Lecture 33 : Actuator dynamics and PD, PID control for robots.
Error Analysis of PD Compensator :
The error in regulation is given by
as
For step reference input
And a constant disturbance As we know from final value theorem Steady state error satisfies
stedy state error due to a constant disturbance will be
Figure 33.5 Stepresponse
Smaller for higher gear reduction ratio r.
Can be made smaller by increasing the gain
Compareing
it with standard second order behavior, we will get
Finding out Closed loop natural frequency and damping ratio
from above equation & using that
It is customary in robotics applications to take so that response is critically damped.
We can adjust to get the desired speed of response and using above formulae we can find gains .
and damping ratio
from above equation & using that 
so that response is critically damped.
