Two schemes for feedback scheduling on hybrid control systems

Chen Xi

Reference

• Feedback scheduling of model predictive controllers

Dan Henriksson, Anton Cervin, Johan Åkesson, Karl-Erik Årzén Dept. of Automatic Control, Lund Institution of Technology . 8th IEEE Real-Time and Embedded Technology and Applications Symposium ,San Jose,CA, September 2002 On pages: 207- 216

• Two main ways for CPU utilization:

(1) tuning task periods

focus : system with small variation in execution time e.g. hybrid

control system

(2) manipulating the execution times focus: systems with large variation on execution time e.g. model

predictive controllers

MPC model

• Feedback scheduling of MPCs

x-state vector; u-control signals vector

y-measured output vector; z-controlled output vector

Goal: make the controlled outputs z follows the reference trajectory r Solve control signal by minimizing a quadratic cost function on the form:

Motivation to scheduling MPC by tuning execution time

• Number of iterations required for the optimization is different from sample to sample– number of active constrains on control signals

and outputs– Reference changes– Un-modeled disturbances acting on the plant– The quality of u(k-1)

Real- time Implementation of MPC

• Sampling jitter

• Computational delay and actuation– preemption from higher-priority tasks – the highly varying execution time of the

optimization algorithm itself

Feedback scheduling of MPC

• Motivation: – Make trade-off between computational delay

and optimization effect

Method for feedback scheduling

• a simpler stop criterion based onthe specification of a maximum allowed delay for the controller

Method (continue)

• let the current values of the MPC cost functions act as dynamic task priorities

Idea

• Apply MPC method to feedback scheduling for hybrid control system– Teak the sampling time using MPC method– Motivation:

• (1) CPU utilization can be estimated on every sampling point

• (2) let current CPU utilization track reference input

by minimizing a cost function which has relation to the performance of each hybrid system

scheme1

scheme2

• Teak sampling time by taking performance error of each system into considerationIf

else