Balanced LQG Compensator for Flexible Structures

The analysis of open-loop balanced flexible structures has been extended for closed-loop structures. LQG compensator gains (i.e., the gains of a controller and of an estimator) are obtained from the solutions of the controller Riccati equation (CARE) and the estimator Riccati equation (FARE). For the balanced compensator the solutions of CARE and FARE are equal and diagonal. Thus, a balanced LQG compensator puts the same effort into control and estimation of the system. An approximate balanced LQG compensator for flexible structures is determined in this paper. Its properties allow one to obtain a reduced-order compensator, which preserves the stability and performance of the full-order compensator. The performance of an LQG compensator depends on the weights of the quadratic performance index and on the variance of the estimator noise. The relationships between weights/variances and characteristic values of the system as well as between weights/variances and plant/estimator pole location are derived in this paper. Thus the weights can be determined in advance to meet the requirements of a closed-loop system.