Improved parametrization for system identification and digital control: Theory and applications to motion control systems

In this dissertation a new operator, the d-operator, which combines the two commonly used operators, the shift (q) and the delta ({dollar}delta){dollar} operators, is proposed for modeling discrete-time systems. This provides a new framework in which some inherent problems associated with digital computer controlled systems are dealt with in a systematic way. This results in better control and system identification.; A new way of realizing a discrete-time system in state space using the d-operator is proposed. Theoretical analyses of numerical characteristics of the realization are carried out. It is shown that for any given constraint on state space realization dynamic range, the optimized d-realization has lower sensitivity than that of the optimized q- and {dollar}delta{dollar}-realizations. It is also shown that an optimal d-realization can always be found to guarantee a lower round-off noise than that of the optimized q- and {dollar}delta{dollar}-realizations. These yield better numerical properties of state space realizations of a system which in turn improve the performance.; The d-operator is then used in system identification. It is shown that by reparametrizing the transfer function using this operator, a lower condition number for the information matrix in the least squares estimation can be obtained. As a result, more accurate and faster converging parameter identification can be achieved, especially for high order systems with wide bandwidth and when sampling rates are high. The numerical superiority of the d-operator parametrization over the q- and {dollar}delta{dollar}-operator parametrizations is demonstrated by simulation results.; An optimal hydrid feedforward controller designed using the d-operator is proposed for high speed and high precision digital motion control systems. Uncancellable discrete-time zeros arising from sampling the continuous plant at high rates, which make the mathematical inverse unstable, are handled in a natural way. The controller is optimized to have good performance in both low and high frequency ranges. It is able to handle uncancellable discrete time zeros in the right half plane. The optimizations problem is then generalized to an {dollar}Hspinfty{dollar} problem. Convex minimizations techniques are used to find the solution to the optimization problem. A model of an NSK high precision X-Y table is used in the simulations. The simulation results have shown that the proposed controller has superior performance over other feedforward control schemes, especially when tracking trajectories with high accelerations. Experiments on a Matsuura MC510V Vertical Machining center have been carried out and good results have been obtained.