Questions tagged [stability]
The stability tag has no usage guidance.
55
questions
0
votes
0
answers
13
views
Accuracy of stable (not backward stable) numerical algorithm
I understand the definition of accuracy for a backward stable numerical algorithm, which shows how such a quantity depends both on machine-epsilon and on the condition number of the problem under ...
1
vote
0
answers
46
views
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....
1
vote
2
answers
99
views
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 ...
1
vote
1
answer
115
views
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:
$$\lambda_{rel.m} = \sqrt{\frac{f_{m,k}}{\...
0
votes
1
answer
91
views
Basic questions about power grid stability with variable loads and sources
I am curious about integration of renewable energy in electricity grids. I am a mechanical engineer and understand energy and power but I have little knowledge about electricity. I will be thankful if ...
0
votes
1
answer
44
views
Stability properties of controllers with independent control laws applied in underactuated systems
I am interested in designing a GNC controller for a 3DOF underactuated vehicle that follows a path in 2D space. The two available control inputs are the thrust force in the surge direction and a ...
1
vote
1
answer
579
views
How do I find the minimum/maximum stable value of scalar gain for a closed loop transfer function?
I have the following transfer function:
$$G(s) = \frac{s + 8}{s^2 − 2s − 3}$$
This function is placed in series with a static gain $k$ and unity feedback. In this case I'm looking for the minimum ...
0
votes
2
answers
40
views
Who takes care of structural health monitoring of civil structures?
There are numerous studies about the possibility of structural health monitoring (SHM) of tall structures, like bridges, skyscrapers, water towers, wind turbines, where, for example, inclination or ...
0
votes
0
answers
64
views
How to determine the stability of an aerodynamic shape in ANSYS Fluent
I have the aerodynamic outer mold line file of a drone. The first task of the school project is to verify that the drone is stable. First, I used the 2021R2 version of ANSYS Fluent to try to find the ...
0
votes
0
answers
167
views
Definition of BIBO stability of a nonlinear system
I am studying an electric motor whose state-space equations are nonlinear.
I am trying to control the system through a closed loop and I would like to verify the BIBO stability.
For linear systems, ...
0
votes
0
answers
39
views
If there is a instability issue inside the control loop, and the control system starts oscillating, what will be the oscillation frequency?
I have a closed loop controller to control the vehicle on the centerline with a bandwidth of 2 rad/s, and I saw the vehicle keeps oscillating around the centerline in a sinusoid whose period is around ...
1
vote
0
answers
46
views
Lyaponuv stability condition of linear systems for homogenous P in V(x) = x^T P x
I am currently learning about using Lyaponuv functions to find Linear Matrix Inequalities (LMIs) as conditions for stability of a linear time invariant system.
i.e.
$$
\dot{x}(t) = Ax(t)
$$
is stable ...
0
votes
2
answers
63
views
Describe the magnitude of a force using real-life comparisons instead of numbers
I already asked this on physics.se, I got a suggestion to ask here, but the question became too old to migrate before I decided to do it. I did also receive an answer, and I am grateful for it but
...
1
vote
0
answers
35
views
Understanding the RMS noise for a given bandwidth
I would like to ask a technical question regarding the current source Keithley Series 2400 Model 2450. I am looking for a high stability current source capable of feeding some Hall probes with a ...
0
votes
1
answer
50
views
Determining stability of a current souce from the datasheet. How to?
Is there any way to calculate the stability of an instrument such as current sources and digital voltmeters from their datasheet?
Let me provide one example. My application requires stable current ...
1
vote
0
answers
77
views
How do I determine the pitch/roll stability of a buoy?
I am designing a loosely-moored spar buoy (large height relative to width), and the equipment on top needs to remain as vertical as possible while floating in the sea, within limitations of buoy cost, ...
-1
votes
1
answer
41
views
Did I get the correct result? Block reduction problem
After solving I got
$$T(s) = \frac{s^{2}+3s+3}{(s+1)(s+2)}$$
and for the stability of the system I got:
$$ s_1 = -1 $$
$$ s_2 = -2 $$
So, is the system stable?
2
votes
2
answers
397
views
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. ...
7
votes
3
answers
263
views
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 $...
1
vote
1
answer
50
views
Why is there a delta for locally stable in the sense of lyapunov?
Why does this definition (screenshotted above) for locally stable i.s.L. require a $\delta$ term? Why not just say, something is locally stable i.s.L. if "for any ball of size $\epsilon$ around the ...
2
votes
2
answers
285
views
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 ...
1
vote
1
answer
479
views
Physical interpretation of a Bode plot
I have a few questions regarding the physical interpretation of the information presented on a Bode plot. I believe it is one of those cases where I "don't know what I don't know", so please bear with ...
1
vote
2
answers
4k
views
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 ...
1
vote
1
answer
49
views
Stability of 3D-printed mask after sterilisation
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6797553/
https://www.hatchbox3d.com/collections/pla
We are 3D printing masks that need to be used by medical staff treating COVID19 patients.
The first ...
