# Tag Info

Accepted

### 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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### 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 ...
• 12.5k
Accepted

### 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 ...
• 1,210

### 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. ...
• 1,210
Accepted

### 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 ...

### 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 \...
Accepted

### 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 ...

### 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 ...
• 12.5k
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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 ...
• 1,734
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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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### What limits the stability of mechanical watches

Another contributor to mechanical watch instability is that the mechanical mechanisms inherently involve a small amount of friction. This is both in the rotating wheels, and also in the escapement ...
• 109

### 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: ...
• 131
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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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### 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 $F_{b_1}=b_1(\dot{x}_i-\dot{x}_0)$ ...
• 1,036
Accepted

### 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 ...
• 14.8k
Accepted

### 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 $G(s)$...
• 540

### 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 ...

### 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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### 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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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 ...
• 4,755
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.
• 2,682
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 ...
• 12.5k

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