Nonlinear Optimal Cue-Shaping Filters for Motion Base Simulators
Robert L. Kosut · Journal of Guidance and Control · 1979
The platform motion cue-shaping problem is formulated as an optimal tracking control problem with a higher than quadratic cost functional. Applying current concepts in nonlinear optimal control theory results in a nonlinear filter where the nonlinearity is exploited to maintain the platform within specified bounds on excursion and velocity. The nonlinearity in' the filter is induced by defining a cost functional which is quadratic in cue-error, and quadratic plus quartic in platform excursion and velocity The quartic terms give rise to cubic terms in the filter. It is shown that the resulting filter is input cue-magnitude sensitive and has the desirable features of utilizing more of the available platform performance envelope for a wider range of cue-magnitudes than the presently employed linear filters. This is accomplished by increasing both the onset duration and the washout-to-onset ratio as the input cue-magnitude decreases. The nonlinear cue-shaping filters presented also have the desirable qualities of being in closed form and asymptotically stable, and the filter gains for the nonlinear terms can be calculated by solving a set of linear equations.