section 7.5 companion and outline

This page contains companion resources and an outline for section 7.5 of the book RTC for MEs, and it therefore lacks most of section 7.5’s contents. While some sections of the book are fully available on this site, many are not. Please consider purchasing a copy from MIT Press.

Digital velocity control of DC motors

Controlling with a voltage amplifier

Controlling with a current amplifier

Digital control

TX
DX

The controller models described previously are continuous. The actual controllers are discrete approximations of these continuous models. For accuracy of the approximation, we need all of the following to be the case:

  • The sampling frequency is much larger than the natural frequency of the system.
  • Time delays caused by computation are insignificant.
  • The control value does not saturate.
  • The mechanical damping B is small in comparison with the effects of the proportional term KP in the controller.

Applying Tustin’s method to the continuous PI controller transfer function KP+KIs, the corresponding discrete transfer function is Ua(z)E(z)=b0+b1z1a0+a1z1,(1) where a0=1,a1=1,b0=KP+12KIT, andb1=KP+12KIT, where T is the sample time. The measured error is E(n)=ΩR(n)ΩJ(n).

For more on Tustin’s method, see subsection 6.4.2. In lab 7, we will implement the corresponding difference equation using the general-purpose algorithm developed in lab 6.

Online resources for Section 7.5

No online resources.