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Title: Analysis and synthesis of nonlinear dynamic systems based on fuzzy model and frequency domain method
Authors: Li, Jingying
Degree: Ph.D.
Issue Date: 2021
Abstract: In aerospace, astronautics and industrial process, it is usually difficult to model and analyze the dynamics of controlled object exactly due to strong nonlinearities, internal/external disturbances, variation of loads, system uncertainties, etc. Classical time and frequency domain theories and methods are not applicable to analyze and control such nonlinear dynamic systems. Thus control and analysis of such complicated nonlinear systems are becoming more and more challengeable. Fuzzy control system, due to its capability of approximating any smooth nonlinear systems on a compact set with arbitrary accuracy, provides an appealing and efficient approach to facilitate analysis and synthesis of nonlinear systems. Nonlinear Characteristic Output Spectrum (nCOS) function has been well developed for analysis and design of nonlinear systems in frequency domain. Although there have been researches on control and analysis of nonlinear dynamic systems based on fuzzy model and frequency domain nCOS function, there are still some technical problems to be solved: explore stability analysis conditions of fuzzy system with lower conservativeness and new frequency domain methods to analyze and optimize nonlinear dynamic systems, etc. Objective of this thesis is to propose new control and frequency domain analysis methods to analyze, synthesize and optimize nonlinear dynamic systems with sampled-data behavior, time delay and imperfect premise matching based on fuzzy model and nCOS function. Some of the obtained results are applied to control and analysis of nonlinear vehicle suspension systems. First, fuzzy adaptive control for nonlinear active suspension system based on a bio-inspired reference model is studied. Fuzzy logic systems are used to approximate unknown nonlinear terms. A general bio-inspired nonlinear structure, which can present ideal nonlinear quasi-zero-stiffness for vibration isolation, is adopted as tracking reference model. Particularly, a nonlinear damping is designed to improve damping characteristics of the bio-inspired reference model. With beneficial nonlinear stiffness and improved nonlinear damping of the bio-inspired reference model, the proposed fuzzy adaptive controller can effectively suppress vibration of suspension systems with less actuator force and much improved ride comfort, thus energy saving performance can be achieved.
Then fuzzy sampled-data control problems for nonlinear dynamic systems under aperiodic sampling are studied. A sampling period dependent Lyapunov-Krasovskii functional together with a novel efficient integral inequality, which has the advantages of reducing conservativeness, is adopted. On the basis of stability conditions, a sampled-data controller that cannot only exponentially stabilize the system but also guarantee the extended-dissipativity performance is then designed. Simulation results of a quarter-vehicle suspension system with considering payload uncertainties and aperiodic sampling are provided to verify effectiveness and advantages of the designed controller. The problems of imperfect premise matching fuzzy altering design for continuous-time nonlinear systems with time-varying delays are investigated. Based on the extended dissipative performance index, a new delay-dependent filter design approach in terms of linear matrix inequalities (LMIs) is obtained by employing Lyapunov-Krasovskii functional method together with a novel efficient integral inequality. The designed filter can guarantee the filtering error system satisfy H∞, L2 -L∞, passive and dissipative performance by tuning the weighting matrices in the conditions. Moreover, the fuzzy filter does not need to share the same membership function with fuzzy model, which can enhance design flexibility and robust property of the fuzzy filter system. An advantageous optimization method developed based on the nCOS function is introduced to optimize mismatched fuzzy controller membership function parameters. Compared to traditional search-based optimization approach, which can only obtain optimal results and parameters, more analytical results can be obtained with less time consuming via this optimization method. This provides an in-depth understanding of nonlinear parameters' influence on system output spectrum. Simulation results demonstrate that with the frequency domain optimization method, disturbance suppression capability of the fuzzy-model-based controller over a concerned frequency band is further enhanced. A novel parametric characteristic function approach for hybrid linear and nonlinear parameters analysis and design of nonlinear systems is proposed based on the nCOS function. Thus influence of linear and nonlinear parameters on system output spectrum can be simultaneously considered. The results of a specific case demonstrate that the proposed hybrid approach can provide a more comprehensive solution for nonlinear system analysis and design. Then the proposed hybrid parameter analysis approach, together with an n-th order output spectrum calculation method is used to identify and locate plant and controller faults of closed-loop control systems, which provides an in-depth insight of fault characteristics analysis and identification of closed-loop control systems.
Subjects: Nonlinear control theory
Adaptive control systems
Fuzzy logic
Hong Kong Polytechnic University -- Dissertations
Pages: [9], xi, 177 pages : color illustrations
Appears in Collections:Thesis

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