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Algebraic Loops

Algebraic loops are circular dependencies between variables. This prevents the straightforward direct computation of their values. For example, in the case of a system of equations

• x = y + 2

• y = -x

the values of x and y cannot be directly computed.

To solve this, either repeatedly try potential solutions for x and y (in an intelligent manner, for example, using gradient based search) or "solve" the system of equations. In the previous example, solving the system into an explicit form leads to

• 2x = 2

• y = -x

• x = 1

• y = -1

An algebraic loop exists whenever the output of a block having direct feedthrough (such as Gain, Sum, Product, and Transfer Fcn) is fed back as an input to the same block. The Simulink engine is often able to solve models that contain algebraic loops, such as the next diagram.

The Real-Time Workshop software does not produce code that solves algebraic loops. This restriction includes models that use Algebraic Constraint blocks in feedback paths. However, the Simulink engine can often eliminate all or some algebraic loops that arise, by grouping equations in certain ways in models that contain them. It does this by separating the update and output functions to avoid circular dependencies. See Algebraic Loops in the Simulink documentation for details.

Algebraic Loops in Triggered Subsystems

While the Simulink engine can minimize algebraic loops involving atomic and enabled subsystems, a special consideration applies to some triggered subsystems. An example for which code can be generated is shown in the following model and triggered subsystem.

The default Simulink behavior is to combine output and update methods for the subsystem, which creates an apparent algebraic loop, even though the Unit Delay block in the subsystem has no direct feedthrough.

You can allow the Simulink engine to solve the problem by splitting the output and update methods of triggered and enabled-triggered subsystems when necessary and feasible. If you want the Real-Time Workshop code generator to take advantage of this feature, select the Minimize algebraic loop occurrences check box in the Subsystem Parameters dialog box. Select this option to avoid algebraic loop warnings in triggered subsystems involved in loops.

Note   If you always check this box, the generated code for the subsystem might contain split output and update methods, even if the subsystem is not actually involved in a loop. Also, if a direct feedthrough block (such as a Gain block) is connected to the inport in the above triggered subsystem, the Simulink engine cannot solve the problem, and the Real-Time Workshop software is unable to generate code.

A similar Minimize algebraic loop occurrences option appears on the Model Referencing pane of the Configuration Parameters dialog box. Selecting it enables the Real-Time Workshop software to generate code for models containing Model blocks that are involved in algebraic loops.

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