Structural control design based on reduced-order observer

An observer-based structural control design method is proposed in this paper. The method is a semi-inverse design procedure in that the control law is not designed before the observer system, but is a result that comes from the observer design. However, the observer design is not completely independent of the control design either, but seeks to yield a control law that is close to a prescribed control law. First, the observer design problem is considered as the reconstruction of a linear function of the state vector. The linear state function to be reconstructed is the given control law. Then, based on the derivation for linear state function observers, the observer design is formulated as a parameter optimization problem. The optimization objective is to generate a matrix that is close to the optimal feedback gain matrix. Based on that matrix, the form of the observer and a new control law can be determined. The semi-inverse design procedure can yield a reduced-order observer with dimension considerably smaller than that of the system. Two examples are used to demonstrate the proposed design procedure.