MIMO Narrowband Disturbance Rejection using Frequency Shaping of Cost Functionals

The linear quadratic regulator control design methodology using frequency shaping of cost functionals (FSCF) is used to address narrowband, linear time invariant disturbance rejection problems. Frequency dependent state weighting matrices are incorporated into an augmented linear quadratic cost functional and result in a dynamic control law with high gain only near the disturbance frequency. For SISO systems the choice of weighting matrices is relatively straightforward, but in MIMO systems the additional latitude in the choice of parameters may be used to increase the performance and stability of the compensator design. A method is presented which extends the FSCF design approach by matching the convergence time constants of each of the closed loop compensator poles. The improved performance and stability properties of the compensator discussed in terms of realistic narrow band disturbances, which in general will have a finite disturbance bandwidth and may be time varying. The resulting compensator design is compared to a classical output feedback design.