Read all linked pages.

- The bulk of this lecture is based on a PDF file summarizing the Proportional (P), Proportional-Integral (PI), and Proportional-Integral-Differential (PID) controllers, and providing methods for choosing the parameters (Gain, Integral Timescale, and Differential Timescale) for these controllers.

- We will start with an example of using a controller to vary pump speed until a desired mass flow (set point mass flow) is obtained.
- If we know mass flow as a function of omega then its just a matter of solving the equation:

- By Newton's method, the first guess at a solution is

- Unfortunately we don't generally know the form of the function f, but the pattern above gives the form of the simplest (proportional) control algorithm.
- Define the error function

- Then a proportionality constant, G (Gain), which replaces the derivative of pump speed in the above linearization.

- Overview of P,PI, and PID controllers
- PI most used for our purposes
- P always has an offset, in this example it will never drive the mass flow rate to the set point value.
- The integration term in PI corrects the offset
- Discuss Gains and time scales
- Gain on P can cause instabilities if too large
- Methods for picking the I and D timescales.
- Cohen and Koon
- Ziegler-Nichols Settings