Algorithm for Robust Eigenstructure Assignment Using the Linear QuadraticRegulator

摘要

The Linear Quadratic Regulator (LQR) can guarantee a robust closed loopeigenstructure for full state feedback. The algorithm developed here takes advantage of the stability guarantees of LQR to achieve an eigenstructure close to desired but within the allowable region of LQR. The algorithm selects the LQR weighting matrices, Q and R, that minimize the distance between the elements of the desired and LQR achievable eigenstructures. The minimization is accomplished by using a simplex based optimization routine. Specific weightings placed on the elements of the desired eigenstructure define the relative importance of each element. The algorithm is programmed in FORTRAN and is designed to be run from the software package MATLAB. Two examples are examined to illustrate the use of the program, including a helicopter flight control system. The results show that this algorithm is a valid technique for achieving robust eigenstructure assignment with full state feedback.