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pmap - Parameter Space Stability Mapping Suite

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30 Mar 2011 (Updated )

Finds the Hurwitz stability region in a parameter space of a continuous time system.

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Description

Given a continuous-time system with parameters, can we find the range (or intervals) of the parameters where the system is stable?

When the system model is written with the Laplacian transform, the question is equivalent to finding all the roots of a parameterized polynomial where the real parts of the roots are negative. Via orthant-based, sign-definite decomposition a set of "vertex polynomials" are created whereby such a test of stability can occur. Through iterative bisection of the parameter space, the region of stable parameters of the dynamic system can be constructed and viewed.

Examples are provided where the parameters are PID gains of a controller, though the parameters may also occur in the plant. Currently, the parameters must be real-valued, though the polynomial need not be real-valued.

For more detailed information, see the papers referenced in the H1 information and the readme.

Similar results are available for discrete-time systems, though these have not been included here.

The screenshot is the stability region of the polynomial:
s^4 + (kd + kp + 10)*s^3 + (2*kp - 4*kd + 35)*s^2 + (50 - 23*kp - 18*kd*kp - 19*kd)*s + 35*kd*kp - 60*kp - 14*kd + 24.

Required Products Parallel Computing Toolbox
Symbolic Math Toolbox
MATLAB release MATLAB 7.11 (R2010b)
Other requirements linewrap.m, File ID# 9099, is used if it is available.
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Comments and Ratings (2)
07 Apr 2011 Timothy Stratton

AWESOME, AWESOME AWESOME!!!

30 Mar 2011 Timothy Stratton  
Updates
01 Apr 2011

For this update, I have added a walkthrough.m script and its 'publish'ed html directory.

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