Control Theory Applications for Dynamic Production Systems

5 Frequency Response

Fundamental dynamic characteristics of production systems and components such as time constants, damping ratios, natural frequencies, and stability were defined in Chapter 4, along with important characteristics of time response such as final value, settling time, and percent overshoot. The response of production systems and components to sinusoidal inputs also is of significant interest because decision rules often must be designed so that the production system reacts differently in various ranges of frequency. For example, production systems may be required to meet goals in the presence of relatively slowly changing disruptions such as fluctuations in demand, but it may not be physically or economically practical to meet the same goals in the presence of relatively quickly changing disruptions. Adjustments made using decision rules therefore may be relatively large when responding to lower frequency fluctuations in production system inputs but relatively small when responding at higher frequency fluctuations in inputs. Response to sinusoidal inputs over a range of frequencies is referred to as frequency response.

In this chapter, important fundamental dynamic characteristics associated with frequency response will be defined. These include the magnitude, phase, zero-frequency magnitude, bandwidth, unity magnitude crossing frequency, and -180° phase crossing frequency. The latter facilitate calculation of gain and phase margins, which are measures of relative ...