1. Two schemes for feedback scheduling on hybrid control systems Chen Xi

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

3. 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

4. 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:

5. 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)

6. 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

7. Feedback scheduling of MPC Motivation: –Make trade-off between computational delay and optimization effect

8. Method for feedback scheduling a simpler stop criterion based onthe specification of a maximum allowed delay for the controller

9. Method (continue) let the current values of the MPC cost functions act as dynamic task priorities

10. 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

11. scheme1

12. scheme2 Teak sampling time by taking performance error of each system into consideration If else