Adaptive Feedback Scheduling with LQ Controller for Real Time Control System Chen Xi

Reference A. Cervin, J. Eker, B. Bernhardsson, and K.-E. Arzen, “Feedback-feedforward scheduling of control tasks,” Real-Time Systems, vol. 23, July 2002, pp. 25–53

Summary of the work It develops a feedback scheduler by LQ controllers. This scheduler adjust s sampling period for different control tasks in order to regulate the CPU load. At the same time, it takes control performance into consideration by optimizing an objective cost function.

Summary of the work Use offline approximation to get the linear cost functions of the control tasks. It calculates sampling periods by optimizing the cost functions. And it uses the CPU utilization requirement as a constraint. Each sampling period rescaled contains the parameters estimated offline.

in order to meet the CPU utilization set-point, the LQ controller gives a simple linear proportional rescaling of the nominal task periods.It means the sampling period assigned to each task should change proportionally. It proves that the rescaling is also optimal for the stationary control performance.

Problems (1) Disturbances acting on each control task is not taken into account in the optimization. (2) The linear or quadratic cost function of each control task estimated offline only relation with its own sampling period. It neglects the correlation with other tasks when executing in real-time system. In actual situation, the sampling periods arranged to other tasks may influence the performance of this task. (3) Separate design of the control task cost function and the utilization function. It is necessary to give a combined control model to mix the state of control system and the real-time resource utilization together.

Idea Establish a MIMO model with dynamically changing parameters – output signals : performance derivation of each control task and the actual CPU utilization – control input signals : the sampling periods of the control tasks. RLS method for online parameters estimation LQ controller to adjust control signals

Advantages Online adjustment Co-design of control tasks and scheduling Due-optimization

Plan Implement in hybrid control system Implement in NCM model