11 votes
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Is a chair with N+1 wheels ever less stable than a chair with N wheels?

Assuming all the wheels are evenly spaced on the same circle, then more wheels is always more stable than less wheels. However, there is diminishing return as the number of wheels gets large. The ...
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5 votes
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A stable transfer function which diverges?

Without any more info, I think your problem arises from the values of $a_0$ and $a_1$. The answer is a little involved, so a bit of systems background is necessary. The short answer Your system should ...
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5 votes

Is a chair with N+1 wheels ever less stable than a chair with N wheels?

I think the "health and safety" regulation about 5 wheels is a compromise between stability and cost. If your weight is on the edge of the chair seat and the chair has only 3 wheels, it is much less ...
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4 votes
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Why is a cart with swiveling casters in front stable, but not if the swiveling casters are in back?

Consider what happens in front wheel steering, such as an automobile: Turn the steering wheel slightly clockwise. The front wheels each turn slightly clockwise. Their rolling action causes the wheels ...
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4 votes

How do I find the minimum/maximum stable value of scalar gain for a closed loop transfer function?

The forward path of your control diagram consists of the following transfer functions connected in series: $$ \begin{align*} G(s) &= \frac{s+8}{s^2-2s-3}\rightarrow \text{Plant}\\ K(s) &= K \...
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3 votes

Stability with eigenvalues' real part equal to zero

If the algebraic multiplicity of an eigenvalue is greater than the geometric multiplicity, then the system matrix is not diagonalizable and there are vectors which are not linear combinations of the ...
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3 votes
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A clarifying question on Lasalle invariance principle

A set is invariant with respect to its dynamics if $x(t_0)\in M \implies x(t)\in M$, this is not the case for the set $E$. The set $E = \left\lbrace x\in \Omega \mid \dot{V}(x) = 0 \right\rbrace$ does ...
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3 votes
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How to solve system's general stability from transfer function?

I would like to extent the already given answer by MrYouMath. So question 1 is pretty straight forward and you already got it right. If there's no right half plane (RHP) pole then it doesn't matter ...
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3 votes
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Control Systems: Why is this system unstable?

Your system is open loop stable as the poles are at $s=-1$, $s=-3$ and $s=0$. Note, that if the order of the pole at $s=0$ is greater then 1, then the open loop system is also unstable. But closing ...
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3 votes
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Controller design with pole placement method with given damping and settling time

Step 1 The first thing to do is to determine the desired poles. The natural frequency can be computed using $\omega =\frac{4}{\zeta T_s}$. This is a rule-of-thumb calculation for underdamped ...
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  • 1,876
3 votes

Passivity in automatic control (Linear and nonlinear control)

A short answer for each of your questions in order: How do I describe passivity without the storage function? Passivity analysis is based around the idea of energy flowing into and out of the system. ...
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2 votes

A stable transfer function which diverges?

I'm also a software guy and not completely master of the subject, but I tried to model your system. Each step is shown, so you can catch mistakes I did. Here is the schematic diagram of DC motor: ...
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  • 131
2 votes

Transfer Function of Spring-Damper System

First, create the free body diagram for this system. If you cut through the spring $k_1$ and the damper $b_1$ you will get two forces $F_{k_1}=k_1(x_i-x_0)$ and $F_{b_1}=b_1(\dot{x}_i-\dot{x}_0)$ ...
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2 votes

Control systems, Nyquist plot and root locus

A root locus plot shows how the poles of the transfer function change, when some parameter of the system changes. The parameter is often the loop gain of the system, but it could be anything. A ...
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2 votes
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Strengtheing a weak bed frame

I would take the wooden slats from the old bed and cut them so they can stand on end and be trapped between the steel tubing and the floor, thereby supporting the load that the steel tubing by itself ...
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2 votes
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Problem finding value of the gain such that the closed loop is stable

To solve this problem I would: Sketch the block diagram of the control network. Derive the required closed loop transfer function in terms of $G(s)$ and $C(s)$. Substitute the expressions for $G(s)$...
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2 votes

Why is there a delta for locally stable in the sense of lyapunov?

This is because even if a system is Lyapunov stable it doesn't mean that $\|x(0) - x^*\| \leq \|x(t) - x^*\|\ \forall\,t \geq 0$. For example consider a simple mass spring system with unit mass and ...
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  • 1,603
2 votes

Analog PID Controller/Filter delay and stability

Forget about the fact that it is supposed to be a PID controller, and think about how your circuit works for a constant (DC) input. Because of the capacitor C2, there is no feedback at all from the ...
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2 votes

A clarifying question on Lasalle invariance principle

The sets $M$ and $E$ can be different. The set $E$ only considers $\dot{V}=0$ while $M$ also considers $f(x)$. Namely, invariant set means that for all $x(0) \in M$ the solution $x(t)\in M$ for all $t&...
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  • 1,603
2 votes

Who takes care of structural health monitoring of civil structures?

In the US, I am aware of at least three types of structures that are closely monitored: Highway Structures - through periodic inventory surveys and structural condition assessment by government ...
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2 votes

Who takes care of structural health monitoring of civil structures?

In the United States, there is a mix of government and state and municipalities that are tsked to do this. National Transportation Safety Board (NTSB), for example, is responsible for checking and ...
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1 vote

Determining stability of a current souce from the datasheet. How to?

I suggest that you take a closer look at typical noise. I have highlight the area of the specification for you reference. The best method is to confirm is measure the output to confirm the output.
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1 vote
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Physical interpretation of a Bode plot

I apologize in advance for the length of the text but as you can understand these concepts can't be easily defined in few words. I will do some research about the second question and come back to ...
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1 vote

Why phase margin and gain margin should be positive?

The gain and phase margins of a system are characteristics that can be obtained by studying one of the following well-known plots: Nyquist Plot, Bode Plot, Nichols Chart, Disk Margin which gives ...
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1 vote

Stability of 3D-printed mask after sterilisation

You are probably using an FMD type printer. No matter how good your printer, or the density of the print, you will have porosity. You need the temperature to denature the proteins of the virus. If ...
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  • 101
1 vote
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Nyquist stability criterion for positive feedback

You could just multiply $H$ with minus one, change the positive feedback to negative feedback and proceed with the standard analysis for the Nyquist stability criterion. Here $H$ is the transfer ...
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  • 1,603
1 vote

Aircraft Longitudinal and Lateral Transfer Function Terms

The object of the game is find an expression for the forces, X,Y,Z; and the moments L,M,N on the airframe expressed as a function of the state vector {x,y,z, phi,theta,psi, u,v,w, p,q,r} and the ...
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1 vote

If a system is globally asymptotically stable AND locally exponentially stable, can we say claim that it is globally exponentially stable?

Nope. A system can have better local stability than global. As an extreme example, a system can be stable within some boundary in the state space, and unstable beyond it.
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1 vote

What are the necessary qualitative criteria for the existence of limit cycles

Your (1) and (3) are along the right lines, but I'm not sure what (2) really means and some limit cycles don't look much like "regular orbits" anyway. There is always a danger in trying to produce a ...
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1 vote

Finding stability of open loop system connected to closed loop system

Since you're worried about an open-loop system, in theory all you need to do is perform standard stability analysis on the open-loop system alone. The source of the input signal to the open loop ...
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