Closed-loop motor velocity control with a digital controller

In chapter 4, we learned how to control the angular velocity of the motor with open-loop control. We based this method on a mathematical model of the system, applying a voltage or current that should result in a desired steady-state angular velocity. This approach can be effective in certain applications, but it has three major drawbacks:

1. If the model is insufficiently accurate, the steady-state angular velocity will not be what we desire. This can be partially mitigated by tuning the model with measurements.
2. We have no control over the transient response, which may be undesirable. For instance, it might take too long to approach the steady-state angular velocity.
3. Disturbances and parameter variations in the system—for instance, if there is a variation in the load—can cause an inaccurate steady-state angular velocity.

It turns out that, within certain bounds, these three drawbacks can be mitigated with a single technique: feedback control. For single-input, single-output (SISO) systems under feedback control, the output is measured and the input to the system is adjusted accordingly. The system to be controlled in this chapter is the target electromechanical system, and its output (angular velocity) will be placed under feedback control. That is, we achieve in this chapter the design requirement R3 of section 1.9:

After a general introduction to continuous feedback control systems in section 7.1, section 7.2 and section 7.3 introduce and apply root locus techniques for proportional-integral-derivative (PID) controller design. Although all necessary ideas will be introduced, these two sections may be challenging for readers unfamiliar with control theory. Section 7.4 introduces digital control systems, and section 7.5 applies digital control theory to the control of direct circuit (DC) motors. In section 7.6, a digital controller is designed for the target system. The results of this section can be applied in lab 7 without an extensive understanding of the root locus technique.