Assignment of poles to a large-scale structure with state-feedback controllers in orthogonal subspaces

In this paper, a practical pole placement technique is proposed to shape the dynamic response of a large-scale structure. To this end, a similarity transformation, which diagonalizes the mass and stiffness matrices of a large-scale structure, is applied to a system of coupled second-order ordinary differential equations (ODE), and this system of equations that represents a large-scale structure is transformed into principal coordinates. In this new coordinate system, a special state-feedback controller, which is the so-called inner loop, is used to decouple this system of equations and reduce them to n uncoupled second-order ODE’s. Since the system is now represented with n uncoupled second-order ODE’s, poles of these n second-order ODE’s can be assigned one at a time using a separate proportional-derivative (PD) controller; set of these PD controllers form the outer loop. In this paper, a full state-feedback controller, which is simply the aggregation of these inner and outer state-feedback loops, is sought to assign poles of a large-scale structure. Analytical proof of the proposed state-feedback controller, which places the poles of a large-scale structure, is provided. In the final part of the paper, poles of a large-scale truss structure are assigned using the pole placement technique proposed in this research.