21 Optimisation-Based Clearance: the Linear Analysis
Abstract:
Summary. We present the clearance results of the HIRM+RIDE control configuration for the linear stability and handling criteria mostly used in the current industrial practice. The performed analysis is based on an optimisation-driven worst-case search. Two classes of linear stability related criteria are considered: the Nichols exclusion region based stability margin criterion and the unstable eigenvalues criterion. The considered handling criteria are the average phase rate and the absolute amplitude criteria. The analysis results clearly illustrate the high potential of the optimisation-based approach in reliably solving clearance problems with many simultaneous uncertain parameters. 21.1 Optimisation-Based Clearance of Linear Criteria Our analysis addresses the linear stability and handling criteria defined in Chapter 10, namely (a) the stability margin criterion, (b) the unstable eigenvalues criterion, (c) the average phase rate criterion, (d) the absolute amplitude criterion. Because of space limitations, we are forced to restrict our presentation to selected results which best illustrate the different aspects of an optimisationbased clearance approach. In this introductory section, we discuss some aspects which are common to all clearance tasks formulated above. Specific aspects and detailed analysis results are presented in separate sections dedicated to particular classes of criteria. The complete results, including results for the classical gridding-based approach, are presented in a GARTEUR AG11 Report [1]. The definition of suitable distance functions is a crucial step in an optimisation-based clearance approach (see Chapter 7). The main requirement for a satisfactory distance function is to enforce at minimum, worst cases where the clearance conditions are potentially most violated. Additionally, a satisfactory distance function to be used for an optimisation-driven 386 Andras Varga worst-case search must not introduce additional local minima, must be continuous and have continuous derivatives, and finally, must be easy to compute. Two categories of clearance problems can be identified, which lead to
