Model-following control applications to nonlinear mechanical systems

Abstract

Model-following control design methodology is introduced for nonlinear plants and models. The plant equations are considered to be linear in the control input. Dynamic matching conditions are presented and the resulting error dynamics are given. The stability of error dynamics is ensured, using Liapunov's second theorem; by modifying the model state rates, which effectively introduces error feedback.

The methodology is applied to two problems. Motion control of an n-link manipulator with torque controllers on each linkage, and control of an aircraft lacking direct control of lift and side force. The former represents the systems where all of the degrees of freedom can be controlled, and the latter represents the systems where only some of the degrees of freedom can be controlled.

The aircraft control problem is analyzed in more detail. The resulting control law does not require any explicit gain scheduling, but instead, requires estimates of the stability and control derivatives. A method is proposed to compensate for actuator dynamics. The control law is then verified by simulating some maneuvers on the aircraft model provided for the AIAA Controls Design Challenge, which includes nonlinear and full-envelope aerodynamic and engine models, and rate and position limited controls. The maneuvers simulated include a level acceleration and a 3-g turn.