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Controller certification : the generalized stability margin inference for a large number of MIMO controllers


In this dissertation, we investigate MIMO stability margin inference of a large number of controllers using pre- established stability margins of a small number of [nu]- gap-wise adjacent controllers. The generalized stability margin and the [nu]-gap metric are inherently able to handle MIMO system analysis without the necessity of repeating multiple channel-by-channel SISO analyses. This research consists of three parts: (i) development of a decision support tool for inference of the stability margin, (ii) computational considerations for yielding the maximal stability margin with the minimal [nu]-gap metric in a less conservative manner, and (iii) experiment design for estimating the generalized stability margin with an assured error bound. A modern problem from aerospace control involves the certification of a large set of potential controllers with either a single plant or a fleet of potential plant systems, with both plants and controllers being MIMO and, for the moment, linear. Experiments on a limited number of controller/plant pairs should establish the stability and a certain level of margin of the complete set. We consider this certification problem for a set of controllers and provide algorithms for selecting an efficient subset for testing. This is done for a finite set of candidate controllers and, at least for SISO plants, for an infinite set. In doing this, the [nu]-gap metric will be the main tool. We provide a theorem restricting a radius of a ball in the parameter space so that the controller can guarantee a prescribed level of stability and performance if parameters of the controllers are contained in the ball. Computational examples are given, including one of certification of an aircraft engine controller. The overarching aim is to introduce truly MIMO margin calculations and to understand their efficacy in certifying stability over a set of controllers and in replacing legacy single-loop gain and phase margin calculations. We consider methods for the computation of; maximal MIMO stability margins b̂P̂, C, minimal [nu]-gap metrics [delta][nu], and the maximal difference between these two values, through the use of scaling and weighting functions. We propose simultaneous scaling selections that attempt to maximize the generalized stability margin and minimize the [nu]-gap. The minimization of the [nu]-gap by scaling involves a non -convex optimization. We modify the XY-centering algorithm to handle this non-convexity. This is done for applications in controller certification. Estimating the generalized stability margin with an accurate error bound has significant impact on controller certification. We analyze an error bound of the generalized stability margin as the infinity norm of the MIMO empirical transfer function estimate (ETFE). Input signal design to reduce the error on the estimate is also studied. We suggest running the system for a certain amount of time prior to recording of each output data set. The assured upper bound of estimation error can be tuned by the amount of the pre- experiment

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