Questions tagged [stability]
The stability tag has no usage guidance.
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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....
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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 ...
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How to show that the infinity norm obtained in the problem given below is correct?
I found the following example problem in page 178 of the book "Nonlinear System" by Hassan K. Khalil, Third Edition. The objective of this problem is to show whether a system is input-to-...
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Stability analysis of pressure relief valve using jacobian matrix
I'm modeling a pressure relief valve in order to find the limits of stability using the Jacobian matrix at an equilibrium point. The equations are the folowing:
$$
\ddot{y} = \frac{1}{m}(A\cdot p\...
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Stability of solid rectangular wood member
I'm reading about buckling of timber members from Eurocode 5: Design of timber structures part 1.
Formula 6.30 gives the relative slenderness of a member:
$$\lambda_{rel.m} = \sqrt{\frac{f_{m,k}}{\...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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
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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 ...
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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 ...
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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, ...
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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?
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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. ...
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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 $...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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'...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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.
...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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