Modelica.Blocks.Discrete

Information

This package contains discrete control blocks with fixed sample period. Every component of this package is structured in the following way:

1. A component has continuous real input and output signals.
2. The input signals are sampled by the given sample period defined via parameter samplePeriod. The first sample instant is defined by parameter startTime.
3. The output signals are computed from the sampled input signals.

A sampled data system may consist of components of package Discrete and of every other purely algebraic input/output block, such as the components of packages Modelica.Blocks.Math, Modelica.Blocks.Nonlinear or Modelica.Blocks.Sources.

Package Content

Name	Description
Sampler	Ideal sampling of continuous signals
ZeroOrderHold	Zero order hold of a sampled-data system
FirstOrderHold	First order hold of a sampled-data system
UnitDelay	Unit Delay Block
TransferFunction	Discrete Transfer Function block
StateSpace	Discrete State Space block
TriggeredSampler	Triggered sampling of continuous signals
TriggeredMax	Compute maximum, absolute value of continuous signal at trigger instants

Modelica.Blocks.Discrete.Sampler

Information

Samples the continues input signal with a sampling rate defined via parameter samplePeriod.

Parameters

Name	Description
samplePeriod	Sample period of component [s]
startTime	First sample time instant [s]

Connectors

Name	Description
u	Continuous input signal
y	Continuous output signal

Modelica.Blocks.Discrete.ZeroOrderHold

Information

The output is identical to the sampled input signal at sample time instants and holds the output at the value of the last sample instant during the sample points.

Parameters

Name	Description
samplePeriod	Sample period of component [s]
startTime	First sample time instant [s]

Connectors

Name	Description
u	Continuous input signal
y	Continuous output signal

Modelica.Blocks.Discrete.FirstOrderHold

Information

The output signal is the extrapolation through the values of the last two sampled input signals.

Parameters

Name	Description
samplePeriod	Sample period of component [s]
startTime	First sample time instant [s]

Connectors

Name	Description
u	Continuous input signal
y	Continuous output signal

Modelica.Blocks.Discrete.UnitDelay

Information

This block describes a unit delay:

          1
     y = --- * u
          z

that is, the output signal y is the input signal u of the previous sample instant. Before the second sample instant, the output y is identical to parameter yStart.

Parameters

Name	Description
y_start	Initial value of output signal
samplePeriod	Sample period of component [s]
startTime	First sample time instant [s]

Connectors

Name	Description
u	Continuous input signal
y	Continuous output signal

Modelica.Blocks.Discrete.TransferFunction

Information

The discrete transfer function block defines the transfer function between the input signal u and the output signal y. The numerator has the order nb-1, the denominator has the order na-1.

          b(1)*z^(nb-1) + b(2)*z^(nb-2) + ... + b(nb)
   y(z) = -------------------------------------------- * u(z)
          a(1)*z^(na-1) + a(2)*z^(na-2) + ... + a(na)

State variables x are defined according to controller canonical form. Initial values of the states can be set as start values of x.

Example:

     Blocks.Discrete.TransferFunction g(b = {2,4}, a = {1,3});

results in the following transfer function:

        2*z + 4
   y = --------- * u
         z + 3

Parameters

Name	Description
b[:]	Numerator coefficients of transfer function.
a[:]	Denominator coefficients of transfer function.
samplePeriod	Sample period of component [s]
startTime	First sample time instant [s]

Connectors

Name	Description
u	Continuous input signal
y	Continuous output signal

Modelica.Blocks.Discrete.StateSpace

Information

The discrete state space block defines the relation between the input u=inPort.signal and the output y=outPort.signal in state space form:

    x = A * pre(x) + B * u
    y = C * pre(x) + D * u

where pre(x) is the value of the discrete state x at the previous sample time instant. The input is a vector of length nu, the output is a vector of length ny and nx is the number of states. Accordingly

        A has the dimension: A(nx,nx),
        B has the dimension: B(nx,nu),
        C has the dimension: C(ny,nx),
        D has the dimension: D(ny,nu)

Example:

     parameter: A = [0.12, 2;3, 1.5]
     parameter: B = [2, 7;3, 1]
     parameter: C = [0.1, 2]
     parameter: D = zeros(ny,nu)

results in the following equations:
  [x[1]]   [0.12  2.00] [pre(x[1])]   [2.0  7.0] [u[1]]
  [    ] = [          ]*[         ] + [        ]*[    ]
  [x[2]]   [3.00  1.50] [pre(x[2])]   [0.1  2.0] [u[2]]
                             [pre(x[1])]            [u[1]]
       y[1]   = [0.1  2.0] * [         ] + [0  0] * [    ]
                             [pre(x[2])]            [u[2]]

Parameters

Name	Description
A[:, size(A, 1)]	Matrix A of state space model
B[size(A, 1), :]	Matrix B of state space model
C[:, size(A, 1)]	Matrix C of state space model
D[size(C, 1), size(B, 2)]	Matrix D of state space model
samplePeriod	Sample period of component [s]
startTime	First sample time instant [s]
nin	Number of inputs
nout	Number of outputs

Connectors

Name	Description
u[nin]	Continuous input signals
y[nout]	Continuous output signals

Modelica.Blocks.Discrete.TriggeredSampler

Information

Samples the continuous input signal whenever the trigger input signal is rising (i.e., trigger changes from false to true) and provides the sampled input signal as output. Before the first sampling, the output signal is equal to the initial value defined via parameter y0.

Parameters

Name	Description
y_start	initial value of output signal

Connectors

Name	Description
u	Connector with a Real input signal
y	Connector with a Real output signal
trigger

Modelica.Blocks.Discrete.TriggeredMax

Information

Samples the continuous input signal whenever the trigger input signal is rising (i.e., trigger changes from false to true). The maximum, absolute value of the input signal at the sampling point is provided as output signal.

Connectors

Name	Description
u	Connector with a Real input signal
y	Connector with a Real output signal
trigger