Physical Modeling and Signal-Based Modeling

This article discusses how Signal-Based Modeling and Physical Modeling can be implemented in an MBD project that is distributed across multiple organizations.

For this article, I’ll define Signal-Based modeling as a network consisting of components with directional signals between them. Each component has clearly-defined inputs and outputs, and each signal runs from a component’s output to a (typically different) component’s input. Each component receives its inputs, and computes it outputs. In this form of simulation, signals have values, such as an angle or a velocity. This type of modeling is exemplified by ordinary Simulink block diagrams. This is sometimes called "1-D" modeling.

Signal-based modeling works well for systems that can be readily defined by input-output relations. For example, consider a simulation of a spacecraft’s attitude dynamics:

The attitude control computer takes inputs in the form of attitude measurements and outputs commands to the actuators on the vehicle. The vehicle dynamics model takes forces from the actuators, and outputs angular position and velocity. These are hooked together into a happy little control loop.

Unfortunately, not all systems can be readily defined as input-output systems.

I’ll define Physical Modeling simulation as a network consisting of components with connections that establish relationships between components. These relationships are not directional and do not directly have a value. Instead, they link physical values between components such as pressure and volume, or voltage and current. The behavior of these physical values is defined collectively by the connected components. This type of modeling is exemplified by Modelica object diagrams or Simscape diagrams.

Most physical systems with discrete components can be simulated with physical modeling, including those that have input-output relationships. A simple automotive drive train can be modeled using signal-based modeling, but to do this you need the counter-intuitive realization that the central component in the modeling is the torque converter. On the other hand, a drive train can be intuitively modeled with physical modeling techniques.

Some physical systems are very difficult to define using input-output relationships. Consider a simulation of the body dynamics semi tractor-trailer:

The input to the chassis dynamics is the spring forces at each end of the various axles, but the forces are a function of the chassis dynamics. There is no clear input or output. For these types of systems, physical modeling is the only realistic approach.

Some real-world components are purely input-output devices, such as the attitude control computer mentioned above. These components should be modeled with input-output relations. Fortunately, signal-based modeling systems can interact with physical modeling systems, allowing hybrid simulations that include both types of modeling.

Note: The above definitions and descriptions are neither precise nor complete, and there are much better definitions in the literature. Instead, I’m merely trying to convey some of the key differences between these two forms of simulation.

Distributed MBD Projects

One of the keys to success in a distributed MBD project is clear, precise, and unambiguous communication between the groups. From this point of view, there are advantages to each style of simulation.

With signal-based modeling, precisely defining the technical aspects of connections between components from different groups is a little easier. For example, it is very easy to declare that the angular velocity output on the component from the attitude dynamics group should connect to the angular velocity input on the component from the gyro group:

The input-output nature of signal-based modeling makes it a little easier to precisely define connections.

With physical modeling, describing connections between the components from different groups is a little more intuitive. Consider a hydraulic system:

It is easy to describe how the simulation component from the hydraulic pump group connects to the valve models, and the valve model connects to the rams and hydraulic motors, without defining the details of every connection.

SystemBlend™

Both signal-based modeling and physical modeling are fully supported by SystemBlend™, including custom-defined physical modeling domains.

A physical modeling connection can be included in a cable, alongside signal buses:

This style of cable in SystemBlend™ is well-suited to signal-based modeling, and defines very sophisticated interfaces. However, these cables are primarily intended for signal-based modeling, so they are point-to-point, connecting two components.

Physical modeling is not necessarily point-to-point, so SystemBlend™ also includes a style of connection that is purely physical modeling:

These connections are not point-to-point. Instead, one such connection can connect to any number of components:

By defining both mixed and physical modeling cables this way, SystemBlend™ fully automates the error-prone and tedious bookkeeping required when connecting components from different groups.

Custom physical modeling domains can be defined with simple drag-and-drop in the GUI of the SystemDesigner desktop application:

By fully supporting physical modeling, SystemBlend™ allows your team to select the simulation style or styles that are best for your project.