Control Of Nonlinear Parameter-varying Systems With Applications

Nonlinearities and the time-varying nature are two challenging issues which commonly exist in control systems.So far,there are still no computationally tractable methods for analysis and synthesis problems of nonlinear time-varying systems.In view of this,this dissertation first proposes the nonlinear parameter-varying(NPV)models to capture the nonlinearity and the time-varying nature of nonlinear time-varying(NTV)systems.With the aid of sum of squares(SOS)programming theory,we investigate the analysis/synthesis problems of nonlinear time-varying systems within the NPV framework and then apply the theoretical results to the conversion flight control of a tilt rotor aircraft.The main contents of this dissertation are outlined as follows:1)Exponential stabilization of NPV systems.Computationally tractable exponential stability criteria are given for NPV systems.Then,exponential stabilization control approaches are put forward for one-dimensional-parameter case and multi-dimensional-parameter case,respectively.Additionally,to facilitate engineering application,results for input-constrained case are provided as well.All of the above results can reduce to the corresponding results in polynomial linear parameter-varying(LPV)systems and polynomial nonlinear systems,therefore,the research of NPV systems can be viewed as the further development and extension of the existing studies on these systems.2)Mixed stabilization of NPV systems.The existing finite-time stability(FTS)analysis/synthesis research is generalized to NTV systems in the NPV framework.Specifically,to guarantee both the transient and steady-state performances,a new concept,mixed stability,is proposed.Differently from the existing FTS-related works,the mixed stability herein consists of properties of uniform exponential stability in addition to FTS.The mixed stability analysis method is developed,which shows that exponential stability may naturally imply FTS to some extent.The mixed stabilization approaches are provided as well,for input-constraints-free case and input-constrained case.3)H? mixed control of NPV systems.Firstly,based on the aforementioned study,the concept of mixed stability with H? disturbance attenuation is proposed for perturbed NPV systems.Secondly,the H? mixed stability analysis method is developed.Thirdly,based on the stability analysis,the H? mixed control approach is given.Lastly,for the case that both parameters and state are subject to restricted regions,local synthesis results are also provided,in which the relevant results are based on a more relaxed assumption,that is,the derivative of the parameter is no longer required to be real-time detectable.Simulation shows that the proposed controller possesses both nice transient/steady-state performance and disturbance attenuation capability.Compared with the FTS results in the sense of Lyapunov,an advantage of the proposed approach lies in the fact that,with a pre-specified state threshold,undesirable large values of the state can be avoided in finite time and thus overshot can be reduced.4)Application of NPV control to the tilt rotor aircraft system.Firstly,the mathematical model for tilt rotor aircraft is developed.Within the NPV framework,control design schemes are provided for both the case that forces/moments are regarded as control inputs and the case that control surfaces are regarded as control inputs.To enhance the robustness of the controller,a disturbance observer is designed to estimate the influence of the uncertainties of the aerodynamic parameters and the modeling errors.The whole design scheme consists of the design of the generalized conversion path,the trajectory of the tilt angle,the control law,the disturbance observer and the control allocation strategy.Simulations validate the effectiveness of the integrated control design scheme.All of the above solvable conditions are in terms of state-and-parameter-dependent linear matrix inequalities(SPLMIs),which can be efficiently solved via SOS programming,thereby circumventing the computational difficulties typically involved in traditional nonlinear time-varying analysis/synthesis methods.The study is a valuable supplement and development to the existing NTV control theory and,from the application perspective,offers new ways to tackle the flight control design problems for tilt rotor aircraft and other high-performance aircraft.