Comments on Achievable Eigenvectors

The eigenstructure approach to control system design can help the designer gain insights into the dynamics of the physical process or system. The approach helps clarify the benefits derived from each measurement and actuator, and it is reasonably easily understood and applied. Eigenstructure control concepts work best if the feedback designer possesses a deep understanding of the physical system to be controlled. With other systems the designer may have some difficulty in selecting appropriate "desired" eigenvectors. Physical system characteristics may place constraints on the "achievable" eigenvectors which may not be obvious to the control system designer. If not appreciated, these constraints (in addition to those imposed by a limited number or instruments and actuators) can complicate or muddle the design process. However, achievable eigenvectors must lie within the column space of an easily computed matrix. We find that examining the singular value decomposition of this matrix helps one understand a physical system and appreciate what can be accomplished with feedback control. An example problem illustrates the idea and shows that the decomposition may broaden the range of control systems which are easily designed with the eigenstructure approach.