Fast Implementation of Direct Allocation with Extension to Coplanar Controls

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The direct allocation method is considered for the control allocation problem. The original method assumed that every three columns of the controls effectiveness matrix were linearly independent. Here, the condition is relaxed, so that systems with coplanar controls can be considered. For fast online execution, an approach using spherical coordinates is also presented, and results of the implementation demonstrate improved performance over a sequential search. Linearized state-space models of a C-17 aircraft and of a tailless aircraft are used in the evaluation. Oincreasethe reliability ofaircraft,cone gurations with a large numberofactuatorsandcontrolsurfacesareadvantageous.Recone gurable control laws may be used to exploit all of the available control power despite failures and damages. 1;2 Control allocation is the problem of distributing the control requirements among multiple actuators to satisfy the desired objectives while accounting for the limited range of the actuators. Although solutions exist for the control allocation problem, an issue of current interest is that of the feasibilityoftheirimplementationonexistingcomputersforaircraft with a large number of actuators. 3 The direct allocation approach 4i6 is based on the concept of the attainable moment set (AMS), which is the set of all of the moment vectors that are achievable within the control constraints. The methodofdirectallocation allowsoneto achieve100%oftheAMS, whereas some other approaches such as daisy chaining, pseudoinverse,and generalized inversesolutionshavebeen shown to achieve