Optimal Local-Loop Shaping and Beyond Nyquist Reconstruction using Model-Based Information Recovery

Abstract

This dissertation develops the multirate model predictor (MMP), a model-based information recovery method for beyond-Nyquist signals, for non-integer sampling ratios between system modules. Although arbitrary beyond-Nyquist signals cannot be reconstructed from slow samples alone, structured disturbances with known narrow-band frequency components can be recovered by explicitly using the signal model. The MMP upsamples the aliased signal by estimating the inter-sample measurements between slow-sampled measurements with a rational up-sampling factor L=N/D>1. The MMP is parameterized using finite impulse response (FIR) and infinite impulse response (IIR) filter-based designs, with improved reconstruction accuracy using the IIR filter under noisy conditions. With a non-integer sampling ratio, synchronization between the slow- and fast-sampled signals occurs less frequently; therefore, a multiphase reconstruction procedure is developed to use all available slow-sampled measurements. The resulting signal processing achieves an effective sampling rate that is D times the original fast sampling rate. This results from the coprime factorization of the non-integer sampling ratio, providing a broader frequency range for compensation. The recovered disturbance signal is then incorporated into an optimally designed disturbance observer (DOB). The multirate forward model disturbance observer (MFMDOB) is then developed for systems such as the in-house selective laser sintering (SLS) scanner, which contains a non-minimum phase zero. The forward model avoids explicit plant inversion, thus maintaining stability for non-minimum phase systems. The DOB Q(z) filter is designed as a notch filter to target beyond-Nyquist narrow-band disturbances while limiting amplification at non-disturbance frequencies through convex optimization, where the design parameters are posed as a set of convex constraints. Both second-order cone programming (SOCP) and semidefinite programming (SDP) formulations are presented for parameterizations of Q(z) using FIR and IIR filter structures. The proposed methods are validated through hardware and simulation studies. Motor control experiments demonstrate that the MMP is capable of recovering beyond-Nyquist signals under fractional-ratio sampling, with the IIR-based design providing improved reconstruction accuracy with over 60% reduction in root mean square (RMS) error for low signal-to-noise ratio (SNR) data (SNR ≤ 5 dB). Simulation studies on a dual-stage hard disk drive benchmark show that the MMP can recover structured beyond-Nyquist disturbances with a reconstruction error of 14.8%; however, reconstruction becomes more challenging for randomly excited narrow-band disturbances. Finally, simulations on the in-house SLS laser scanner model show that the optimized MFMDOB attenuates beyond-Nyquist disturbances, with the MMP and Q(z) filter using the IIR-based design providing over 90% reduction in output error compared to the FIR-based design.