Algebraic Constraint

Constrain input signal to zero

Library

Math Operations

Description

The Algebraic Constraint block constrains the input signal f(z) to zero and outputs an algebraic state z. The block outputs the value that produces a zero at the input. The output must affect the input through a direct feedback path, that is, the feedback path contains only blocks with direct feedthrough. For example, you can specify algebraic equations for index 1 differential-algebraic systems (DAEs).

Algorithm

The Algebraic Constraint block uses a dogleg trust-region algorithm to solve algebraic loops [1], [2].

Data Type Support

The Algebraic Constraint block accepts and outputs real values of type double.

Parameters and Dialog Box

Initial guess

An initial guess for the solution value. The default is 0.

Example

By default, the Initial guess parameter is zero. You can improve the efficiency of the algebraic-loop solver by providing an Initial guess for the algebraic state z that is close to the solution value.

For example, the following modelmodel solves these equations:

z2 + z1 = 1
z2 - z1 = 1

The solution is z2 = 1, z1 = 0, as the Display blocks show.

Characteristics

Direct Feedthrough

Yes

Sample Time

Inherited from driving block

Scalar Expansion

No

Dimensionalized

Yes

Zero-Crossing Detection

No

References

[1] Garbow, B. S., K. E. Hillstrom, and J. J. Moré. User Guide for MINPACK-1. Argonne, IL: Argonne National Laboratory, 1980.

[2] Rabinowitz, P. H. Numerical Methods for Nonlinear Algebraic Equations. New York, NY: Gordon and Breach, 1970.

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