Stability Margin

Stability margin of a closed loop system is defined as the inverse of the infinity norm of a matrix containing four sensitivity functions as follows:

  1. A(z-1)S(z-1)/P(z-1)
  2. B(z-1)R(z-1)/P(z-1)
  3. A(z-1)R(z-1)/P(z-1)
  4. B(z-1)S(z-1)/P(z-1)

where B(z-1)/A(z-1) is the plant model and R(z-1)/S(z-1) is the controller and P(z-1) is the closed loop polynomial:

P(z-1)=A(z-1)S(z-1)+B(z-1)R(z-1)

The infinity norm of the matrix is computed using the grid method and singular value decomposition technique. In each frequency the maximum of the singular value of the matrix is computed and then the maximum in all frequencies gives the infinty norm. In order to have a correct answer for the lightly damped system the frequency grid should be sufficiently dense by choosing "tol" enough small.

See: Controller order reduction module .

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(file smarg.htm)