Questions tagged [stability]
56 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
votes
2 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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4
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
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
1 answer
Stability with eigenvalues' real part equal to zero
I know, from Lyapunov criteria, that a system is stable (not asymptotically) if the system has eigenvalues with negative real part or it has eigenvalues with real part equals to zero, but in this case the algebraic multiplicity must be equal to the…
th3gr3yman
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2
votes
1 answer
What are the necessary qualitative criteria for the existence of limit cycles
The literature on the existence of limit cycles is replete with complex and abstract mathematical analysis. Or for specific systems of specific structure, specific mathematical criteria that determine the existence or non-existence of limit cycles.…
docscience
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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
2 answers
What limits the stability of mechanical watches
This question is about a "standard mechanical watch". I don't actually know much about mechanical watches, but I'm imagining a timepiece whose movement involves a lever escapement and balance wheel. Let's consider timepieces that are the size of a…
Jagerber48
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1
vote
1 answer
Stability of solid rectangular wood member
I'm reading about buckling of timber members from Eurocode 5: Design of timber structures part 1.
Formula 6.30 gives the relative slenderness of a member:
$$\lambda_{rel.m} = \sqrt{\frac{f_{m,k}}{\sigma_{m,crit}}}$$
where $\sigma_{m,crit}$ is the…
S. Rotos
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