Design of set-point tracking systems incorporating inner-loop compensators and fast-sampling error-actuated digital controllers for irregular linear multivariable plants using step-response matrices

Singular perturbation methods are used to exhibit the asymptotic structure of the transfer function matrices of discrete-time set-point tracking systems incorporating irregular linear multivariable plants (ie, plants with rank-defective first Markov parameters) which are amenable to inner-loop compensation and associated fast-sampling error-actuated digital control but for which mathematical models are unavailable for design purposes. It is shown that these results facilitate, using only the step-response matrices of compensated open-loop plants, the determination of controller matrices which ensure that the closed-loop behaviour of such discrete-time tracking systems becomes increasingly non-interacting as the sampling frequency is increased. These general results are illustrated by designing a fast-sampling error-actuated digital flight controller for the longitudinal dynamics of an aircraft, using only the open-loop step-response matrix of the compensated plant. It is indicated that similar general results are also available for discrete-time set-point tracking systems incorporating regular linear multivariable plants (ie, plants with full-rank first Markov parameters).