ℓ2 Gain Estimation and Visualization of A Control Parameter Set in 3D Space Using Plant Response Data

In this paper, a novel parameter space approach that uses volume rendering is proposed to visualize controller parameter sets that consist of three controller parameters. An off‐line design method for robust control using plant response data is also studied. A solution set with equal ℓ2 gain can be visualized as isosurfaces in three‐dimensional space, and the designer can visually select an appropriate parameter. This numerical method is applicable to many practical specifications, in contrast to analytical methods based on solving equations. An estimation method based on the extension theorem and a method using bandpass filters are both considered as possible methods for estimating the ℓ2 gain of the sensitivity functions when using grid points on the order of tens of thousands to create the volume data.The former method is superior to the latter with respect to accuracy but impractical with respect to computational load. The latter method is hence practical, because the computing time is reduced to less than 0.05 s for about 300,000 grid points by parallel computation with a graphical processing unit.