The cheapest temperature pid controller

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rEaLiTy asked What is the main purpose of each parameter in a PID controller?

I am trying to find out what is the main purpose of the PROPORTIONAL, INTEGRAL and DERIVATIVE in a PID control system. Please can anyone explain in detail?

And got the following answer:

Basically, Proportional, stands for "gain", i.e., a negative feedback multiplier. It will reduce the drift of the controlled variable. However, there is only so much negative feedback gain you can apply, before the system turns unstable. On the other hand, some systems can take infinite negative feedback, in which case it becomes an "on-off" system. Integral action, aka by its inverse, or "reset", is the accumulation of the error over time. IOW, negative feedback is increased over time. Its purpose is to reduce the residual error that "P", or gain only, cannot eliminate. It has a clearly destabilizing effect and works only after the disturbance dies out. Derivative action, aka as "rate". generates a negative feedback proportional to the "rate of change" of the error signal. This, in turn, anticipates the disturbance and reduces the excursion of the output error, in theory. It is mostly used when controlling temperature, because of the many time lags a temperature loop has. It requires an additional effort from the power source. .

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