LAB #5 report. MAE 106. UCI. Winter 2005

Nasser Abbasi, LAB time: Thursday 2/10/2005 6 PM

Answer 1.

a) MATH

The output is $\theta $ and the input is $\theta _{d}$

But MATH

Take Laplace transform we get MATH

Hence the transfer function MATH

Compare this transfer function with MATHthe one we used in the Lab. We see that new $G\left( s\right) $ has a zero at MATHwhile MATH has no zero. This controller will perform better as it tracks speed error as well as position error. This will make it more sensitive to changes.

Answer 2.

$\ $For p1, we are asked to plot the predicted response of MATH for a step input for $\zeta =0.1,1,2$

Write the equation in standard form, we get MATH

Hence MATH and MATH

Where MATH and MATH

I will use $J=1\,$hence the transfer function becomes

MATH

The following are the plots generated by a small program


Figure

For p3, we are asked to show plots for step input response for $C=1,2,3,4\mu F$ These are plots:


Figure
for p4, we are asked to plot the step response with higher k on top of the step response using original gain. this is the result


Figure

We see that with higher k, then the system responded more quickly.

Answer 3

Here we are asked to plot the frequency response for the predicted response. p2:


Figure

This is the result for p5


Figure