-1
votes
1
answer
64
views
Strengtheing a weak bed frame
I bought a 200x90 sq.cm. bed and assembled it. The bed frame is assembled out of hollow iron rods. After using for a few days I started having back pain. So I checked the bed and found that some of ...
0
votes
1
answer
94
views
Problem finding value of the gain such that the closed loop is stable
I have the following transfer function:
$G(s)=\frac{-s^3 +s}{s^4+3s^3+2s^2}$
and this is a transfer function of a plant with two poles in the origin. So I want to desing a controller with two poles ...
-1
votes
1
answer
89
views
Nyquist stability criterion for positive feedback
it is known that the stability of a system with negative feedback may be analized through the Nyquist stability criterion, which is based on observing the number of turns around the point (-1;0) in ...
1
vote
1
answer
539
views
Aircraft Longitudinal and Lateral Transfer Function Terms
The figure shows input and output variables for both longitudinal and lateral stability transfer functions.
I completely understand what each term stands for but I was wondering what would be the ...
1
vote
1
answer
550
views
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 ...
1
vote
0
answers
267
views
How to find Ship Transverse Metacentic Height
I did a Civil Engineering course some years ago and from my textbook I had this question. I found that a very interesting question, but unfortunately I haven't been able to find a solution to this.
I ...
4
votes
3
answers
9k
views
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 ...
0
votes
1
answer
64
views
Stability of lattice or mesh supports for printing
Support structures like lattice supports, tree supports or wire supports are being widely used in metal printing or FDM as they minimise the wastage of material and power consumption. In addition, ...
0
votes
1
answer
131
views
If a system is globally asymptotically stable AND locally exponentially stable, can we say claim that it is globally exponentially stable?
I am taking a nonlinear control class. As we were discussing stability, we came across 'weaker' and 'stronger' stability conditions. For example asymptotic stability (AS) is stronger than stability in ...
1
vote
0
answers
284
views
Does the characteristic polynomial contains all the poles of a closed-loop transfer function?
The Transfer Function of a Closed-Loop system is: $T(s)=\frac{Z(s)}{1+G(s)Z(s)}$.
The BIBO stability of $T(s)$ is guaranteed if all the poles of $T(s)$ have negative real value.
In many textbooks I'...
1
vote
1
answer
30
views
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 ...
0
votes
1
answer
3k
views
Control systems, Nyquist plot and root locus
I need help in understanding the connection between Nyquist plot and root locus plot.
Let's say I have a Nyquist plot, what can I infer about the root locus plot? and vise versa.
Given the root ...
1
vote
0
answers
62
views
Does open loop stability guarantee an MPC stability?
In the following publication
...
1
vote
2
answers
153
views
Solar panel actuator control
I'm looking to design a system that can control a solar panel through an electrical actuator for a range of motion of -45 to +45 degrees for maximum solar exposure. The panel will be mounted on a 10 ...
3
votes
1
answer
192
views
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 ...
2
votes
1
answer
43
views
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 ...
1
vote
0
answers
543
views
Maximum slope of the road for a car pulling a trailer
I have a five meter long, 2.40 meter wide, 200 kg portable catamaran I've built at home. To transport, I bought a semi-finished trailer, just the running chassis; and built the upper structure, namely ...
0
votes
2
answers
92
views
How to solve system's general stability from transfer function?
I have a homework which should solve by me. My problem is questions are really simple or should I think outside of the box? Like, bode diagram, nyquist or etc.? And, are my answers correct?
Thanks.
...
1
vote
0
answers
71
views
PID control for UAV [closed]
I'm working on a deltawing model airplane where I want to implement a PID controller to stabilize the pitch, roll and yaw (which are only controlled by two elevons). However, I don't know too much ...
1
vote
0
answers
38
views
Exponential stability under a global coordinate transformation
Consider a system of the form
\begin{equation}
\Sigma\colon\ \dot{x}=f(x),
\end{equation}
where $x\in \mathbb{R}^n$ and $f\colon \mathbb{R}^n\to \mathbb{R}^n$ is a sufficiently smooth function ...
3
votes
2
answers
94
views
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 ...
0
votes
1
answer
2k
views
Control Systems: Why is this system unstable?
I am currently doing a control systems course and I was lead to believe that if a pole lies on the imaginary axis in the s-plane (i.e s=0), then the system was marginally/critically stable.
However, ...
0
votes
2
answers
4k
views
Transfer Function of Spring-Damper System
Given the spring-damper system below where $x_i$, $x_i$, and $y_i$ are position values, how do I find the transfer function $\frac{X_o(s)}{X_i(s)}$? Wouldn't it require mass? I tried neglecting the ...
0
votes
1
answer
88
views
Vertical Linear Actuator Sway Movement
I'm designing something with a vertical linear actuator. It is a quite large actuator lifting a load. I'm anticipating sway from the actuator as it moves up and down so I'm creating a support ...
1
vote
0
answers
47
views
What will be the effect of torque and wheel diameter on the stability of a robot?
I'm building a self balancing robot and would like to know how the wheel diameter and the torque provided by DC motors, would affect the overall stability and response of the robot. The balancing bot ...
4
votes
1
answer
167
views
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, ...