Roundoff noise and scaling in the digital implementation of control compensators

Researchers in digital signal processing have examined at length the effects of finite wordlength in the design of digital filters. The issues that have been considered apply to any digital system. In particular, the design of digital control systems must consider these issues. In this paper we will use, adapt, and extend the ideas developed in digital signal processing to the issue of roundoff noise in digital linear-quadratic-Gaussian (LQG) compensators. We will then examine the roundoff noise effects for a particular LQG example and several different implementation structures.