A New Perspective on Coupling Numerator Models

Coupling numerator models are a well-established tool for predicting the closed-loop dynamics of multiple-input multiple-output systems. They describe the input-output dynamics of the open-loop path in a partially controlled system given tight controls and thus may serve as an approximation of the actual dynamics "seen" by the single-axis controller in a controlled multiple-input multiple-output plant. Such models can therefore be employed for a decentralized initial design of multivariable controllers. This paper presents a new, unifying approach for the computation of such constrained input-output dynamics. Connections to existing methods in the literature are established and a general procedure for state-space calculations is given. The use of coupling numerator models for controller design is motivated and different decoupling structures are discussed. The controller design is illustrated using a coupled high-order helicopter model.