On the Control Rate versus Quantizer-Resolution Trade Off in Networked Control

This paper addresses the control-rate versus quantizer-resolution trade-off in networked control. The case presented considers the situation where the bit rate between controller and plant is constrained to a fixed number of bits per unit of time and an underlying fixed fast sampling rate is deployed to take measurements. However, a variable control update rate can be used between the controller and the plant. Inspired by the practical problem of inner loop power control in WCDMA, we assume the plant is an integrator. This assumption covers more general plants when fast sampling is used. Also, a restricted architecture in which linear filters are used for the encoder/decoder is considered and a quantizer with linear feedback is deployed. These choices give maximal insights into the underlying problem. It is shown that, in this case, it is best to use one bit per sample, in which case, the control update frequency is equal to the bit rate.