Symbolic manipulation
After coordinate selection, the tool automatically generates system equations, which are simplified with symbolic techniques. These include index reduction, differential elimination, separation of independent systems, symbolically resolving algebraic loops, and algebraically manipulating the system to produce a smaller set of equivalent equations. These techniques all combine to reduce the differential algebraic equations' complexity and make many previously difficult to solve problems numerically solvable.
Providing simplified equations to the numerical solver in such a computationally efficient form also reduces the total simulation time, in some cases by many orders of magnitude. As an example, engineers have used MapleSim to develop a full vehicle multibody model of a Chevy Equinox, which included pneumatic tires (22 degrees of freedom and 26 state space variables), and exported the model to a dSPACE simulator. Even a modest performance simulator (a 1-GHz PowerPC) achieved update rates of 63s.
Analysis with symbolic equations
There are advantages to having access to a model's symbolic equations when doing analyses such as optimization or sensitivity analysis. This is a feature of some tools. Furthermore, for multi-body applications, having access to the system equations also allows for a symbolic solution to the inverse kinematics problem. This translates to the ability to generate highly efficient code for the inverse kinematics that can be embedded in real-time HIL applications. Without this symbolic solution, these problems typically can't be used in real-time applications because the numeric, iterative solution is too slow.
In a real-world example, MapleSim was used at the University of Waterloo to develop an HIL test platform for a solar-powered planetary rover. This approach allows component testing within a simulation loop before a full rover prototype is available, reduces overall development time, and allows component testing under dangerous scenarios without risking the full prototype. In addition to simulating the rover dynamics, the modeling environment was used to automatically generate the rover's kinematic equations. With these equations, they used the tools to develop a path planner algorithm, which finds the optimum path between point A and point B, such that the rover maintains the highest level of internal energy storage while avoiding obstacles and high risk sections of the terrain.
— Bonnie Yueholds an MA of Science in mechanical engineering from the University of Waterloo. During her research, she collaborated with the Canadian Space Agency to develop an HIL platform for space rovers.
It is a good article however I would disagree that the traditional approach would start with solving the ODE. We normally start using an Laplace transform and writing the transfer funtion. From this, the poles of the system can be identified and any significant problems identified before spending the time to create a complex model.
I would recommend never skipping the back of the envelope analysis. It is very valuble to use it check that your model is locked in.
Excellent article. HIL testing just makes all kinds of sense, and the Rover example illustrates how the modeling environment can be used for other purposes. Thanks.
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