Multi-rate real-time simulation techniques

The simulation of systems based on differential-equation models normally uses a single numerical integration algorithm that applies a uniform step-size regime to all parts of the model. An alternative is to divide the model into segments based on their different dynamic behaviors and use different step sizes in different segments. This approach is referred to as multi-rate simulation. It can be used to advantage in some current real-time applications, such as power electronics and automobile engine simulations. These applications can require real-time execution with frame times of a few microseconds or less. These frame times require expensive special-purpose hardware and software. In many cases the components that require this approach represent only a small part of the total system and it is unnecessary to apply it to the rest of the system, which can be simulated with longer frame times. Research is described that aims to combine special-purpose DSP-based high-speed simulations with a conventional realtime Linux system to produce a distributed, multi-rate, realtime simulation. Multi-rate simulation introduces its own problems. Care has to be taken in the communication of data between segments operating at different frame rates. In some cases the use of multi-rate algorithms can induce unstable behavior in the simulation.