If you have been following the thread of this column,
you will recognize that we now have all the background we need to
create an adaptive PID controller. With this installment we will
proceed with its design. Writing this installment presented me
with a difficult problem. Some of you are aware that I have been
very gentle with the mathematics behind the topics that I have
covered in the past. From the feedback that I have received, it
would seem that in spite of my efforts to go easy, this column has
a reputation for being a bit challenging. No matter how much you
try to avoid or hide it, understanding adaptive controllers involves
a lot of math.
As I looked at how to
present adaptive controllers I came to the conclusion that if you
consider where these controllers get used (typically machinery,
frequently *dangerous* machinery), one shouldn't be doing this
as if it was from a cookbook. You really should know the math if
you are doing this stuff. So be forewarned, there is a bit of
math in this installment. There is enough here that we will be
presenting the adaptive controller in two parts, this time we will
do the math and next time we will look at an implmentation.