Modeling and Design Implications of Noncollocated Control in Flexible Systems

In this paper we investigate generic properties of structural modeling pertinent to structural control, with emphasis on noncollocated systems. Analysis is performed on a representative example of a pinned-free Euler-Bernoulli beam with distributed sensors. Analysis in the wave number plane highlights the crucial qualitative characteristics common to all structural systems. High sensitivity of the transfer function zeros to errors in model parameters and sensor locations is demonstrated. The existence of finite right half plane zeros in noncollocated systems, along with this high sensitivity, further complicates noncollocated controls design. A numerical method for accurate computation of the transfer function zeros is proposed. Wiener-Hopf factorization is used to compute equivalent delay time, which is important in controls design.