An Experimental Evaluation of the Delta Operator in Digital Control

Abstract

Interest in digital control systems has been on the rise over recent decades with the ever decreasing cost and increasing performance of microprocessors and the academic advancements in control theory. Although there are many benefits to digital control, there are many challenges. This study explores one obstacle presented by finite word-length microprocessors: the limited range of numbers that can be represented. The goal is to compare its effects using two different discrete operators---the shift operator and the delta operator.

The experiment is designed in order to accommodate a second challenge in digital controls: most engineers and technicians are far more experienced with continuous controller design. Therefore, this analysis's control design takes place in continuous-time. Both shift and delta-operator-based difference equations are derived from the continuous transfer function. The ability of each competing model to perform under finite word-length conditions is evaluated through mathematical analysis, simulation, and experimentation. These demonstrations are made using a PID controller to compensate a DC-DC buck converter. It is concluded that the delta operator representation is less susceptible to the numerical limitations and shows greater performance resemblance to the original continuous compensator.