Faster computation of closed loop transfers with frequency response data for multivariable loopshaping

Abstract

For industrial applications containing high-precision motion systems, feedback controllers are typically designed via loopshaping using measured frequency response data. Often, these positioning systems have multiple degrees of freedom including cross-coupling. If the cross-coupling is significantly large, then it should be taken into account carefully. This, to be able to guarantee stability, robustness, and performance. For multiple frequency responses with multiple degrees of freedom, the required calculation time with a ”standard” implementation slows down the loopshaping process and hampers an automated implementation. Moreover, a high frequency grid density is needed for, often weakly damped, motion systems which further complicates the computational process. In this paper, a number of methods are proposed which significantly reduce the calculation time to compute relevant closed loop frequency responses for multivariable control systems. This enables that loopshaping for a set of multivariable frequency responses can still be carried out without too much time lag.