Maximum Number of Bracketing Iterations

The Maximum number of bracketing iterations parameter limits the number of search iterations used by Simulink for locating a zero-crossing event once the event has been detected. In general, a higher number of bracketing iterations will provide a more accurate event location, but this option is computationally costly.

Consider this model with a sine wave driving a Hit Crossing block. Zero-crossings are detected when the Hit Crossing block detects that its input signal has crossed zero, which should occur at multiples of pi. The scope displays this result.

model = 'mFixedStepZcParameters';
open_system(model);
set_param(model, 'Solver', 'VariableStepAuto');
sim(model);

Too few bracketing iterations results in locating zero crossings with less accuracy. To see the number of bracketing iterations simulation results, enable fixed-step zero-crossing, change to a fixed-step solver, and set the Maximum number of zero-crossings per step parameter to 2. Use a fixed-step size of 0.5.

set_param(model, 'EnableFixedStepZeroCrossing', 'on',...
    'MaxZcBracketingIterations', '2',...
    'SolverName', 'ode3',...
    'FixedStep', '0.5');

Increasing the number of bracketing iterations to 4 results in more accurate location of the events in this model. The zero crossing is located closer to the expected value of pi.

set_param(model, 'MaxZcBracketingIterations', '4');

Maximum Number of Zero-Crossings per Step

Use Maximum number of zero-crossings per step parameter to limit the maximum number of zero crossings that Simulink will locate in one simulation time step. Once this maximum number is reached in a step, any additional zero-crossings that occur within that step are ignored. To see how this can affect simulation results, consider the following example. Set the Sine Wave block to output two sine waves that are slightly offset by using scalar expansion on the 'Bias' parameter of the sine wave block. Two zero crossing events should be located near pi.

sineWaveBlock = [model '/Sine Wave'];
set_param(sineWaveBlock, 'Bias', '[0.0 0.1]');
set_param(model, 'Solver', 'ode45');
simoutVS = sim(model);

Setting the maximum number of zero-crossings to locate per step to 1 will restrict Simulink to only locating the first zero crossing that occurs within a single time step. In this example, Simulink only locates the first zero-crossing in the step at pi in the step from t = 3 to t = 3.5. As a result, the second state of the Integrator block is less accurate due to the missed zero crossing.

set_param(model, 'Solver', 'ode3',...
    'EnableFixedStepZeroCrossing', 'on',...
    'MaxZcPerStep', '1');
simoutFS_1ZC = sim(model);
f = figure();
tiledlayout(f,'flow','TileSpacing','compact','Padding','compact');
nexttile;
plot(simoutVS.tout, simoutVS.xout.signals(1).values(:, 1),...
    simoutFS_1ZC.tout,simoutFS_1ZC.xout.signals(1).values(:,1), '-x');
title('State 1')
nexttile;
plot(simoutVS.tout, simoutVS.xout.signals(1).values(:,2),...
    simoutFS_1ZC.tout,simoutFS_1ZC.xout.signals(1).values(:,2), '-x');
title('State 2')
legend('Variable-Step (Expected Result)', 'Fixed-Step with One Zc Per Step',...
    'Location', 'northwest');

Since you know to expect a maximum of two zero crossings to be located within the fixed-step size of 0.5, setting the Maximum number of zero-crossings per step parameter to 2 should yield more accurate simulation results. This plot shows that both continuous states of the Integrator block match the expected result.

set_param(model, 'MaxZcPerStep', '2')
simoutFS_2ZC = sim(model);
f = figure();
tiledlayout(f,'flow','TileSpacing','compact','Padding','compact');
nexttile;
plot(simoutVS.tout, simoutVS.xout.signals(1).values(:, 1),...
    simoutFS_2ZC.tout,simoutFS_2ZC.xout.signals(1).values(:,1), '-x');
title('State 1')
nexttile;
plot(simoutVS.tout, simoutVS.xout.signals(1).values(:,2),...
    simoutFS_2ZC.tout,simoutFS_2ZC.xout.signals(1).values(:,2), '-x');
title('State 2')
legend('Variable-Step (Expected Result)', 'Fixed-Step with Two Zc Per Step',...
    'Location', 'northwest');