Transfer Function

Implements transfer function

Category: Dynamics

Description:

The Transfer Function can be described by the following equation:

Y(s)U(s)=num0Sm+num1Sm1+num2Sm2+...+nummden0Sn+den1Sn1+den2Sns+...+denn\frac{Y(s)}{U(s)}=\frac{num_0S^m+num_1S^{m-1}+num_2S^{m-2}+...+num_m}{den_0S^n+den_1S^{n-1}+den_2S^{n-s}+...+den_n}

num0...mnum_{0...m}
and
den0...nden_{0...n}
are polynomial coefficients defined by the user. It is possible to set them by the Transfer Function Properties as shown in Figure 1.

Figure 1 - Transfer function parameters configuration

Figure 1 defines a first-order transfer function equivalent to:

G(s)=1s+1G(s)=\frac{1}{s+1}

Figure 2 shows an example using the transfer function from Figure 1.

Figure 2 - Step response of a transfer function

The step response of the system is depicted in Figure 3. In this simulation, the Task Frequency was set to 5Hz. Internally, it is implemented using Backward Euler for numerical integration, since S-domain can only be emulated. This implementation is very imprecise due to numerical integration and fixed-point issues. It is recommended to use discrete-time transfer function defined in Z-domain when using high order transfer functions.

Figure 3 - Discrete-time step response in a Scope

Parameters:

Vector row that sets the coefficients of the polynomial function of the numerator.

The number of elements of this vector must be less or equal the number of elements in the Denominator Coefficients.

Vector row that sets the coefficients of the polynomial function of the denominator.

The maximum number of coefficients is five, i.e., the Transfer Function block can implement up to fifth order transfer functions.

Ports:

Input

The signal flowing through this port acts as an input signal to the transfer function.

Data Types:
Output

The signal flowing from this port is the response of the transfer function to the input signal injected.

Data Types:

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