This work investigates power flow and energy transfer in controlled structures. If the goal of control is to stop an initially vibrating structure, energy must be forced out through dissipating components. The analysis performed here quantifies energy being transferred internally and externally to dissipative mechanisms in the primitives of a spring-mass-damper system and a beam-piezoelectrics-electronics system over the transient period of the systems’ response to initial conditions. The systems studied were broken down into capacitive, inertial, resistive and sourcing primitives. All systems containing primitives from all domains can be modeled this way. The analysis started from first principles and investigated energy flow in general. Energy flowing from the mechanical primitives to the electrical primitives is especially important because controlled structures often integrate primitives from these two domains. Computer simulations showed that power seemingly flows into sources used to control the structures. This work also laid the groundwork for the development of control design methods based on energy flow. / Master of Science