A single sensor and single actuator approach to performance tailoring over a prescribed frequency band

Restricted sensing and actuation control represents an important area of research that has been overlooked in most of the design methodologies. In many practical control engineering problems, it is necessitated to implement the design through a single sensor and single actuator for multivariate performance variables. In this paper, a novel approach is proposed for the solution to the single sensor and single actuator control problem where performance over any prescribed frequency band can also be tailored. The results are obtained for the broad band control design based on the formulation for discrete frequency control. It is shown that the single sensor and single actuator control problem over a frequency band can be cast into a Nevanlinna-Pick interpolation problem. An optimal controller can then be obtained via the convex optimization over LMIs. Even remarkable is that robustness issues can also be tackled in this framework. A numerical example is provided for the broad band attenuation of rotor blade vibration to illustrate the proposed design procedures.