Adaptive Control for Deterministic and Stochastic Disturbances with Application to Precision Motion Control

The research in this dissertation investigates adaptive control algorithms for rejecting unknown stochastic and deterministic disturbances. Experimental results for several precision motion control applications are demonstrated to confirm the effectiveness of the adaptive control approaches. A Halbach linear motor stage has been setup for nano-precision positioning. Using an FPGA based decoding scheme and sensor signal processing, a 0.23mn root-mean-square (RMS) sensor noise level has been obtained from a 4 micrometer period sinusoidal quadrature encoder. Disturbances to the linear motor are then studied at nanometer scale. A method to synthesize internal model principle type controllers for rejection of sinusoidal disturbances is proposed. The frequencies of the disturbance are not required to be of rational ratios of the sampling interval or each other, thus addressing both periodic and aperiodic signals. The control synthesis utilizes positive feedback around cascaded notch filters to create the internal model and employs stable inversion of the plant dynamics to achieve closed loop stability. Based on this internal model structure, two adaptive control algorithms are proposed to reject unknown stochastic and deterministic disturbances. The first control algorithm is based on Youla-parametrization. The proposed algorithm contains two adaptive control actions. One rejects a set of unidentified deterministic disturbances by an adaptive internal model with online frequency identification. The other minimizes the output variance using an adaptive finite impulse response filter. In another control algorithm, the two adaptive loops are decoupled by filtering. The stability and performance of proposed two adaptive algorithms are analyzed and demonstrated by experimental results on a Halbach linear motor for nano-precision positioning. The previous adaptive control algorithms are both based on adaptive filtering of FIR filter. However, Laguerre-based adaptive filters provide an attractive alternative to adaptive FIR filters in the sense that they provide better approximation of system with a long impulse response with a restricted order. Laguerre also keeps many of the advantages of adaptive FIR filter, such as unique global minimum and guaranteed stability. The proposed control algorithms are extended to Laguerre based adaptive filtering. The proposed approach is implemented in FPGA with 100kHz sampling rate and applied to piezoelectric actuator for nanopositioning. Experimental results show effectiveness of the proposed approach.