Robust Reduced-Order Controller Design And Its Application To Aeroengines

Many physical plants are modeled as high order dynamical systems, and thecontroller designed by H∞control theory for those plants generally have ordercomparable to the plants. But the low-order controllers not only have manyconveniences, but also have low mamufacturing cost.With the improvement of the performance of modern airplane, more and moremaneuverability requirements of aeroengine have been offered. However, aeroenginesare very complicated nonlinear multivariable time-variant aerothermodynamic systems.Therefore, we need adopt H∞robust control theory to deal with various uncertaintiesof systems effectively. However, the high-order controllers designed by H∞controltheory are difficult to implement, and the real-time of the controllers is restricted. So itis very necessary to design H∞robust reduced-order controller for aeroengines.In this paper, we mainly study robust reduced-order controller design problem. Theextant H∞robust controller reduction methods are analyzed, and new frequencyweighted balanced reduction methods are proposed. Furthermore, the methods cansucessfully use in robust reduced-order controller design to aeroengines. The main workof this thesis as follows:1. A detailed description for robust reduced-order controller design and itsapplication to aeroengines is given, and the extant H∞robust controller reductionmethods are summarized and analyzed. The controller reduction methods which basedon the thought of balanced realization are mainly discussed.2. Moore balanced reductin methoh have the desired results in both stability anderror of the reduced-order model. But when Enns extented it to the field of frequencyweighted, the stability of reduced-order model could not be guaranteed. Though themodified frequency weighted balanced reduction method solved the potential drawbackof instability, the reducton error was increased. Then we propose the joint frequencyweighted balanced reduction method which is based on a combination of theunweighted balanced technique with the modified frequency weighted balancedreduction method by introducing two free parameters α and β. From the numericalexamples we can see that by properly chosing free parameters this method is possible to obian reduced-order model with smaller than other well-known techniques on thepremise of ensuring the stability of reduced-order model. In addition, since the errorbound formula has a special form because of the introduction of parameters, a moreconcise and easily calcuatable error bounds are derived.3. The parameter selection problem of the joint frequency weighted balancedreduction method is discussed. Since reducton error is a function of the parameters, sothe effect of reductin depends largely on the parameters value. But in different circs,there is no uniform law for reduction error when the parameters change. It is difficult touse experience on the selection of appropriate parameters. The computationalcomplexity is increased. Therefore, we consider translating the reduction method withthe parameters into the optimization problem. Taking the reduction error as objectivefunction, then using the particle swarm optimization algorithm to optimize theparameters. Through the numerical examples we can see that the optimal parameters aresearched automatically, while the reducton error is global minimum in the parametersvariation scope. Thus the algorithm not only solves the lack of time-consuming andlaborious, but also further improves the accuracy.4. For a four-variables small perturbation state variable model of aeroengine, therobust controller is designed by using H∞design method based on genetic algorithms.The methods proposed in this paper can triumphantly transform the high-order controller tolow-order controller. The simulation results show that the designed robust reduced-ordercontroller not only satisfies the required performance requirements, but also possesses robuststability and robust performance.