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Questions tagged [stability]

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11 votes
2 answers
422 views

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 ...
Dennis's user avatar
  • 263
7 votes
3 answers
339 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 $...
jbgujgu's user avatar
  • 215
5 votes
2 answers
550 views

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 ...
lesurp's user avatar
  • 153
4 votes
3 answers
10k 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 ...
rclocher3's user avatar
4 votes
1 answer
172 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, ...
Payam30's user avatar
  • 203
3 votes
1 answer
202 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 ...
user15540's user avatar
3 votes
2 answers
104 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 ...
damian's user avatar
  • 131
2 votes
2 answers
512 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. ...
refa's user avatar
  • 23
2 votes
1 answer
44 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 ...
ar2015's user avatar
  • 143
2 votes
1 answer
262 views

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 ...
user3717679's user avatar
2 votes
1 answer
33 views

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 = ...
Daniel V.'s user avatar
2 votes
2 answers
307 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 ...
Rob Wilkinson's user avatar
1 vote
1 answer
871 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 ...
user avatar
1 vote
2 answers
103 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 ...
Jagerber48's user avatar
1 vote
1 answer
52 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 ...
user3180's user avatar
  • 119
1 vote
1 answer
731 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 ...
th3gr3yman's user avatar
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}}{\...
S. Rotos's user avatar
  • 2,259
1 vote
1 answer
754 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 ...
Richard E.'s user avatar
1 vote
2 answers
6k 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 ...
Cris waran's user avatar
1 vote
1 answer
50 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 ...
SagarM's user avatar
  • 111
1 vote
1 answer
621 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 ...
John's user avatar
  • 111
1 vote
1 answer
33 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 ...
docscience's user avatar
1 vote
0 answers
52 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....
Ashutosh Mukherjee's user avatar
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 ...
Chryron's user avatar
  • 141
1 vote
0 answers
43 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 ...
jeb's user avatar
  • 11
1 vote
0 answers
98 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, ...
MechtEngineer's user avatar
1 vote
0 answers
328 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 ...
Rob Wilkinson's user avatar
1 vote
0 answers
292 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'...
DoronS's user avatar
  • 11
1 vote
0 answers
63 views

Does open loop stability guarantee an MPC stability?

In the following publication ...
Adams's user avatar
  • 115
1 vote
2 answers
161 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 ...
PentaKon's user avatar
  • 111
1 vote
0 answers
599 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 ...
user2800464's user avatar
1 vote
0 answers
76 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 ...
nd97's user avatar
  • 11
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 ...
Mehran's user avatar
  • 111
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 ...
user87877's user avatar
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 ...
BartoNaz's user avatar
  • 101
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 ...
MEGUSH's user avatar
  • 1
0 votes
2 answers
97 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. ...
sphinxlike's user avatar
0 votes
1 answer
1k views

Controller design with pole placement method with given damping and settling time

I was given the following equations and asked to design a controller for $u=-Kx$ using a pole placement method with the closed loop system having the damping and settling time $T_s$ given. Am I ...
spe4ker's user avatar
  • 409
0 votes
1 answer
106 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 ...
J.D.'s user avatar
  • 225
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, ...
oodan123's user avatar
  • 103
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 ...
John Smith's user avatar
0 votes
1 answer
111 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 ...
Saeed's user avatar
  • 148
0 votes
2 answers
82 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 ...
pateksan's user avatar
  • 101
0 votes
1 answer
53 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 ...
jeb's user avatar
  • 11
0 votes
1 answer
152 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 ...
k_j's user avatar
  • 1
0 votes
1 answer
160 views

stability/controllability of a finite time linear quadratic regulator

If I have a linear quadratic regulator (quadratic objective function with linear dynamics) and use an open loop control - are there stability/controllability requirements on the system? I know that ...
lkj kjkjl's user avatar
0 votes
0 answers
34 views

Do transfer function changed in vertically placed spring damper system when an additional mass is added

Title: Calculating the Transfer Function and Displacement for a Spring-Damper System with Additional Mass I am working on a problem involving a spring-damper system, and I need help with calculating ...
sandun herath's user avatar
0 votes
3 answers
91 views

I don't understand how the pneumatic control precession actuation on the Brennan Monorail's gyros further balances the vehicle

I linked a YouTube video from Primal Space, The Self Balancing Monorail, discussing how the Brennan Monorail works. @6:40 timestamp the narrator explains how the pneumatic pressure "[pushes] the ...
Adam Yassine's user avatar
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 ...
Federico Toso's user avatar
0 votes
1 answer
45 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 ...
Meeron's user avatar
  • 1