Ironwood,
First, it is important that you provide the version of the Toolkit you are using. Notice that the Control Design Toolkit and the Simulation Module were merged into one product called "Control Design and Simulation Module 8.5". So, if you have a previous version of the toolkit, we strongly recommend to upgrade to the newest version. Please contact you sales representative since you could be entitle to a cheaper upgrade.
Now, for your specific question, if you have nonlinearities in your simulation, you should use the Simulation Loop instead of the Control Design part. The Control Design part do not handle nonlinearities in the simulation. In Simulation, the integrator (1/s) has a build-in limits. You just need to configure to you the limits that you need. You can have upper, lower or both limits and define different values for this node.
Another information: the integrator equation is (1/s). If you have 1/(s+1), then you have a filter and you could limit the output with a Coerce function in the Comparison pallette.
Hope it helps!
Barp - Control, Simulation, RTT and HIL - National Instruments