Decentralized robust control of interconnected resonators

The control of multiple, interconnected resonators under parametric uncertainty is addressed. The control objective is to provide closed-loop stability and asymptotic regulation of the frequency, gain, and phase of each resonator. It is desired to use a minimal controller configuration to reduce implementational complexity and production costs. Since a resonant system's energy is mainly distributed in the passband, a frequency translation technique based on the Hilbert transform is applied to the nominal plant to obtain a low-frequency equivalent model that also includes the dynamics of the (nonlinear) amplitude/phase detectors and modulators. Feedforward and robust feedback control systems are then synthesized for the baseband system using the controller identification approach. Various control structures such as centralized, partially decentralized, or fully decentralized are considered. In each case, the stabilizing controller gain can be determined by performing a limited number of steady-state experiments on the plant. A synthesis algorithm is provided to summarize the design steps in a systematic manner