Analysis of methods for multivariable frequency response function estimation in closed loop

Abstract

Estimation methods for the multivariable frequency response function are analyzed, both in open and closed loop. Approximate bias and covariance expressions are derived for the closed loop case. The usefulness of these expressions is illustrated in simulations of an industrial robot where three dierent estimators are compared. The choice of estimator depends on the signal-to-noise ratio as well as the measurement setup and a bias-variance trade-o.Keywords: Nonparametric identication, Multivariable systems, Closed Loop Analysis of Methods for Multivariable Frequency Response Function Estimation in Closed Loop Erik Wernholt and Svante GunnarssonAbstract-Estimation methods for the multivariable frequency response function are analyzed, both in open and closed loop. Approximate bias and covariance expressions are derived for the closed loop case. The usefulness of these expressions is illustrated in simulations of an industrial robot where three different estimators are compared. The choice of estimator depends on the signal-to-noise ratio as well as the measurement setup and a bias-variance trade-off.

Frequency-Domain Gray-Box Identification of Industrial Robots

“…Various aspects of the procedure are also treated in Wernholt and Gunnarsson (2006b), Wernholt and Löfberg (2007), Wernholt and Gunnarsson (2007) and Wernholt and Moberg (2007). Using an FRF-based procedure allows for data compression, unstable systems are handled without problems, it is easy to validate the model such that all important resonances are captured, and model requirements in the frequency domain are also easily handled.…”

“…See also, e.g., Wernholt and Gunnarsson (2007) and Wernholt and Moberg (2007) for other FRF estimators for multivariable systems.…”

Experimental Comparison of Methods for Multivariable Frequency Response Function Estimation

“…The JIO estimator is asymptotically unbiased, and the bias of the other estimators varies depending on the SNR. A recent study on the rst three estimators can be found in Wernholt and Gunnarsson (2007). See also , Guillaume (1998), andVerboven (2002).…”

Active hard mount vibration isolation for precision equipment

“…The H 1 -estimator is the best estimator if the output noise is much larger compared to the input noise (which is assumed zero in this chapter) [43]. If the system is excited using an orthogonal random phase multisine signal, the variance of the FRF estimates is minimized [65]. A scalar random phase multisine signal x(t) can be written as …”

“…The method is adopted from [65] and is summarized in subsection 6.3.1. The use of this method results in avoiding leakage effects and minimizing the variance of the FRF estimates.…”