LQG-Based Scheduling and Control Co-Design Using Harmonic Task Periods

Harmonic task scheduling has many attractive properties, including a utilization bound of 100% under rate-monotonic scheduling and reduced jitter. At the same time, it places a severe constraint on the task period assignment for any application. In this paper, we explore the use of harmonic task scheduling for applications with multiple feedback control tasks. We investigate the properties of harmonic scheduling and give an efficient algorithm to calculate response times for harmonic tasks. We present two algorithms for finding harmonic task periods: one that minimizes the distance from an initial set of non-harmonic periods and one that finds all feasible harmonic periods within a given set of ranges. We apply the algorithms in a control and scheduling co-design procedure, where the goal is to optimize the total performance of a number of control tasks that share a common computing platform. The procedure is evaluated in simulated randomized examples, where it is shown that, in general, harmonic scheduling combined with release offsets gives better control performance than standard, non-harmonic scheduling.