Southpark:
And..... depending on what the initial temperature is and what the temperature would be (without heating for a long enough time), one set of PID coefficients might work better than another set.
I have come to the conclusion that it is better to have some separate (non-PID) code to get the temperature (or motor speed) into the range where PID control works.
If it works for 6 second sampling period, then it should work for 1 second sampling period.
I wonder. Take for example two different clocks. One of them moves the minute hand in a big jump once per minute and the other moves its minute hand continuously. There would not seem to be any value in sampling the first clock more than once per minute. If you sampled it (say) 10 times per minute you would think it was stopped on 9 of those occasions.
...R