Control design and analysis for systems with redundant limited controls

Systems with redundant control effectors are prevalent today, and this will continue to be so. Issues, such as solution freedom to address actuator command requirements, arise in the design and analysis of systems with redundant controls that are non-existent in systems without redundant controls. Control analysis and design strategies are developed in this document for systems with redundant limited controls.;New analysis tools are developed that address the allocation of redundant controls in the feedback loop and account for a proposed separation of control allocation from other control elements. The focus of these tools are for the daisy chain control allocation method, however many are shown to be applicable to other common allocation methods as well. Aircraft flight control examples are given to demonstrate the new analysis techniques.;It is shown that control allocation directly leads to the development of a control design model that has an equal number of inputs and outputs, i.e. a square system. A control design strategy for square systems is developed that accounts for different small and large amplitude command response objectives. Control for small amplitude commands is accomplished with a feedback and feedforward structure that provides robust tracking of the commanded variables. Proportional-plus-integral feedback gains provide second-order command response and are chosen using loopshaping design techniques to guarantee robustness. The feedforward gain provides additional freedom for transient command response requirements. Control for large amplitude commands is accomplished with minimum-time control to provide rapid capture of a new equilibrium. Lyapunov level sets of the closed-loop system are used to provide transition between large and small amplitude commands. Longitudinal axis flight control of a statically unstable aircraft with thrust vectoring is used to demonstrate the new control design strategy where precision attitude tracking objectives differ from gross acquisition objectives.