Estimation of Nonlinear Contributions in Human Controller Frequency Response Functions

Traditional Frequency Response Function (FRF) estimation techniques used for analysis of Human Controller (HC) dynamics in tracking tasks assume HC dynamics to be linear, but generally do not quantify or compensate for the effects of human nonlinearities. The robust and fast Best Linear Approximation (BLA) techniques for estimating an FRF do provide such quantification of nonlinear distortions caused by Period-In-Same-Period-Out (PISPO) nonlinearities and can reduce the effect of PISPO nonlinear operations on the FRF estimate. This paper investigates the application of these BLA techniques to both measured and simulated HC data. For the simulated data, a linear HC model was deliberately extended with a symmetric PISPO deadzone nonlinear operator and a realistic level of HC "remnant" noise. Overall, both the measured and the simulated data indicate that due to the high levels of remnant noise inherent to HC data, no consistent estimate of PISPO nonlinear contributions could be made. This also means that the improvement of using BLA techniques and averaging over multiple forcing function realizations does not result in a substantial improvement over the current practice of estimating HC FRFs from repeated measurements of a single forcing function.