Stepalize is a small, standalone Matlab program for the identification of linear, time-invariant (LTI) dynamic models from step responses. It has been successfully applied to the identification thermal dynamics for electronics packaging, though it has many potential uses.
- Generates a linear, discrete-time estimate of a dynamic system from a
measured step response.
- Works with multi-output step responses.
- Allows for model order selection via GUI at runtime.
- With YALMIP and SDPT3 installed, the following convex constraints are also
possible:
- Fix eigenvalues to lie within convex regions of the complex plane (such as the unit circle, real number line, etc.).
- Fix the steady-state value of the system estimate.
- Constrain estimates to have no overshoot and/or no undershoot.
The method uses a variant of the Ho-Kalman-Kung algorithm for impulse responses but generalized to step responses. This is more accurate and far more robust than trying to estimate an impulse response from differentiating a step response.
In addition to identifying LTI systems, the method can be used to optionally place constraints on the eigenvalues of the identified model. The eigenvalues may be constrained to lie within any convex region of the complex plane that is an intersection of ellipses, parabolas, and half spaces that is symmetric about the real axis. Constraints that prevent the resulting model from having any overshoot or undershoot in its step response are also feasible.
Applying the constraints requires the (free) semidefinite program solver
SDPT3 and the modeling
language parser YALMIP.
Just make sure stepalize.m is in your path. If you intend to use
semidefinite constraints, then make sure SDPT3 and YALMIP are in your
path and run stepalize_test.m to make sure everything works.
NOTE: The semidefinite program solver sometimes eats up a lot of memory, and performance will vary quite a bit based on computing power. Try a small problem first to make sure nothing crashes.
See the help documentation for usage. Theoretical discussion can be found in a preprint of the paper "Thermal Dynamical Identification of LEDs by Step-Based Realization and Convex Optimization," which will appear in IEEE Transactions on Components, Packaging, and Manufacturing Technology sometime in the near future. It will have the doi 10.1109/TCPMT.2012.2229464 once it is published. (The link should work in the future.) A preprint may be found here.
This software is released under the 3-clause BSD license. See LICENSE.txt
for details.