Limits of Performance in Systems with Periodic Irregular Sampling and Actuation Rates

This paper examines the limits of performance in systems with periodic irregular sampling rate when the actuation is not necessarily synchronized with the sampling. For such a system, three sampling and actuation schemes are considered: when the sampling and control rate are both regular, when they are both irregular, and when the sampling rate is irregular while the control rate is regular. To ascertain the limits of performance of this type of systems under each sampling and actuation scheme, the system is modeled as a linear periodically time-varying (LPTV) system; optimal LQG control design with a variance constraint is applied to find the smallest achievable mean variance of the performance signal subject to a constraint on the mean control effort variance. In addition, to deal with the computational delay of the controller, an innovative discretization method is proposed which does not introduce any extra states into the state space model. The proposed method is exploited to determine the performance of a hard disk drive (HDD) in track-following mode. A simulation study demonstrates that in the presence of 30% irregularity in sampling time, using the irregular sampling and regular control action scheme for the HDD achieves an RMS 3σ value of the position error signal (PES) that is 40% smaller than the corresponding value achieved by using a controller provided by our industry partner, in which both the sampling and control rates are irregular.