Design of Nonlinear Sampled-Data System for Acceleration Measurement

The design of a sampled-data nonlinear system for three-axes acceleration measurement is discussed. The basic specific force equation is given, and the equation for the indicated velocity (integral of indicated acceleration) is derived to show the dependence of the error on the shape of the limit cycle trajectory. Emphasis is on how certain physical parameters, such as damping and dead zone width, may be chosen to fulfill the design requirement of minimum error in the indicated velocity output of the system. Expressions for design purposes relating physical parameters, such as damping, and phase plane switch line spacing to limit cycle period are derived. High limit cycle frequencies, or low periods, are shown to be less objectionable. An expression is given for the approximate dead zone width for minimum error from dynamic average and static offsets of the limit cycle trajectories. A multiscale-normalized phase plane technique is described and used to determine both the transient and final limit cycle trajectories for assumed step acceleration inputs at arbitrary points during an existing limit cycle.