Optimal Control Using Frequency Weighted Cost Functionals

摘要

A simple lightly damped second-order system is augmented with an optimal controller using linear quadratic regulator theory. However, instead of using conventional optimal control design methods, the controller is designed with frequency weighted cost functionals. This report investigates the effect of frequency shaping on the frequency and time response characteristics of the closed-loop system. The effects of frequency shaping on the state and control penalty matrices are analyzed separately. Each test case yields improved damping ratios compared with the baseline open-loop system. Each system, including the baseline model, has a high frequency asymptote slope of -40 dB/decade. There is very little difference in the high-frequency response characteristics of the frequency shaped augmented systems and the open-loop system. The most important result is that the low frequency magnitude response can be reduced by using frequency shapings. This is particularly useful in attenuating low frequency system modes as well as low frequency noise. (Author)