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Block Diagram Components

Block Diagram Components¶

So far, the focus of this chapter has been on acausal modeling. But Modelica also supports causal formalisms. The main reason for the emphasis on acausal modeling is that it lends itself very well to the modeling of physical systems. It enables models of physical systems to be assembled schematically rather than mathematically while also automatically formulating conservation equations to ensure proper bookkeeping.

Block diagrams are a different way of approach modeling. The emphasis in block diagram is on creating component models that represent a wide range of mathematical operations. The operations are then performed on (generally time-varying) signals and yield, in turn, other signals. In fact, we will introduce a special kind of model in this section, called a block, that is restricted to having only input and output signals.

In this section, we’ll first look at how to construct causal blocks representing some basic mathematical operations. We’ll then see how those blocks can be used in two different ways. The first way will be to model a simple physical system. We’ll include some discussion contrasting the causal and acausal approaches. The second way to use such blocks is to model control systems. As we’ll see, using blocks to construct control systems is a much more natural fit for the block diagram formalism.

Fortunately, Modelica allows both causal and acausal approaches and, as we’ll see shortly, even allows them to be mixed. The result is that Modelica allows the model developer to use whichever approach works best in a given context.

Blocks¶

Modelica Standard Library¶

In this section, we will leverage several definitions from the Modelica Standard Library starting with the connectors:

connector RealInput = input Real "'input Real' as connector";
connector RealOutput = output Real "'output Real' as connector";

As the names suggest, RealInput and RealOutput are connectors for representing real valued input and output signals respectively. When drawn in a diagram, the RealInput connector takes the form of a blue solid triangle:

The RealOutput connector is a blue triangle outline:

We will leverage the Modelica Standard Library for several different partial block definitions. The first partial definition we’ll use is the SO, or “single output”, definition:

partial block SO "Single Output continuous control block"
  extends Modelica.Blocks.Icons.Block;

  RealOutput y "Connector of Real output signal" annotation ...
end SO;

Obviously, this definition is used for blocks that have a single output. By convention, this output signal is named y. Another definition we’ll use is the SISO or “single input, single output” block:

partial block SISO "Single Input Single Output continuous control block"
  extends Modelica.Blocks.Icons.Block;

  RealInput u "Connector of Real input signal" annotation ...
  RealOutput y "Connector of Real output signal" annotation ...
end SISO;

This model adds an input signal, u, in addition to the output signal, y. Finally, for blocks with multiple inputs, the MISO block defines the input signal, u, as a vector:

partial block MISO "Multiple Input Single Output continuous control block"
  extends Modelica.Blocks.Icons.Block;
  parameter Integer nin=1 "Number of inputs";
  RealInput u[nin] "Connector of Real input signals" annotation ...
  RealOutput y "Connector of Real output signal" annotation ...
end MISO;

The parameter nin is used to specify the number of inputs to the block.

It is worth pointing out that all of the blocks we are about to define are also available in the Modelica Standard Library. But we’ll create our own versions here just to demonstrate how such models can be defined.

`Constant`¶

Probably the simplest block we can imagine is one that simply outputs a constant value. Since this model has a single output, it extends from the SO block:

within ModelicaByExample.Components.BlockDiagrams.Components;
block Constant "A constant source"
  parameter Real k "Constant output value";
  extends Icons.Axes;
  extends Interfaces.SO;
equation
  y = k;
end Constant;