Numerical Control: Performance Analysis and Implementation Issues

In this thesis, a digitalization method with finite word-length (resolution $N$) of a given stable analog controller guaranteeing the minimum difference in terms of frequency responses is treated. The challenge has consisted in finding a relevant frequency responses mismatch metric and in relating it to the word finiteness issue. The analog controller is represented in modal state-space form and digitalized with a stability-maintaining approximation (ramp invariance) for different sampling periods. It results in digital controllers with block diagonal transition matrices whose coefficients (poles) are inside the unit circle. The format is chosen to match the poles dynamical range. The matrix is then coded and the mismatch measure allows for the selection of the "best" poles coded controllers. The remaining matrices are then scaled and coded for these selected controllers. The measure is computed for each of them. The procedure finally gives the "optimal" coded controller. This algorithm is shown to perform well and better that a simple rounding after the analog controller discretization phase.