Robust Optimization And Stability Analysis Of Spacecraft Dynamic Control Allocation

As a key part of control system, control allocation maps the desired controlcommand to the actuators. Control allocation algorithm realizes optimal allocationof control command, improves the performance of the control system, and increasesthe utilization efficiency of actuators when the actuators are redundant. In this paper,control allocation with parameter uncertainties, the allocation error control systemstability analysis and control algorithm of the three aspects of the allocationalgorithm are discussed, the results follows.A robust optimization method is used to find its alternative or transformedmodel. It always happens in the control allocation model that parameters turn out tobe uncertain, such as actuators failed unexpectedly, the control efficiency matrixdeviated from its nominal value and outputs deviation. We describe the uncertainparameters as ellipsoid uncertainty set. In this way, control allocation error can bereduced by mathematical simulation. After stochastic simulation many times, it isproved that the allocation error is closer to the zero value when10%uncertainty isexist by using the proposed robust optimization control allocation algorithm.Control allocation is assigned to track the desired control command, but theallocation error always happens in the actual allocation process. It affects the controlsystem pole-zero distribution directly and thus affects the stability of the controlsystem. We analysis and list several types of allocation errors. The lyapunovprinciple is used to guarantee the stability of control system when some conditionsare satisfied.Several control allocation algorithms are proposed due to some typical cases inspacecraft control problems. In order to make full use of the actuators, the energybalance problem is proposed. We introduction the concept of weighting matrix, andthen we present a mathematical model to solve the problem. After that, we explainedthe concept of a weighting factor to evaluate the allocation results. Considering thedynamics of actuators, the first and second order dynamic models are put forward.After the dynamic model discrete, a pre-correction compensation is used to modifythe control signals so as to achieve the goal of reducing the allocation error. Wecome up with the maximum resultant force in certain direction and its lower boundwhen attitude control can be ensured.