California Partners for Advanced Transportation Technology

In this report, we present a hybrid discrete/ continuous time version of the observer-based adaptive control system for MEMS gyroscopes developed in [8], which can be readily implemented using digital processors. The control algorithm considered in this report is not fully a discrete time controller, since only the feedback control, parameter adaptation algorithms and feedforward control law are implemented in discrete time, while the velocity observer is still implemented in continuous time. A stochastic analysis of this algorithm is developed and it shows that the estimates of the angular rate and the fabrication imperfections are biased due to the signal discretization errors in the feedforward control path introduced by the sampler and holder. Thus, a two-rate discrete time control is proposed as a compromise between the measurement biases due to discretization errors and the computational burden imposed on the controller due to a fast sampling rate. The convergence analysis of this algorithm is also conducted and an analysis method is developed for determining the trade-off between the controller sampling frequency and the magnitude of the angular rate estimate biased errors. All convergence and stochastic properties of a continuous time adaptive control are preserved, and this analysis is verified with computer simulations.