# Tagged Questions

201 views

### deriving second order transfer function from spring mass damper system..

I am having a hard time understanding how a differential equation based on a spring mass damper system $$m\ddot{x} + b\dot{x} + kx = 0$$ can be described as an second order transfer function for an ...
39 views

### From position to velocity?

I have an transfer function which tells what the angular displacement of an DC motor. This transfer function is in the S-domain, and normally when you differentiate (*s) the angular position you would ...
48 views

### laplace transform of a sine function

I'm a little confused about how to find Laplace transforms of a sine function when it is a function of time. As in, suppose the function is $x(t)=\sin(at)$ , then I can proceed to get ...
69 views

### Why does the Final Value Theorem not hold for a transfer function with more than one pole at the origin?

The Wikipedia article on the Final Value Theorem states the following for cases where it does not hold: There are two checks performed in Control theory which confirm valid results for the Final ...
51 views

### Why does this phase calculation go to 180 instead of 90?

This is all coming from the following video I am studying from http://www.youtube.com/watch?v=XSS6L42ce88 So I am working from this system $$G(s)\,=\,\frac{4}{s^{2}+s+2}$$ and the video states the ...
84 views

### Finding Transfer functions for linearised systems

I'm using Nise for my control systems class. Finding a linearised system is all gravy baby, but when it comes to finding the transfer function Nise does some stuff which confounds me: See page 6/7, ...
224 views

### Finding the steady state error in the Laplace domain

I have the following block diagram: Now I like to find the steady state error for theta_ref being a step input and for several values of n, Td, K1 and K2. For the moment we can assume all gains ...
81 views

### Nyquist criterion

When using the Nyquist stability criterion, amplitude-frequency characteristic etc. we go from the Laplace image $G(s)$ to $G(j\omega )$. By definition of the Laplace transform, $s=\sigma + j\omega$. ...
117 views

### Identifiability of a state space system

I'm trying to solve assignment 4E.5 from this sheet (ship steering dynamics). My question are: Do I need to perform the Laplace Transform in order to check for identifiability? The state space model ...
264 views

### How can I efficiently sketch a Nyquist diagram?

I have the following transfer function: $$P(s) = \frac{3}{(s-1)(s+2)(s+3)}, s= j\omega$$ I got the starting and endpoints: $$\omega_0 = -\frac{1}{2}, \omega_\infty = 0$$ When I split the ...
8k views

### How can I find the time constant of a first order system transfer function?

How can I obtain the time constant of the transfer function of a first order system, such as the example below? $$\frac{C(s)}{R(s)} = \frac{2}{s + 3}$$ Where $C(s)$ is the output of the system and ...
Assume a system with dynamics: $\dot{\omega}(t) = \alpha \omega^2(t) + \beta i(t)$, where $\dot{\omega}(t), \omega(t)$ are system's states and $i(t)$ is the system's input. I'd like to approximate ...
I'm trying to simulate a control system whose transfer function is $H(s)$. I'm comparing different numerical methods for this. I have already used these two methods: - Converting the transfer function ...