Questions tagged [stability]

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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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30 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?
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65 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. ...
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61 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 $...
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1answer
42 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 ...
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1answer
49 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 ...
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1answer
65 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 ...
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1answer
50 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 ...
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1answer
46 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 ...
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1answer
37 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 ...
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45 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 ...
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28 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 ...
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1answer
42 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 ...
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1answer
77 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 ...
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96 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 ...
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856 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 ...
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39 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, ...
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1answer
28 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 ...
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193 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'...
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23 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 ...
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1answer
147 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 ...
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39 views

Does open loop stability guarantee an MPC stability?

In the following publication ...
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1answer
75 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 ...
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1answer
96 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 ...
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1answer
33 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 ...
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208 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 ...
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72 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. ...
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67 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 ...
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34 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 ...
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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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1k 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, ...
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2k 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 ...
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70 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 ...
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45 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 ...
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1answer
127 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, ...
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77 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 ...
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374 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 ...
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1answer
505 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 ...
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1answer
202 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 ...
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277 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 ...