Modified Pseudoinverse Redistribution Methodsfor Redundant Controls Allocation

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Introduction I N recent years, control allocation problems have been intensively studied following the work of Durham.1−3 There are several solution methods: direct control allocation,1−3 daisy chaining,4 a linearprogramming (LP) method,5−6 a quadratic-programming (QP) method,7−11 and a pseudoinverse-redistribution (PIR) method.10−13 In this Note, a PIR method is discussed. A pseudoinverse has been used as a selector or a distributor.14 Shtessel et al. applied a pseudoinverse to the control allocation problem for a tailless aircraft.15 However, it is fixed, and it does not consider the control surfaces’ limits. Virnig and Bodden developed a PIR method for a short takeoff and vertical landing aircraft and then demonstrated the algorithm by means of a simulator.12 The PIR method repeats the process of calculating a pseudoinverse and a control vector by setting the saturated elements of a control vector to their limit values until a solution is obtained or there is no unsaturated element. Bordignon and Bessolo developed a modified method and applied it to the X-35 aircraft’s control allocation problem.16 Although the PIR method sets the saturated control elements to their limit values, the modified method selects only one saturated element and sets it to its limit value during the redistribution process. The purpose of this Note is to propose other modified methods and to compare them with the conventional PIR method and Bordignon and Bessolo’s method. A different selection of one saturated element results in a difference in performance. For this purpose, two different selections are proposed. The performance metrics of concern are the calculation times, the percentage of times that a method converges to an optimal solution, and the characteristics of the errors between the optimal solutions and the redistributed solutions. Numerical examples are presented for comparisons.