Using Simulink

Determining Step Size for Discrete Systems

Simulating a discrete system requires that the simulator take a simulation step at every sample time hit, that is, at integer multiples of the system's shortest sample time. Otherwise, the simulator might miss key transitions in the system's states. Simulink avoids this by choosing a simulation step size to ensure that steps coincide with sample time hits. The step size that Simulink chooses depends on the system's fundamental sample time and the type of solver used to simulate the system.

The fundamental sample time of a discrete system is the greatest integer divisor of the system's actual sample times. For example, suppose that a system has sample times of 0.25 and 0.5 second. The fundamental sample time in this case is 0.25 second. Suppose, instead, the sample times are 0.5 and 0.75 second. In this case, the fundamental sample time is again 0.25 second.

You can direct Simulink to use either a fixed-step or a variable-step discrete solver to solve a discrete system. A fixed-step solver sets the simulation step size equal to the discrete system's fundamental sample time. A variable-step solver varies the step size to equal the distance between actual sample time hits. The following diagram illustrates the difference between a fixed-step and a variable-size solver.

In the diagram, arrows indicate simulation steps and circles represent sample time hits. As the diagram illustrates, a variable-step solver requires fewer simulation steps to simulate a system, if the fundamental sample time is less than any of the actual sample times of the system being simulated. On the other hand, a fixed-step solver requires less memory to implement and is faster if one of the system's sample times is fundamental. This can be an advantage in applications that entail generating code from a Simulink model (using the Real-Time Workshop^®).

Purely Discrete Systems

Sample Time Propagation