Hi Peter,
This is not about whether or not PID could be made to work or whether it is a appropriate engineering choice. I have been "making it work" for a great deal of time. This is about raising the bar and moving forward, leaving the past behind, if possible. Put another way, I think that if you looked around you could find a appropriate transportation application for a Model T. Yet in 2021, they are only in shows and museums.
A PID is more than good enough for temperature control systems as long as the dead time isn't too long relative to the time constants of the plant.
You have provide no data or specifications. A trend would be helpful. What do you want to be better?
Do you know that gains can be calculated? Do you know that the desired response can be achieved as long as the closed loop time constants aren't much faster than the open loop time constants.
Do you know that most instructors and what you read on the internet are really ignorant of what the PID gain(s) or time constants really do? Most say the integrator does this and the proportional gain does that and maybe you need a derivative gain for some reason.
The controller gains/time constant place closed loop poles. Closed loop poles, and zeros, determine the response of the system. In the case of temperature control systems you can ignore the zeros.
My approach is to chose a desired response. Then I know where to place the closed loop poles that will result in my desired response. Then I can calculate the controller gain(s)/time constants that will place the closed loop poles where I want. In short, my way is totally backwards from the way most people are taught. Most are taught to tweak gains without regards to how it moves the closed loop poles and how it affects the closed loop response.
I really relish the chance to beat down idiots, some are professors, that think some other method is better than PID. What they usually show is that they don't really understand control theory and the fact that no matter what method they are using they must place the closed loop poles in the right spot to get the desired response.
Now if you really wanted to improve your system you would provide a model of the system.
There is a Lord Kelvin quote I like
Lord Kelvin said:
I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind.
another
Lord Kelvin said:
If you cannot measure it you can not improve it
yet another
Lord Kelvin said:
Can you measure it? Can you express it in figures? Can you make a model of it? If not, your theory is apt to be based more upon imagination than upon knowledge.
So far you haven't reached this point.
Complaining about PIDs will not help because any other, modern and decent, system will require a model. That is if you want to "engineer the ***** out of it." A quote from "The Martian"
If you really wanted help you would provide data in the form of time, control output and temperature for a few disturbances. Without this information the rest of us can only guess as to what the problem is and what can be improved.