Mechatronics
Assignment # 1
K. Craig
1
Mechatronics
Assignment # 1
•
Problem # 1
–
Consider a closedloop, rotary, speedcontrol system with a
proportional controller K
p
, as shown below. The inertia of the rotor
is J.
The damping coefficient B in mechanical systems is usually
difficult to estimate accurately.
Because the computed gain value
depends on the estimate of B, the actual system performance can
be quite different than the predicted value if our estimate of B is
very inaccurate.
+

S
K
p
T
d
(s)
Σ
+
+
1
Js
B
+
( 29
d
s
Ω
( 29
s
Ω
Mechatronics
Assignment # 1
K. Craig
2
–
Suppose the nominal value of B = 1.
Discuss the sensitivity of the
steadystate response to uncertainties in B, for a step command
input.
Specifically, compare the sensitivity for K
p
=1 and for K
p
=
9.
–
Discuss the sensitivity of the closedloop transfer function to
uncertainties in B (whose nominal value is B = 1).
Assume J = 1.
Here, the sensitivity is a function of the Laplace variable s.
Use
the magnitude frequency response plot to compare the sensitivities
for K
p
= 1 and K
p
= 9.
–
Consider now
the position control system shown below with K
p
=
0.05, J = 20, and B = 1.
+

S
K
p
T
d
(s)
Σ
+
+
(
29
1
s Js
B
+
R(s)
C(s)