Analysis And Synthesis Of Control Performance For Uncertain Structures(Systems)

Due to the uncertainty exists in practical, studying the influence of uncertainty to performance of structures or systems, and the synthesis analysis and design of control methods for uncertainty structures and systems are more and more important problems to scientists and engineers. These problems have been one of the focus researches in present structural mechanics and control theory field. In this dissertation, the static and dynamic responses of uncertainty structures, and the control performance and controller design of uncertainty systems are analyzed. The main research works can be described as follows.1. The static responses and dynamic characteristics of truss analysis structures with fuzzy interval parametersWhen the fuzziness of the truss structures with interval parameters was represented by the interval-valued membership function, the uncertainty of the interval variables was represented by fuzzy interval factors, and the interval variables were expressed as the product of their mean values and interval factors. And then, the static finite element equations and dynamic equations of the structure are built. Based on the interval analysis theory and interval-valued fuzzy sets theory, the explicit calculation expressions of structural displacement responses , stress response and natural frequencies are developed to truss structures with fuzzy interval parameters. The computational method for solving the interval-valued membership function of structural displacement response , stress response and natural frequencies are given. Feasibility and validity of the proposed method are illustrated by two numerical examples. The advantages of this method are that the effect of the uncertainty of one of the structural parameters on the uncertainty of the structural static response and natural frequencies can be reflected expediently and objectively. In additional, it is easy to realized the proposed method with small amount and high calculation efficient.2. Closed-Loop Response Analysis of Optimal Vibration Control System with Stochastic ParametersBased on mode coordinate, the optimal vibration control of truss and plane beam structures were designed. By using the approximately discrete method, the approximate solutions of structural closed-loop response are obtained. The approximate solutions can substitute the exact solutions. The randomness of physical and geometric dimensions parameters of truss structure and the randomness of physical of plane beam structure were considered and represented in the form of random factors. And then, the computational expressions of the mean value and the variance of closed-loop response of the stochastic parameters structure under the optimal vibration control are derived by means of the random variable's functional moment method. Finally, the influences of the randomness of structural parameters on the structural closed-loop responses are analyzed by an example with the proposed method and the Monte Carlo method, which validate the feasibility of the proposed method.3. Eigenvalues analysis of intelligent beam structure vibration control system with stochastic parametersThe control model of intelligent beam structure was built. And then, under the mode coordinate, the vibration control of intelligent beam was designed by using the method of pole allocation. Considering the randomness of intelligent beam structural physical and geometric dimensions parameters, the random factors were abstracted from the stiffness matrix and the mass matrix, and then, were introduced into the vibration control equation, so the randomness of parameters in the vibration control equation was represented by the random factors. By using the algebra synthesis method, the expressions of the mean value and the standard variance of the open-loop and closed-loop eigenvalues of vibration control equation were developed. The closed-loop stability of the vibration control equation of random structures was discussed and the stability criterion was obtained by the 3σcriterion. Finally, an example of intelligent cantilever beam structure was used to illustrate the feasibility of the proposed method, which show that the effect of the physical parameters on the eigenvalues are bigger than that of the geometric dimensions parameters.4. Robust PID vibration control of uncertainty intelligent beam structures and its time-delay stability analysisThe design of the robust PID vibration control of uncertainty intelligent beam structures was studied. Considering the uncertainty of the structural mode damping ratio and mode frequency in a intelligent beam structure, and the excellent performance of PID control, guaranteed cost control and H∞control, a new method to design robust PID vibration control was presented, and the processes of derivation and demonstration are given. The optimal parameters of PID controller were obtained by solving a convex optimal problem of LMI. Considering the practical time-delay factors, the analysis of the time-delay stability of the robust PID vibration control system was studied and the value of maximum time-delay of the stable system was obtained. Finally, an example was used to illustrate the feasibility and validity of the method given here. From the example, we can conclude that the robust PID controller can keep the system stable within the range of maximum time-delay, furthermore, the anti-interference performance of system and the accepted value of maximum time-delay restraint each other.5. Application of intelligent PID controller in an uncertainty arc furnace systemAn intelligent PID controller is proposed for an arc furnace system with uncertainty parameters and three-phase current coupled . By using genetic algorithm with real number coding, a group of optimal parameters of this intelligent PID controller are obtained, which are used as the original values for the real-time tuning of PID parameters. Based on the principle of integral detached, a fuzzy decoupled inference is designed for the PID parameters real-time tuning to ensure that the system response has optimal dynamic and steady-state performances. The results of computer simulation show that the intelligent PID controller has the advantages of better dynamic, static, and robust performance over the conventional PID controllers in the uncertainty arc furnace control system.