Calculating the time taken for the step response of a system

[MattH150197]

Homework Statement

I have worked out the transfer function of a block diagram in 1st order form To = (K/1+ts) and the 2nd part of the question asks to calculate the time for the output temperature to change by 80% when k1=1, k2=2, k3=3 and k4=4

Homework Equations

where K = (k1k2)/(k1k2k4+k2k3) and t= 1/(k1k2k4+k2k3)

The Attempt at a Solution

So K = 0.2 and t = 0.1 and i thought that the equation to do this would be y=K(1-e^(-T/t)) giving 0.8=0.2(1-e^(-T/0.1)) but this doesn't work can anyone see where I am going wrong? Is the y=K(1-e^(-T/t)) right? Thanks!

 

[gneill]

Presuming that your transfer function represents the impulse response, then your solution form is correct for the step response.

Check your values for $K$ and $\tau$. If your k values are as you've specified and the formulas for $K$ and $\tau$ are correct, I don't get the same values that you do.

The final (steady state) value for y will be equal to $K$. So you're looking for the time when y is 80% of that final value.

 

[MattH150197]

sorry K4 = 2 and if the solution is correct how come i get T = 0.109 seconds, on the booklet it says it should be 0.16 seconds however it doesn't show the methodology of it, but i noticed taking K completely out of the equation would give that answer, is that just a coincidence

 

[gneill]

sorry K4 = 2 and if the solution is correct how come i get T = 0.109 seconds, on the booklet it says it should be 0.16 seconds however it doesn't show the methodology of it, but i noticed taking K completely out of the equation would give that answer, is that just a coincidence

I didn't say that your solution was correct, I said that its form was correct. I should have been more clear about that, for which I apologize.

The steady state value for y is not 1, so 0.8 does not represent 80% of the final value...

 

[MattH150197]

ah okay i got it now, thanks!