# mdlProjection

Perturb the solver's solution of a system's states to better satisfy time-invariant solution relationships

## Required

No

## Languages

C, C++

## Syntax

```
#define MDL_PROJECTION
void mdlProjection(SimStruct *S)
```

## Arguments

`S`

SimStruct representing an S-Function block.

## Description

This method is intended for use with S-functions that model
dynamic systems whose states satisfy time-invariant relationships,
such as those resulting from mass or energy conservation or other
physical laws. The Simulink^{®} engine invokes this method at each
time step after the model's solver has computed the S-function's states
for that time step. Typically, slight errors in the numerical solution
of the states cause the solutions to fail to satisfy solution invariants
exactly. Your `mdlProjection`

method can compensate
for the errors by perturbing the states so that they more closely
approximate solution invariants at the current time step. As a result,
the numerical solution adheres more closely to the ideal solution
as the simulation progresses, producing a more accurate overall simulation
of the system modeled by your S-function.

Your `mdlProjection`

method's perturbations of system states must fall within
the solution error tolerances specified by the model in which the S-function is embedded.
Otherwise, the perturbations may invalidate the solver's solution. It is up to your
`mdlProjection`

method to ensure that the perturbations meet the error
tolerances specified by the model. See Perturbing a System's States Using a Solution Invariant for a simple method
for perturbing a system's states. The following articles describe more sophisticated
perturbation methods that your `mdlProjection`

method can use.

C.W. Gear. “Maintaining Solution Invariants in the Numerical Solution of ODEs,”

*Journal on Scientific and Statistical Computing*7, no. 3 (July 1986).L.F. Shampine. “Conservation Laws and the Numerical Solution of ODEs I.”

*Computers and Mathematics with Applications*12B (1986): 1287–96.L.F. Shampine. “Conservation Laws and the Numerical Solution of ODEs II.”

*Computers and Mathematics with Applications*38 (1999): 61–72.

## Examples

## See Also

## Version History

**Introduced in R2006b**