4.12 Consider the second-order plant
1
G(s) =
( s + 1)(5s + 1)
(a) Determine the system type and error constant with respect to tracking polynomial reference
inputs of the system for P, PD, and PID co
1
. Consider the following types of controllers
s s +1
(a ) C ( s ) = k p , (b) C ( s ) = k p + k I / s, (c) C ( s ) = k D s + k p , (d ) C ( s ) = k D s + k p + k I / s
Given G ( s ) =
2
For each typ
16.413 Linear Feedback Systems
Midterm Exam
Name: _
ID: _
Total 26 points. 20 is a full score.
1. (2) Match time domain specifications and regions of pole locations.
Im
Im
Re
Im
Re
Re
(b)
(a)
Im
Re
(d
3.2 Find the Laplace transform of the following time functions:
Solution: (b) f (t ) = 3 + 7t + t 2 + (t )
cfw_ f (t ) = cfw_3 + cfw_7t + cfw_t 2 + cfw_ (t )
3 7 2!
= + 2 + 3 +1
ss
s
3
2
s + 3s + 7 s
3.19 Find the transfer functions for the block diagrams in Fig. 3.54:
G1
1 + G1
Solution: Simplify the block diagram as above,
Y ( s)
G1
T (s) =
=
+ G2
R( s ) 1 + G1
3.22 Use block-diagram algebra to
3.32 In aircraft control systems, an ideal pitch response (qo ) versus a pitch command (qc ) is
described by the transfer function
Q0 ( s )
2 ( s + 1/ )
=2n
2
Qc ( s ) s + 2n s + n
The actual aircraf
4.4 The DC-motor speed control in Fig. 4.38 is described by the differential equation
y + 60 y = 600va 1500 w,
where y is the motor speed, va is the armature voltage, and w is the load torque. Assume