1
4
0.1
50
200
2000
W (rad/s)
Magnitude
Figure 10.8 - Bode plot of the open loop transfer function
For the given example, the crossover frequency was computed numerically resulting in 200 rad/s.
Next, we determine the phase of A(s) at the crossover frequency.
A(j200) = 390,000 (j200+51)/[(j200)2 . (j200 + 2000)]
α
= Arg[A(j200)] = tan-1(200/51)-180
°
-tan-1(200/2000)
α
= 76
°
- 180
°
- 6
°
= -110
°
Finally, the phase margin, PM, equals
PM = 180
°
+
α
= 70
°
As long as PM is positive, the system is stable. However, for a well damped system, PM should
be between 30 degrees and 45 degrees. The phase margin of 70 degrees given above indicated
overdamped response.
Next, we discuss the design of control systems.
System Design and Compensation
The closed-loop control system can be stabilized by a digital filter, which is preprogrammed in the
DMC-1600 controller. The filter parameters can be selected by the user for the best
compensation. The following discussion presents an analytical design method.
The Analytical Method
The analytical design method is aimed at closing the loop at a crossover frequency,
ω
c, with a
phase margin PM. The system parameters are assumed known. The design procedure is best
illustrated by a design example.
Consider a system with the following parameters:
Kt Nm/A
Torque
constant
174
•
Chapter 10 Theory of Operation
DMC-1600
