User`s guide

3 Writing S-Functions As C-MEX files
3-82
#define MDL_ZERO_CROSSINGS
#if defined(MDL_ZERO_CROSSINGS) && (defined(MATLAB_MEX_FILE) || defined(NRT))
/* Function: mdlZeroCrossings =================================================
* Abstract:
* This will only be called if the number of nonsampled zero crossings is
* greater than 0, which means this block has a continuous sample time and the
* the model is using a variable step solver.
*
* Calculate ZC signals that help the solver find the
* exact instants at which equation switches occur:
*
* if UpperLimit < u then use (1)
* if LowerLimit <= u <= UpperLimit then use (2)
* if u < LowerLimit then use (3)
*
* The key words are help find. There is no choice of a function that will
* direct the solver to the exact instant of the change. The solver will
* track the zero crossing signal and do a bisection style search for the
* exact instant of equation switch.
*
* There is generally one ZC signal for each pair of signals that can
* switch. The three equations above would break into two pairs (1)&(2)
* and (2)&(3). The possibility of a "long jump" from (1) to (3) does
* not need to be handled as a separate case. It is implicitly handled.
*
* When a ZCs are calculated, the value is normally used twice. When it is
* first calculated, it is used as the end of the current time step. Later,
* it will be used as the beginning of the following step.
*
* The sign of the ZC signal always indicates an equation from the pair. In the
* context of S-functions, which equation is associated with a positive ZC and
* which is associated with a negative ZC doesn't really matter. If the ZC is
* positive at the beginning and at the end of the time step, this implies that the
* positive equation was valid throughout the time step. Likewise, if the
* ZC is negative at the beginning and at the end of the time step, this
* implies that the negative equation was valid throughout the time step.
* Like any other nonlinear solver, this is not fool proof, but it is an
* excellent indicator. If the ZC has a different sign at the beginning and
* at the end of the time step, then a equation switch definitely occured
* during the time step.
*
* Ideally, the ZC signal gives an estimate of when an equation switch
* occurred. For example, if the ZC signal is -2 at the beginning and +6 at
* the end, then this suggests that the switch occured
* 25% = 100%*(-2)/(-2-(+6)) of the way into the time step. It will almost
* never be true that 25% is perfectly correct. There is no perfect choice
* for a ZC signal, but there are some good rules. First, choose the ZC
* signal to be continuous. Second, choose the ZC signal to give a monotonic
* measure of the "distance" to a signal switch; strictly monotonic is ideal.
*/