Partial pole assignment with time delay by the receptance method using multi-input control from measurement output feedback

• Partial pole assignment of multi-input time-delay systems is investigated.
• Control gains of measurement output feedback using the receptance method are derived.
• A numbering system is proposed when certain elements of the output are unmeasurable.
• Effects of time delay on partial pole and modal constraints assignments are studied.

This study investigates the receptance method for the partial pole assignment of time-delay nonlinear systems using multi-input control from measurement output feedback (i.e., acceleration, velocity and displacement). The receptance method has a remarkable advantage compared to other methods in that there is no need to know the mass, damping and stiffness matrices of the system, which are typically obtained from the finite element method. We achieve partial assignment of the desired poles with no spillover using the assigned and unchanged poles and the corresponding eigenvectors of the closed-loop system. We used different types of generalised inverse matrices to obtain the realisable control gains. The modal constraints for the assigned eigenvectors are thus obtained. Because certain components of the measurement output were found to be unmeasurable, a numbering system is proposed for determining zero elements in the control gains. Then, realisable control gains are obtained after zero-column substitutions are made in the corresponding matrix with the numbering system. Our theoretical results show that having multi-input control from the measurement output feedback is effective for a partial pole assignment with time delay in structures. This theory is demonstrated by several numerical examples of a three-degree-of-freedom damped mass-spring system.