Tracking and regulation in linear multivariable systems: A frequency domain approach

This paper outlines a constructive procedure for the synthesis of linear multivariable systems subjected to constant reference input and constant disturbance in the partial state. The synthesis procedure is capable of producing a stable desired closed loop transfer matrix which can be expressed as the product of an open loop transfer matrix and any proper rational transfer matrix, assuming that the given system has no zeros at the origin. The closed loop transfer matrix is realized via integral feedforward compensation with asymptotic state estimation while simultaneously eliminating the effect of steady state disturbance at the output and track a constant reference input. The conditions for achieving a variety of specific design goals such as (1) closed loop stability, (2) static decoupling with complete and arbitrary closed loop pole placement, and (3) dynamic decoupling subjected to step disturbance is also determined. The compensation scheme is presented in the frequency domain and is equivalent to the type 1 servo design in the time domain when the plant has no integrator.