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- Summary:
- TL;DNR: Would it be as effective to just use a polynomial function that is interpolated from an input-error-to-controller-output table instead of the effort of tuning gains of a PID controller?

So, I had a discussion with a friend of mine, neither of us are in controls but I was curious about an answer here. In a PID controller, we essentially take in an error value, do a mathematical operation on it and determine the input (

Now as a substitute to this whole thing, could we create a table of the desired error and controller output response, and then interpolate it have a polynomial function? So we close in on the set point more aggressively when the error is high, and less when it's lower. And we could just define this mathematically.

The only thing I could think of as to why this isn't as good is because a PID controller defines three variables (

**controller output signal B**) needed to the actuator to produce a desired output (position, temperature etc) based on the error (**controller input signal A**). This output from the actuator, is read by a sensor and fed back to generate the error and so on till it singles in on the setpoint value (position, temperature etc).Now as a substitute to this whole thing, could we create a table of the desired error and controller output response, and then interpolate it have a polynomial function? So we close in on the set point more aggressively when the error is high, and less when it's lower. And we could just define this mathematically.

The only thing I could think of as to why this isn't as good is because a PID controller defines three variables (

**Ki**,**Kp**and**Kd**), while this polynomial function would required probably 8 or 10 constants depending on the degree of the polynomial needed to make the controls good enough for our application. But are there any other reasons why this polynomial function approach (based on a table), wouldn't be preferred over tuning a PID controller?