Questions tagged [stability]
65 questions
11
votes
2 answers
Is a chair with N+1 wheels ever less stable than a chair with N wheels?
My workplace has a policy to provide standing desks upon request, but no policy to provide chairs of matching height. (I work for the government...) We can buy our own, or build our own. However they added a stipulation that the chairs must be…
Dennis
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7
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3 answers
A clarifying question on Lasalle invariance principle
Given a nonlinear system \begin{equation}
\dot{x}=f(x),~x(0)=x_0 \tag{1}
\end{equation}
where $f\in{\mathcal{C}^{1}}:D\to\mathbb{R}^{n}$. The Lasalle invariance theorem statement goes as follows:
Let $\Omega\subset{D}$ be a compact set that is…
jbgujgu
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5
votes
2 answers
A stable transfer function which diverges?
This question might sound stupid as I'm more of a software guy and never really had to do control engineering (besides the 101 classes).
So I have a second order system I could approximate, with the following denominator:
$$s^2 + a_1s + a_0$$
Both…
lesurp
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5
votes
3 answers
Why is a cart with swiveling casters in front stable, but not if the swiveling casters are in back?
Consider a four-wheeled cart that has swiveling casters for the two front wheels, and has wheels that don't swivel in back. For example, a common shopping cart, or trolley if you prefer. If such a cart is pushed and let go, it will continue to…
rclocher3
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4
votes
1 answer
Passivity in automatic control (Linear and nonlinear control)
The definition of passivity for control systems is:
$\langle y,u \rangle _T \geq 0 \: \: \: \forall T >0 \: \: \: \forall u$.
Considering signals $u,y :[0,T] \rightarrow R^m$.
As I understand it, passivity is when the system is still stable and…
Payam30
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3
votes
1 answer
Finding stability of open loop system connected to closed loop system
I have a simple cruise control closed-loop system with negative feedback and have no problem using the Nyquist stability criterion to find its stability. However, I have another function that describes the fuel consumption of the throttle in the…
user15540
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3
votes
2 answers
Eliminating lateral motion in a pair of 4-bar mechanisms
As my first serious mechanical engineering project, I've built a wall-mounted folding table using of a pair of 4-bar mechanisms (WIP, ignore the wall mounts):
I'm using fisheye bar ends with spherical bearings, like this:
The mechanism behaves…
damian
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2
votes
1 answer
Stability of a closed-loop with disturbance in output. Characteristic equation alone or substitution
A general block diagram of a feedback controlled process with a disturbance in the output is:
If we assume that the following blocks are equal to 1, and therefore we remove them:
$$ K_m = G_v = G_m = 1$$
We have the following expression in…
Daniel V.
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2
votes
2 answers
Analog PID Controller/Filter delay and stability
recently I had an exercise where I had to build and measure an analog PID controller/filter. The starting point was this circuit.
This is a tamed PID controller implemented with a single opamp. Resistor and capacitor values are calculated regarding…
refa
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2
votes
2 answers
Longtitudinal Centre of Gravity for Ship Cargo
I did a Civil Engineering course some years ago and this question from my textbook, I have found what seems impossible to get the correct answer of 46.2 m for. By putting this question up I am hoping that I will be able to come to a conclusion on…
Rob Wilkinson
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2
votes
2 answers
Why phase margin and gain margin should be positive?
In many textbooks it's given that gain margin (in db) and phase margin of the system needs to be positive for the system to be stable. I could not find the reason behind this. Could someone explain this?
Cris waran
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2
votes
1 answer
Can I replace terminal weight with an even stricter matrix yet ensuring stability?
Terminal Penalty is used to ensure stability of Model Predictive Control (MPC).
where the initial cost function is
$$J(u)=\Sigma_{i=1}^{\infty}[x(k+i)^TQx(k+i)+u(k+i−1)^TRu(k+i−1)]$$
it is modified…
ar2015
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2
votes
1 answer
Equilibrium of rigid bodies
I wanted to evaluate the safety of a walking aid device (walker). For example, if the way it is constructed and whenever I handle it, there are no risk of rotation, around its center of mass, turning over, i.e imbalance/instability.
For example, a…
user3717679
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1
vote
1 answer
What ribs can I add to avoid warping and increase stiffness?
I'm drawing a box for a small electronic project:
It measures about 200x110 mm and I'm going to print it with PLA.
The first attempt was without the ribs you can see on the bottom and it was very easy to twist the box.
Adding them gave a perception…
Mark
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1
vote
0 answers
Internal Stability and Small Gain Theorem
I am currently working on a MIMO feedback system and trying to determine its internal stability. The open loop gain of the system is stable and has no internal right half-plane pole-zero cancellations. The closed-loop feedback system has 4…
Ashutosh Mukherjee
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