Week #13 & #14: (4/15-26) PID Controller Math

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Week #13 & #14: (4/15-26) PID Controller Math

Post by rjagodowski »

This week we're going take a detour from the regular Control Systems text in order discuss Chapter 8 in the Parallax Process Control Text about PID Control. (At this point, you should have completed up to Chapter 7 on Level Control in the Bartelt text.) This week our emphasis will be on the the processes through which a computer (microcontroller in this instance) can perform Proportional, Integral and Differential calculations. I've attached a pdf of Chapter 8 here for your convenience:
Process-Control-Text-Chapter 8_v1.0.pdf
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Figure 8-1 on page 249 shows a block diagram of a PID Control System and Figure 8-4 on page 252 shows a typical analog circuit showing the PID control elements (op-amps, R's & C's mostly).

Our task in class will be to complete this chart and hopefully understand the calculations the BS2 will use to perform the PID calculations required in Chapter 8 experiments. Our focus will be on Table 8-1 on page 272. It's attached here and printed copies will be distributed in class on 4/22.

This table is based upon the Classical PID Formula presented on page 248 of the Process Control Text:
Classical PID Formula.jpg
Classical PID Formula.jpg (147.74 KiB) Viewed 342 times
Table 8-1_p272.jpg
Table 8-1_p272.jpg (65.06 KiB) Viewed 342 times
A pdf containing the above formula and Table is attached below and a hardcopy will be distributed in class on 4/22.
PID Controller Handout Worksheet v18.1.pdf
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Here's what the Table 8-1 should look like when it's completed. Note the value in RED indicates a correction from the solution given in the Parallax Process Control text. NOTE: Your final exam will have a problem containing a chart similar to this one and you will be required to do the same PID calculations. You should understand the process.
Table 8-1_p272_Complete.jpg
Table 8-1_p272_Complete.jpg (71.64 KiB) Viewed 342 times

In addition, for reference, here is the schematic for the Incubator Circuit:
Ch. 6 & 7 Incubator Schematic & Layout.pdf
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along with this annotated version to aid in troubleshooting procedures:
Annotated_Incubator_Schematic.jpeg (64.33 KiB) Viewed 342 times

Here's an Explanation of Derivatives and Integrals from The School of Physics, Sydney, Australia.

Derivative Control Mode Analogy and a PID Position Control Simulation from Wisc-Online.
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