Synthesis of Embedded Control Systems with High Sampling Frequencies

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Javad Lavaei, Somayeh Sojoudi, Richard M Murray
Conference on Decision and Control (CDC), 2010 (Submitted)

Motivated by current technological advances in the design of real-time embedded systems, this work deals with the digital control of a continuous-time linear time-invariant (LTI) system whose output can be sampled at a high frequency. Since a typical sampled-data controller operating at a high sampling frequency needs heavy (high-precision) computation to alleviate its sensitivity to measurement and computational errors, the objective is to design a robust hybrid controller for high- frequency applications with limited computational power. To this end, we exploit our recent results on delay-based controller design and propose a digital-control scheme that can implement every continuous-time stabilizing (LTI) controller. This robust hybrid controller, which consists of an ideal sampler, a digital controller, a number of modified second-order holds and possibly a unity feedback, can operate at arbitrarily high sampling frequencies without requiring expensive, high-precision computation. Later on, it is discussed how to find a continuous-time LTI controller satisfying prescribed design specifications so that its correspond- ing digital controller requires the least processing time.