Discrete Transfer Function - MapleSim Help

Discrete Transfer Function

Description

The Discrete Transfer Function component defines the transfer function between the input signal, $u$, and the output signal, $y$. The numerator has the order $\mathrm{nb}-1$, and the denominator has the order $\mathrm{na}-1$.

 $y=\frac{{b}_{1}\cdot {z}^{\mathrm{nb}-1}+{b}_{2}\cdot {z}^{\mathrm{nb}-2}+...+{b}_{\mathrm{nb}}}{{a}_{1}\cdot {z}^{\mathrm{na}-1}+{a}_{2}\cdot {z}^{\mathrm{na}-2}+...+{a}_{\mathrm{na}}}\cdot u\left(z\right)$

The state variables, $x$, are defined according to the controller in canonical form. Initial values of the states can be set as start values of $x$.

The Signal Size parameter allows the block to operate on a vector of signals rather than a single signal.

Connections

 Name Description $u$ Continuous input signal connection $y$ Continuous output signal connection

Parameters

 Symbol Default Units Description Modelica ID $b$ $\left[1\right]$ - Numerator coefficients of the transfer function b $a$ - - Denominator coefficients of the transfer function a Sample Period $0.1$ $s$ Sample period of the component samplePeriod ${T}_{0}$ $0$ $s$ First sample time instant startTime Signal Size $1$ - Dimension of input and output signals signalSize

Initial Conditions

 Symbol Units Description Modelica ID ${x}_{0}$ $-$ State of transfer function from controller canonical form x(0)