Power-based control of physical systems: two case studies

It is well known that energybalancing control is stymied by the presence of pervasivedissipation. To overcome this problem in electrical circuits, the alternative paradigm of powershaping control was introduced in (Ortega et al., 2003)where, as suggested by its name,stabilization is achieved shaping a function akin to power instead of the energy function. Ina previous work (Garcıa-Canseco et al., 2006) we have extended this technique to generalnonlinear systems. The method relies on the solution of a PDE, which identifies the openloopstorage function. Despite the intrinsic difficulty of solving PDEs, we show through some physicalexamples, that the powershaping methodology yields storage functions corresponding to thepower of the system. To motivate the application of this control technique beyond the realm ofelectrical circuits, we illustrate the procedure with two case studies: a microelectromechanicalsystem and a twotank system.