
- 128
1
vote
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 ...
1
vote
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 ...
- 633
1
vote
Accepted
State space representation of a 2 tank system
They got cancelled.
At equilibrium when $dh₂/dt = 0$, the equation for the second tank is $0 = k√ħ₁ - k√ħ₂$.
- 1,951
1
vote
Accepted
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...
...
- 66
1
vote
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(...
- 176
1
vote
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 ...
- 395
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 ...
- 2,472
1
vote
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 ...
- 951
1
vote
Accepted
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 ...
- 951
1
vote
$\mathcal H_2$ 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 ...
- 21
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 ...
- 1,901
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 ...
- 757
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 ...
- 757
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