Control Theory in One Hour

Assignment :

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

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