Documentation |
Access polynomial coefficients and uncertainties of identified model
[A,B,C,D,F] = polydata(sys)
[A,B,C,D,F,dA,dB,dC,dD,dF]
= polydata(sys)
___ = polydata(sys,J1,...,JN)
___ = polydata(___,'cell')
[A,B,C,D,F] = polydata(sys) returns the coefficients of the polynomials A, B, C, D, and F that describe the identified model sys. The polynomials describe the idpoly representation of sys as follows.
For discrete-time sys:
$$A\left({q}^{-1}\right)y\left(t\right)=\frac{B\left({q}^{-1}\right)}{F\left({q}^{-1}\right)}u\left(t-nk\right)+\frac{C\left({q}^{-1}\right)}{D\left({q}^{-1}\right)}e\left(t\right).$$
u(t) are the inputs to sys. y(t) are the outputs. e(t) is a white noise disturbance.
For continuous-time sys:
$$A\left(s\right)Y\left(s\right)=\frac{B\left(s\right)}{F\left(s\right)}U\left(s\right){e}^{-\tau s}+\frac{C\left(s\right)}{D\left(s\right)}E\left(s\right).$$
U(s) are the Laplace transformed inputs to sys. Y(s) are the Laplace transformed outputs. E(s) is the Laplace transform of a white noise disturbance.
If sys is an identified model that is not an idpoly model, polydata converts sys to idpoly form to extract the polynomial coefficients.
[A,B,C,D,F,dA,dB,dC,dD,dF] = polydata(sys) also returns the uncertainties dA, dB, dC, dD, and dF of each of the corresponding polynomial coefficients of sys.
___ = polydata(sys,J1,...,JN) returns the polynomial coefficients for the J1,...,JN entry in the array sys of identified models.
___ = polydata(___,'cell') returns all polynomials as cell arrays of double vectors, regardless of the input and output dimensions of sys.
sys |
Identified model or array of identified models. sys can be continuous-time or discrete-time. sys can be SISO or MIMO. |
J1,...,JN |
Indices selecting a particular model from an N-dimensional array sys of identified models. |
A,B,C,D,F |
Polynomial coefficients of the idpoly representation of sys.
Each entry in a cell array is a row vector that contains the coefficients of the corresponding polynomial. The polynomial coefficients are ordered the same way as the SISO case. |
dA,dB,dC,dD,dF |
Uncertainties in the estimated polynomial coefficients of sys. dA, dB, dC, dD, and dF are row vectors or cell arrays whose dimensions exactly match the corresponding A, B, C, D, and F outputs. Each entry in dA, dB, dC, dD, and dF gives the standard deviation of the corresponding estimated coefficient. For example, dA{1,1}(2) gives the standard deviation of the estimated coefficient returned at A{1,1}(2). |