Nonlinear time-domain models of human controllers

Data from a compensatory tracking task are analyzed by using time-domain models. The linear time-domain results are transformed and compared with frequency-domain results. The nonlinear time-domain model of the same data reduced the remnant or residual power by only a small amount. The need for testing models on independent data is discussed. A novel, but attractive, method of generating functions for an efficient functional expansion of time-domain models is offered.Notation c Pilot output (control deflection), inches - E Error matrix - e Error, radians - F[·] Fourier transform - h Time interval, seconds - h_i Sample of impulse response of pilot - h_p Impulse response of pilot, inches/radian or inches/degree - i Input (external disturbance function), radians - M Maximum value ofm, M=T_M/ - m Index for the argument ofh_p - N Maximum value ofn - n Index for time - o Linear output of pilot model (control deflection), inches - r Remnant signal of pilot model (control deflection), inches - S Matrix - s Laplace variable - T_M Maximum memory time of the pilot model, seconds - t Time, seconds - Y_c Transfer function of controlled element - Y_cj) Controlled-element transfer function, radians/inch - Y_pj) Pilot-describing function, inches/radian - Argument ofh_p, seconds - Incremental value of, seconds - Frequency, radians/second - ^ Estimate - Absolute value - Phase angle