Mutual Direct Controllability of MIMO Systems and Application to Longitudinal Aircraft Control

Further investigation of the recently developed concept of mutual direct state controllability (MDC) is presented. The MDC identifies the subsets of state variables in a control system that are simultaneously and independently controllable by direct actions of the system's control authority. The MDC analysis adopts the tools of virtual constraint dynamics (VCDs) on the open loop system, the controls coefficients of these VCDs along the trajectories of the system, and successive generalized dynamic inversion (SGDI) of these VCDs. The analysis leads to a systematic multivariable control system design that results from SGDI of individual VCDs on a mutually directly controllable (M-DC) subset of state variables. The produced SGDI control system design is in the nested generalized dynamic inversion (GDI) control loops paradigm. The number of control loops is equal to the number of VCDs on the open loop system, which must be less than or equal to the number of independent control variables. The dynamics of each loop of the control system is governed by a GDI control law, and each GDI control law is in the nullspace of the controls coefficient vector of the VCD that corresponds to the preceding control law. The dynamics of the control loops are independent, such that the order of loop closure is irrelevant and can be arbitrary. The MDC analysis is applied to the linearized underactuated three degrees of freedom longitudinal equations of motion for a conventional fixed wing aircraft to unveil the M-DC state variables.