Output feedback in the design of eigenstructures for enhanced sensitivity. (November 2018) - Bernal, D.; Ulriksen, M.D.
Highlights: It is shown that the SVD assignment fails for homogeneous sensors and output feedback. The high coherence of the latent vectors real and imaginary parts is identified as the culprit. Least square placement of the full spectrum resolves instability but limits sensitivity improvements. A weighted least squares solution is shown to offer adequate control of the stability sensitivity tradeoff. Abstract: The problem of closed-loop enhanced sensitivity design is as follows: given a linear, time-invariant system, find a (realizable) feedback gain such that (1) the closed-loop is stable in the reference and the potentially damaged states, and (2) the eigenstructure includes a subset of poles, with desirable derivatives, that lie in a part of the plane where identification is feasible. For state feedback the eigenstructure is typically assignable and stability in the reference state is easily enforced. For output feedback, however, only partial assignment is possible, and it is here shown that the standard SVD design scheme leads to generically unstable eigenstructures when measurands are homogeneous (that is, when all sensors measure displacements, velocities, or accelerations). The mechanics that govern this behavior are clarified and a mitigating strategy that retains the convenience of homogeneous sensing is offered.