Multi-input/multi-output controller design for longitudinal decoupled aircraft motion

Abstract

For the AFTI/F-16 aircraft a multi-input/multi-output controller design is described which decouples pitch rate and normal acceleration, A controllable state space is determined which forms the model used by the linear quadratic Gaussian synthesis technique. The dynamic model guarantees zero steady-state tracking, and the LQG synthesis technique produces the compensator structures with theoretical robustness guarantees. To ensure that the nominal system remains robust with respect to model and parameter uncertainties, singular value analysis is used. A combination of symmetric root locus, time response, and singular value analysis is used to describe the performance of the design. errors in the presence of parameter uncertainty. This is be- cause integral compensation is introduced by this state space.7 However, in the AFTI/F-16 longitudinal decoupling prob- lem, a state space which produces integral compensation for both the errors in acceleration and pitch rate is not controlla- ble. A controllable state space is determined by reducing the order of the state space by using a particular linear combina- tion of the state variables. LQR synthesis is applied to this final state space. All of the states are not measured. In fact, the only assumed measurements are normal acceleration, pitch rate, and angle of attack. An observer is designed to estimate the required actuator states, since there are no measurements on any of the elevator or flap states. The design procedure is divided into two parts. First, the weightings on the states in the LQR synthesis are chosen so that the system response remains slow relative to the higher-order actuator dynamics. This allows a reduced-order controller and alleviates the need to estimate the higher-order actuator states. Second, the observer is de- signed to capture the full feedback results of LQR synthesis. By using the suggestion of Doyle and Stein,6 the observer weightings are chosen so that the full-state feedback transfer function is obtained asymptotically, impressive robust re- sponse is obtained for large parameter variations. This robust- ness is evaluated by using singular value techniques. The singular values of the error models due to parameter varia- tions and the higher-order actuators are derived and plotted on the singular value frequency charts. The gap between the singular values of the nominal inverse return difference matrix and the largest singular value of the error models guarantees stability. Time responses, which include the higher-order actu- ator dynamics and parameter variations, are also displayed to ensure that the desired transient response is obtained.