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Control and real-time scheduling co-design

Control and Real-Time Scheduling Codesign (NSF 0712502)

Self-triggered control

Physical systems are controlled by measuring several physical quantities used to compute a feedback control law determining how actuators influence back the physical system. The computation of the feedback control law is typically done on a microprocessor since digital implementations offer many advantages (accuracy, flexibility,..) with respect to analog implementations.

Under digital implementations, one important question is to determine when to measure the physical quantities of interest, when to execute the control law, and when to update the actuators in order to achieve desired levels of control performance. Traditionally, engineers and researchers have opted for conservative strategies, such as periodic sampling of signals and periodic execution of control laws. However, due to the growing complexity of systems, more efficient strategies are required, since resources are usually shared between several subsystems. Our goal is to go beyond the periodic paradigm and, drawing inspiration from event-triggered control, to develop self-triggered feedback control laws that decide their next execution time based on the current state of the system. This approach considerably reduces resource utilization while ensuring stability and desired levels of control performance.

To illustrate some of the advantages of self-triggered control, let´s look at a simple example: the control of a jet engine compressor. Below we can see the evolution of the pressure rise and the mass flow under a stabilizing feedback control law (the goal is to steer both quantities to the origin).

The performance is very similar since we almost cannot distinguish between the blue and black lines, representing the evolution of the physical system under a self-triggered strategy, and the red and green lines, representing the evolution of the physical system under a periodic strategy. Yet, when we observe the evolution of the actuator values over time the differences are important.

At the beginning, both strategies update the value of the actuator at the same rate, but as time evolves and the system tends to the equilibrium point, the self-triggered strategy enlarges the times between executions.

The self-triggered strategy adapts the inter-execution times according to the current state of the system, and thus leads to a lower number of executions. 

Real-Time Scheduling of Self-Triggered Tasks

So far we haven't discussed an important point. How do we guarantee that self-triggered control tasks are executed before the deadlines since the deadlines change depending on the state of the system? And how do we take advantage on the reduced processor utilization resulting from self-triggered control tasks? We are currently investigating several generalizations to the control server model, introduced by Cervin and Eker in 2003 [CE03], to address the self-triggered case.

Here is an illustration of these techniques for the scheduling of two jet engine control tasks, one periodic hard real-time task and several soft real-time tasks. At the beginning, both control tasks require a high number of executions to achieve the desired performance, and hence there is no spare CPU time for the soft tasks. However, as time evolves the relative deadlines tend to enlarge as the system steers to the equilibrium point, giving more CPU time to the soft tasks. At t=0.7s, a disturbance steers the system far away from the origin, and therefore the CPU reduces the relative deadlines accordingly to guarantee the required performance at the expense of delaying other soft tasks.

Simulating Self-Triggered Control Tasks

Simulating different scheduling strategies for self-triggered control tasks is also challenging since the real-time properties of these tasks such as deadlines depend on the evolution of the physical system. We thus have to integrate the simulation of the physical system with the simulation of the real-time scheduler and all the other tasks requiring processor time. We are currently extending the real-time simulation environment TrueTime [CHL+03] to the context of self-triggered control tasks. The files for the above described example can be downloaded here. A brief manual is also available here.

Publications

To learn more about these techniques please see the links below (in reverse chronological order)

    Isochronous manifolds in self-triggered control
    A. Anta and P. Tabuada
    48th IEEE Conference on Decision and Control, December 2009 (To appear).
    PDF file

    On the benefits of relaxing the periodicity assumption for networked control systems over CAN
    A. Anta and P. Tabuada
    Real Time Systems Symposium, December 2009 (To appear).
    PDF file

    Space-time scaling laws for self-triggered control
    A. Anta and P. Tabuada
    Proceedings of the 47th IEEE Conference on Decision and Control, December 2008.
    PDF file

    To sample or not to sample: Self-triggered control for nonlinear systems
    Accepted for publication in IEEE Transactions on Automatic Control.
    arXiv:0806.0709

    Self-triggered stabilization of homogeneous control systems
    A. Anta and P. Tabuada
    In Proceedings of the 2008 American Control Conference, June 2008.
    PDF file

    On the benefits of relaxing the periodicity assumption for control tasks
    A. Anta and P. Tabuada
    In Proceedings of the 14th IEEE Real-Time and Embedded Technology and Applications Symposium, Work-In-Progress track, April 2008.
    PDF file

    Event-triggered real-time scheduling of stabilizing control tasks
    P.Tabuada
    IEEE Transactions on Automatic Control, 52(9), 1680-1685, September 2007.
    PDF file

    Preliminary results on state-triggered scheduling of stabilizing control tasks
    P. Tabuada and X. Wang
    Proceedings of the 45th IEEE Conference on Decision and Control, December 2006.
    PDF file

References

[CE03] A. Cervin and J. Eker. The control server: a computational model for real-time control tasks. 15th Euromicro Conference on Real-Time Systems, pp. 113–120, 2003.

[CHL+03] A. Cervin, D. Henriksson, B. Lincoln, J. Eker, and K.E. Arzen. How does control timing affect performance? Control Systems Magazine, IEEE, 23(3):16–30, 2003.