Analysis and synthesis of self-powered linear structural control with imperfect energy storage

Self-powered vibration control systems are characterized by a distributed network of regenerative force actuators, which are interfaced with a common power bus. Also connected to the power bus is an energy-storing subsystem, such as a supercapacitor, flywheel, or battery. The entire system is controlled using switch-mode power electronics, and the only power required for system operation is that necessary to perform these switching operations. The resultant energy conservation constraint restricts the set of feedback laws that are feasible. This paper reports on an LMI feasibility constraint for linear self-powered feedback laws, in terms of actuator and storage hardware parameters. Two design applications of this constraint are illustrated. The first is the determination of the least-efficient energy storage parameters necessary to realize a given passive control law. It is shown that this problem is quasiconvex, and may be posed as a generalized eigenvalue problem. The second example uses an extension of positive-real-constrained H₂ optimal control, to optimize a control law subject to the feasibility constraint. Both examples are illustrated in the context of base-excited vibrating structures, subjected to stationary stochastic excitation.