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

Block SymbolLicensing group: STANDARD

Function Description

Function block MX_CTODPA discretizes a continuous state space model using Padé approximations of matrix exponential and its integral and scaling technique ([7]). The used technique is similar to method 3 Scaling and squaring described in [11].

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 M,
number of elements of any matrix referenced by uAd, uP, uQ or uR is less than $N * N$ ,
number of elements of the matrix referenced by uBd is less than $N * M$ ,
the return code nRes of the function mCtoD is not equal to zero.

This block does not propagate the signal quality. More information can be found in the 1.4 section.

Input

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

Parameter

is	Pade approximation order $↓$ 0 $↑$ 4 $⊙$ 2	Long (I32)
eps	Approximation accuracy $↓$ 1e-20 $↑$ 0.001 $⊙$ 1e-15	Double (F64)

Output

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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