For g relation between time and exponential decay

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: elation between time and exponential decay Relation Final value theorem Examples Examples 5% settling time is about 3T! 2% settling time is about 4T! 9 Step response for some K & T K=1,T=1 K=1,T=2 Amplitude Amplitude 1 5 Time K=2,T=1 1 Unknown 5 Time K=2,T=2 5 Time Obtain step response Obtain 10 10 2 Amplitude Amplitude Suppose that we have a “black-box” system Suppose 0 0 10 2 1 0 0 System identification 2 2 0 0 10 5 Time 10 1 0 0 Can you obtain a transfer function? How? Can 11 12 Ramp response for 1st-order system Ramp response for 1st-order system K =1 ,T =1 5 Input a unit ramp function to a 1st-order system. Input Then, what is the output? y(t) y(t) 0 0 4 Amplitude Amplitude u(t)=t u(t)=t K=1,T=1 y(t) y(t) u(t)=t u(t)=t 3 slope 2 1 0 0 1 2 T im e Time 3 4 5 Steady state response Steady We may want to modify the system s.t. We (Partial fraction expansion) 13 How to eliminate steady-state error Make a feedback system with a controller having Make a double integrator (copy of Laplace transform of ramp function): u(t)=t u(t)=t Controller 14 Summary and exercises Time response for 1st-order systems Time Step and ramp responses Step Time constant and DC gain Time System identification System Next, time response for 2nd-order systems Next, Exercises Exercises 0 Review examples in this lecture. Review One has to select controller parameters to stabilize the feedback system. Suppose K=T=1, and obtain such parameters! 15 16...
View Full Document

Ask a homework question - tutors are online