INC 341 Feedback Control Systems Home Work 3
Assign: 9 Sep 2016 Due for 3AE, 3A, 3WIL: 15 Sep 2016
Instruction: Hand in your work with name and code by hand before the class is started.
DO NOT copy homework from your classmates or lend it to others. Anyone who violates
this regulation will be given -10 for the homework.
1. For the electric circuit shown in Fig. 1, find the following:
• The time-domain equation relating i(t)and v1(t). (2 points)
• The time-domain equation relating i(t)and v2(t). (2 points)
• Assuming all initial conditions are zero, the transfer function V2(s)/V1(s)and the
damping ratio ζand undamped natural frequency ωnof the system. (3 points)
• The values of Rthat will result in v2(t)having an overshoot of no more than
25%, assuming v1(t)is a unit step, L= 10 mH, and C= 4µF. (3 points)
LR
C
i(t)
+
−
v1(t)
+
−
v2(t)
Figure 1: Problem 1.
2. The equations of motion for the DC motor is given as
Jm¨
θm+(b+KtKe
Ra)˙
θm=Kt
Ra
va,
where Jm= 0.01 kg·m2,b= 0.001 N·m·sec, Ke= 0.02 V·sec, Kt= 0.02 N·m/A,
Ra= 10 Ω.
(a) Find the transfer function between the applied voltage vaand the motor speed
˙
θm. (2 points)
(b) What is the steady-state speed of the motor after a voltage va= 10 V has been
applied? (1 point)
(c) Find the transfer function between the applied voltage vaand the shaft angle
θm(2 points)
1
