Analysis And Synthesis For Uncertain Systems And Its Application To Flight Control

Since the naissance of the modern control theory at the end of 19’50, the control theory has got rapid development. Many results of the modern control theory are based on an accurate math model. However, inevitably practical systems suffer different uncertainties which include either model imperfections, such as unmodeled dynamics, structured parametric uncertainties, changes of the operating environment, model reduction and linearization approximations, etc., or external disturbances, for examples, various disturbances with unknown statistical characteristic and bounded energy. On the other hand, large-lag links, transmission process and complicated on-line analysis usually lead to delay phenomenon in practical industrial processes, which influences stability and performance index of the system seriously. Therefore, the stability problem of uncertain systems with or without delay has been a hot topic in the control field.Based on Lyapunov-Krasovskii functional method and linear matrix inequality(LMI) techniques, this thesis investigates the problem of analysis and synthesis for uncertain systems with or without delay and applies it to concrete problems of flight control. The main works of this thesis are as follows:By virtue of LMI approach, the problems of non-fragile and exponential control for polytopic systems and its application to flight control are studied. Firstly, a sufficient condition for the existence of a robust non-fragile controller is given based on parameter-dependent Lyapunov functions combined with a descriptor system approach. Secondly, in the framework of LMI, handling quality criteria for pitch axis are derived for high and low order aircraft with multiple operating points, respectively. At last, on the basis of the results above, a compound and non-fragile controller, which consists of a feed-forward controller and a state feedback controller, is designed under the switch strategy and the multi-objective strategy, respectively. This controller can satisfy both handling quality index and robust exponential stability requirement simultaneously. The adjusting range of a parameter that influences the sensitivity of aircraft responses and feasibility of LMIs is obtained by introducing convex optimization algorithms. Simulation results show that the obtained controller can meet design requirements.The problems of robust stability analysis and stabilization for uncertain systems with time-varying delay are investigated based on Lyapunov-Krasovskii functional. Firstly, a delay-dependent and rate-dependent robust stability criterion of the system is obtained in terms of LMI techniques. This stability criterion is less conservative and can ensure a larger upper bound of time delay. Secondly, in consideration of controller uncertainties and external disturbances, a delay-dependent robust non-fragile H∞controller is designed for a vertical take-off and landing (VTOL) helicopter with flight delay by taking advatages of obtained results. Simulation results show that the designed controller has good robust and non-fragile performance and is suitable for practical abominable flight environment.The problem of robust stability analysis and synthesis for a polytopic system with time-delay is investigated by LMI approach. Firstly, on the basis of parameter-dependent Lyapunov-Krasovskii functional and a descriptor model transformation, free-weighting matrix method and delay partitioning technique are introduced to establish a delay-dependent robust stability criterion in terms of LMI, repectively. This stability criterion is less conservative and has less computational burden. Secondly, in consideration of actuator faults, a delay-dependent robust reliable controller is designed for an aircraft with multiple operating points and flight delay by means of the results above and fault tolerent techniques. Simulation results demonstrte that in the case of actuator faults, the designed controller can still secure robust stability of the system.The problem of robust stability for an uncertain system with random time-delay is investigated based on the stochastic variable model with probability ditribution characteristics of dealy. A delay-dependent and delay-distribution dependent robust stability criterion of the system is derived by using an appropriate Lyapunov-Krasovskii functional and integral inequality. Without exercising any influence on conservatism of the result, no free-weighting matrix is needed in the derivation of the condition, which simplifies the result and reduces computational burden accordingly. In addtion, conservatism of the condition is reduced further by introducing a descriptor model transformation approach. Numerical examples illustrate the effectiveness of the proposed method.In consideration of probability ditribution feature of dealy, the problem of robust H∞control for an uncertain system with interval delay is investegated based on the stochastic variable model. Firstly, a less conservative delay-distribution dependent robust stability criterion is established by integral inequality and Lyapunov-Krasovskii functional characterized by delay bound partitioning. For the routine delay whose low bound is zero, this criterion is still less conservative. On the basis of this, a delay-distribution dependent H∞performance criterion and the design method of the corresponding H∞controller are given. Numerical examples illustrate the effectiveness of the proposed method.Finally, the conclusions of the dissertation are drawn and further research directions are put forward.