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

Block SymbolLicensing group: STANDARD

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 $\mathtt{\text{N}}\ast \mathtt{\text{N}}$,
• number of elements of the matrix referenced by uBd is less than $\mathtt{\text{N}}\ast \mathtt{\text{M}}$,
• 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 $\odot$2.00E+00 Long (I32) eps Approximation accuracy  $↓$1e-20 $↑$0.001 $\odot$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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