MX_CTODPA – Discretizes continuous model given by (A,B) to (Ad,Bd) using Pade approximations

Block SymbolLicensing group: STANDARD
PIC

Function Description

This function block discretizes a continuous state space model using Padé approximations of matrix exponential and its integral and scaling technique ([5]). The used technique is similar to method 3 Scaling and squaring described in [8].

The output references yA, yB, yAd, yBd, yP , yQ and yR are always set to the corresponding input references uA, uB, uAd, uBd, uP, uQ and uR. If HLD = on then nothing is computed otherwise the function mCtoD is called internally:

mCtoD(nRes, uAd, uBd, uA, uB, N, M, is, Ts, eps, uP, uQ, uR);

where parameters of mCtoD are set in the following way:

  • nRes is return code from the function mCtoD.
  • N is number of rows of the square system matrix referenced by uA.
  • M is number of columns of the input matrix referenced by uB.
  • Ts is sampling period for the discretization, which is equal to sampling period of the task containing this function block.

The error flag E is set to on if:

  • the reference uA or uB or uAd or uBd or uP or uQ or uR is not defined (i.e. input uA or uB or uAd or uBd or uP or uQ or uR is not connected),
  • number of columns of the matrix referenced by uA is not equal to N,
  • number of rows of the matrix referenced by uB is not equal to N,
  • number of elements of any matrix referenced by uAd, uP, uQ or uR is less than NN,
  • number of elements of the matrix referenced by uBd is less than NM,
  • the return code nRes of the function mCtoD is not equal to zero.

Inputs

uA

Input reference to matrix A

Reference

uB

Input reference to matrix B

Reference

uAd

Input reference to discretized matrix A

Reference

uBd

Input reference to discretized matrix B

Reference

uP

Input reference to a helper matrix

Reference

uQ

Input reference to a helper matrix

Reference

uR

Input reference to a helper matrix

Reference

HLD

Hold

Bool

Parameters

is

Pade approximation order   0  4 2.00E+00

Long (I32)

eps

Approximation accuracy   1e-20  0.001 1e-15

Double (F64)

Outputs

yA

Output reference to matrix A

Reference

yB

Output reference to matrix B

Reference

yAd

Output reference to discretized matrix A

Reference

yBd

Output reference to discretized matrix B

Reference

yP

Output reference to a helper matrix

Reference

yQ

Output reference to a helper matrix

Reference

yR

Output reference to a helper matrix

Reference

E

Error indicator

Bool

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