Optimal Digitizing Method with Application to the Design of Digital Control Systems

In digital control systems, the discrete equivalents to analog models are traditionally designed to process sequences of input and output samples such that each new output value accurately reproduces the corresponding analog output at the current sampling time. This paper addresses the fact that the performance of the resulting discrete equivalents is decreased by the inherent phase delay of analog models that alters the correlation between input and output sequences. Accordingly, a mini-max procedure is proposed to reduce the digitizing error by shifting the entire output sequence with respect to the input sampling times. Then, a previously proposed interpolation based digitizing method is used to provide (i) a synchronous output, or (ii) an output that compensates for both the latency in computing the control law and the delay due to the zero-order hold in the D/A converter, or (iii) a state-space design with a hybrid controller that eliminates the zero-order hold altogether