8
votes
Minimal realization of a MISO system
One way of doing this is using the Kalman decomposition. For this you need the reachable and unobservable subspaces. These subspaces can be constructed using the image of the controllability matrix ...
- 1,653
7
votes
Accepted
Why is it impossible to create an observer for this not fully observable system?
Observability means that you can estimate the complete state using only the output, without knowing the initial state. In other words, you have to figure out where you are without knowing where you ...
5
votes
Controllability of $x' = Ax + Bu(t)$ implies controllability of $\left \{ \begin{matrix} x' = Ax + By \\ y'=u(t) \end{matrix} \right.$
The solution is fairly straightforward.
Short answer
The system is controllable without any modifications. You made a small mistake calculating the new controllability matrix: you are missing the ...
- 1,220
4
votes
Accepted
System identification of a simple motor with only position measurements
The process of system identification consists of the following steps:
Choose an appropriate input for the system. The input should definitely satisfy the Persistence of Excitation condition and ...
- 1,019
2
votes
Linear Nastran model not converging
Found the solution. Looks like there is a bug in Nastran where if it doesnt see enough space in your C: drive (even if your scratch directory is in your D: drive), it just hangs. Once I cleared out ...
- 151
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
1
vote
Quality of the transient response for an arbitrary transfer function
Those are parameters on time domain, so calculate them in spectrum domain (laplace or fourier) is almost impossible.
So, you should apply inverse Laplace transform to get the solution in time domain, ...
- 171
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
Finding a signal output $y(n)$ with input signal $x(n)$ and impulse response $h(n)$ with a DTFT
As seen here at Wikipedia, the DTFT of signals of the form $a^n u[n]$ is
$$
a^n u[n] \leftrightarrow \frac{1}{1 - a e^{-i \omega}}
$$
To perform convolution of two sequences, it is enough to use to ...
- 951
1
vote
System identification of a simple motor with only position measurements
Another approach that has not been mentioned here, but which is applicable also to nonlinear systems, is to use a gradient-based optimization scheme over a simulation. Say that you simulate the (...
- 144
1
vote
Feedback Control Question: Finding compensator numerator (B(s)) and denominator (A(s)) polynomials to satisfy a specific requirement
your question is ill-conditioned:
If $A$ must have a higher degree than $B$, 2 things can happen:
$A$ is a constant, meaning $B$ must be 0: which means you cannot solve the equation as there is no $s$ ...
- 1,069
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