Automating Manufacturing Systems - Process Control and ...

plc pid - 25.8
next two sections describe different approaches to controller design.
25.3.3 Proportional Controllers
Figure 25.8 shows a block diagram for a common servo motor controlled positioning
system. The input is a numerical position for the motor, designated as C. (Note: The
relationship between the motor shaft angle and C is determined by the encoder.) The difference
between the desired and actual C values is the system error. The controller then
converts the error to a control voltage V. The current amplifier keeps the voltage V the
same, but increases the current (and power) to drive the servomotor. The servomotor will
turn in response to a voltage, and drive an encoder and a ball screw. The encoder is part of
the negative feedback loop. The ball screw converts the rotation into a linear displacement
x. In this system, the position x is not measured directly, but it is estimated using the motor
shaft angle.
C desired
+ e
V
V ωθ , actual x
Controller Current DC
Ball
-
Amplifier Servomotor
Screw
C actual
Encoder
Figure 25.8
A Servomotor Feedback Controller
The blocks for the system in Figure 25.8 could be described with the equations in
Figure 25.9. The summation block becomes a simple subtraction. The control equation is
the simplest type, called a proportional controller. It will simply multiply the error by a
constant Kp. A larger value for Kp will give a faster response. The current amplifier keeps
the voltage the same. The motor is assumed to be a permanent magnet DC servo motor,
and the ideal equation for such a motor is given. In the equation J is the polar mass
moment of inertia, R is the resistance of the motor coils, and Km is a constant for the
motor. The velocity of the motor shaft must be integrated to get position. The ball screw
will convert the rotation into a linear position if the angle is divided by the Threads Per
Inch (TPI) on the screw. The encoder will count a fixed number of Pulses Per Revolution
(PPR).
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