Techniques of Model-Based Control

Appendix D. Review of Random Variables and Random Processes

Objectives

• Introduce some basic notions of probability.

• Introduce random variables and random processes.

• Introduce white noise and colored noise.

• Introduce frequency (spectral) decomposition of random processes.

Introduction to Random Variables

Most measurements contain a random component that fluctuates from one measurement to the next. We refer to this as measurement noise. In order to properly account for the effect of this noise on identification, estimation, and control, we need to introduce a few concepts and terms associated with the mathematical description of such noise processes. The disturbances that enter a process also exhibit random behavior. We need tools to model and describe ...