Putting Energy Back in Control

Energy is one of the fundamental concepts in science and engineering practice, where it is common to view dynamical systems as energy-transformation devices. This perspective is particularly useful in studying complex nonlinear systems by decomposing them into simpler subsystems that, upon interconnection, add up their energies to determine the full system’s behavior. The action of a controller may also be understood in energy terms as another dynamical system—typically implemented in a computer— interconnected with the process to modify its behavior. The control problem can then be recast as finding a dynamical system and an interconnection pattern such that the overall energy function takes the desired form. This “energy-shaping” approach is the essence of passivity-based control (PBC), a controller design technique that is very well known in mechanical systems. Our objectives in this article are threefold: • First, to call attention to the fact that PBC does not rely on some particular structural properties of mechanical systems, but hinges on the more fundamental (and universal) property of energy balancing. • Second, to identify the physical obstacles that hamper the use of “standard” PBC in applications other than mechanical systems. In particular, we will show that “standard” PBC is stymied by the presence of unbounded energy dissipation, hence it is applicable only to systems that are stabilizable with passive controllers. • Third, to revisit a PBC theory that has been recently developed to overcome the dissipation obstacle as well as to make the incorporation of process prior knowledge more systematic. These two important features allow us to design energy-based controllers for a wide range of physical systems.