Control of Mechatronic Systems, A Geometric Approach

The introduction of differential geometric methods has significantly changed the control of nonlinear systems. The coordinate free description of the system allows us to get rid of artefacts caused by the choice of a special coordinate system. Since we will identify dynamic systems with geoemtric objects defined on abstract manifolds, we put the necessary notation and concepts at the readers disposal. It is shown that port controlled Hamiltonian systems form an import and adaptable subclass of nonlinear systems, especially for applications in mechatronics. The presented theory is applied to the Cuk-converter, a dc-to-cd converter that is easy to sign is based on an H2-approach, the control law includes an integral term and it follows from a special solution of the Hilton-Jacobi-Bellman inequality. The performance of the closed loop is demonstrated by simulations, as well as by measurements.