Proportional Control
Without realizing it you were applying proportional control to the
car speed. In other words the corrective action you took in response to an
incorrect speed was in proportion to the amount of error. A large drop in
speed caused you to floor the accelerator and, as your speed came up, you
gradually eased off the pedal until achieving the target of 30mph. So much
easier than the switch, but more complex control. With the switch control,
your input (reading the speedometer), only had to decide above or below
the target. Now you have to know how much above or below. Your output was
a simple on-off, now its a pedal position. Is it worth it for controlling
the car? Of course it is. Would you use it for central heating control?
Probably not. Knowing where it is appropriate to apply specific control
techniques is as important as knowing how to apply them.
Let’s adjust our car control environment a little more to examine a
limitation in proportional control. We are driving along a flat road with
our proportional control of the pedal responding to changes in the
speedometer reading when suddenly we start to climb a steep hill. The
speed drops very quickly and we match the drop by a carefully proportioned
depression of the accelerator. The net result is that eventually we get
back up to 30mph but only after we have dropped right down to about 10.
We could see the speed dropping quickly but we constrained ourselves to
only apply a fixed proportion of accelerator based on the difference
between actual speed and target speed. What we feel we needed to do is
produce a lot more accelerator power than we actually needed for a short
duration to counteract the sudden decrease in speed followed by a more
proportioned response. How do we relate this “gut” feeling to control
theory? The answer is derivative control.
Let’s adjust our car control environment a little more to examine a
limitation in proportional control. We are driving along a flat road with
our proportional control of the pedal responding to changes in the
speedometer reading when suddenly we start to climb a steep hill. The
speed drops very quickly and we match the drop by a carefully proportioned
depression of the accelerator. The net result is that eventually we get
back up to 30mph but only after we have dropped right down to about 10.
We could see the speed dropping quickly but we constrained ourselves to
only apply a fixed proportion of accelerator based on the difference
between actual speed and target speed. What we feel we needed to do is
produce a lot more accelerator power than we actually needed for a short
duration to counteract the sudden decrease in speed followed by a more
proportioned response. How do we relate this “gut” feeling to control
theory? The answer is derivative control.