Could I have your opinions on PID type selection?
- Here comes a very simple system: Output(t) = \$ k * (Input(t) + systemVariable(t)) \$. \$k\$ is constant and \$systemVariable(t)\$ is a system constant which may change according to time.
- The goal of the whole system is to maintain system output at \$0\$. It has to be as close to zero as possible. The controller has to compensate the \$systemVariable\$.
- The change (\$ systemVariable\$ ) is modeled by a very slow ramp.
The controller's input is the output of the system. However, the measurements are always noisy, and I modeled Band-Limited White Noise into the measurements.
After PID controller, the output goes into an integrator, since the PID controller always calculates the "change" of the plant input.
My original thoughts: Add a PID controller with P=1/k is enough. Since every time the controller gets an error \$e\$, it can be calculated back that the compensation on controller output shall be \$e/k\$. However, Matlab auto-tuning always give me a PID. Why is that?
What is the relation between P of PID and measurement noises? If P is large, the system will tend to be rambling largely, due to the noises. If P is small, the system will tend not to converge to the correct value or very slow. How to make the trade-offs? Or how to prevent system from rambling largely and get quick system responses?
Thanks a lot!