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MM4006 M o t i o n Control Tutorial
4.3.1 P I D Servo Loops
The PID term comes from the proportional, integral and derivative gain fac-
tors that are at the basis of the control loop calculation. The common
equation given for it is:
de
K1, • e + K, e d t 4- Kd • d t
where K1) = Proportional gain factor.
= integral gain factor.
K11 = derivative gain factor.
e = instantaneous following error.
The problem for most users is to get a feeling for this formula, specially
when trying to tune the P1D loop. Tuning the PID means changing its three
gain factors to obtain a certain system response, task quite difficult t o
achieve without some understanding of its behavior.
The following paragraphs explain the PID components and their operation.
P Loop
Lets start with the simplest type of closed loop, the P (proportional) loop.
The diagram in Fig. 4.14 shows its configuration.
Motor
Trajectory
Generator
Motion Controller
x K1,
Servo Controller
1.1 D r i v e r
Fig. 4.14 — P Loop.
Encoder •
Every servo cycle, the actual position, as reported by the encoder, is com-
pared to the desired position generated by the trajectory generator. The
difference e is the positioning error (the following error). Amplifying it
(multiplying it by KO generates a control signal that, converted to an ana-
log signal, is sent to the motor driver.
There are a few conclusions that could be drawn from studying this circuit:
• T h e motor control signal, thus the motor voltage, is proportional to the
following error.
• T h e r e must be a following error in order to drive the motor.
• H i g h e r velocities need higher motor voltages and thus higher following
errors.
• A t stop, small errors cannot be corrected if they don't generate enough
voltage for the motor to overcome friction and striction.
• Increasing the Kp gain reduces the necessary following error but too
much of it will generate instabilities and oscillations.
ED1.10181En1020 0 3 / 0 3
4.14 N e v v p o r t .