In this notebook, we have demonstrated the use of Mathematica in modeling of dynamic systems and controller design. The symbolic capabilities of Mathematica are very useful for deriving dynamic equations according to the Lagrangian formalism. Furthermore, rewriting these equations in state-space form, suitable for controller design, is also easily done using Solve. A unique solution is always obtained since the unknown second-order derivatives always appear linearly in the equations derived from the partial differential equation (6) that the Lagrangian of the system has to satisfy.

We have also shown how efficient C++ code for simulation can be generated using the application package MathCode C++. The pendulum/seesaw example is only a toy example compared to many of them. Industrial applications motivate the efforts to be able to automatically generate C++ code that can be compiled and run outside Mathematica for increased performance.

In the fighter aircraft example, we illustrated how Mathematica can be used as a prototyping environment for controller design. First the model of the system is analyzed and different controllers can be evaluated. When a satisfactory solution has been found, MathCode C++ can be used to generate standalone C++ code that can be used in the real application.