Lab 3 Grading, Prelab, 45 points a.) Draw the integrator block diagram -Block Diagram for the motor torque 2 -Block Diagram for the tape dynamics 2 b.) Finding the transfer functions -ang_vel(s)/ang_vel_ref(s) 3 (hint, the leading 's' term in the denominator must have a coefficient of 1. Multiply the transfer function as needed.) -ang_vel(s)/disturbance_torque(s) 3 c.) Give the range of K which gives a stable system 3 d.) What K gives a steady state response less than 0.01 rad/s (hint: use the Final Value Theorem -- FVT) 3 e.) What should Kr be interms of K 3 f.) Using K -the new zeta value 1 -the new omega_n value 1 -the new Mp value 1 -the new tr value 1 -the new ts value 1 g.) Controller 2 -What K value is needed 2 -What is omega_steady-state 2 -Can we achieve both goals 2 -What Mp do we achieve 2 h.) Controller 3 -New Transfer Functions 4 -What K range is stable 1 -What Kd range (in terms of K) is stable 1 i.) Controller 3 -K value 2 -Kd value 2 -the new Mp value 1 -the new tr value 1 -the new ts value 1 Lab 3 Part 1: 15 pts 2 plots, - disturbance response for 3 controllers 3 - omega_ref response for 3 controllers 3 - M_p, t_r, t_s for three controllers prelab and lab values 6 - Compare/contrast Mp, tr, and ts from Prelab with those from Lab. Which controllers met the specifications? 3 Part 2: Deriving ess components, 12 pts -ess due to c1(t) 3 -discussion on values of omega_n that minimize c1(t) error 3 -ess due to c2(t) 3 -discussion on values of omega_n that minimize c2(t) error 3 Part 3: controller 3, 18 pts - equation for omega_n 3 - equation for zeta 3 - Discussion of effects on zeta and omega from increasing K 3 - Discussion of effects on zeta and omega from increasing K_d 3 - Derive pole equation in terms of omega and zeta in simplest form 3 - Discuss effect on poles of increasing K_d, when K_d > 0 3 Report: 45 Prelab: 45 Checkout: 10 ------------ total: 100 pts