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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
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3 answers
83 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
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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
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
2 answers
102 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
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
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1 answer
110 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
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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
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1 vote
1 answer
849 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
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
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0 answers
67 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 ...
Faito Dayo's user avatar
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0 answers
223 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, ...
Nik's user avatar
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0 answers
41 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 ...
LHX's user avatar
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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
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2 answers
78 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
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1 vote
0 answers
42 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
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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
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1 vote
0 answers
97 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 votes
1 answer
42 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?
stormy2020's user avatar
2 votes
2 answers
492 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
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7 votes
3 answers
333 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
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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
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2 votes
2 answers
301 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
725 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
5k 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 votes
1 answer
67 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 ...
anotherone's user avatar
0 votes
1 answer
105 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
-1 votes
1 answer
136 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 ...
Kinka-Byo's user avatar
  • 111
1 vote
1 answer
615 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
716 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
0 answers
315 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
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
0 votes
1 answer
68 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, ...
Gaurav Sharma's user avatar
0 votes
1 answer
146 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
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1 vote
0 answers
291 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
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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
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
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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
3 votes
1 answer
200 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
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
1 vote
0 answers
584 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
0 votes
2 answers
96 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
1 vote
0 answers
75 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
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
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
93 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 ...
Dana's user avatar
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