Experimental Study Of H_∞Time-delay Control For Flexible Structures

With the development of science and technology, modern engineering structures become moreand more large and complex, lightweight and flexible components have been widely used inengineering structures, at the meantime the requirements on system performance and operatingprecision of the structures become higher and higher. Research in this area comes to the so-calledflexible structural system. Flexible structure generally exists small modal damping, if no controlstrategy is used the vibration of the structure will last for a very long time once the structure isexcited by a certain external excitation. The vibration will not only affect the normal performanceof the structure, but also result in early fatigue breaking and shortening of service life of thestructure. Therefore, it is of great importance to develop efficient control strategies to reduce thevibration of flexible structures.Robust Control is a strategy proposed in modern control theory. Roughly speaking,robustness refers to the “strength” level of system performance against uncertainty of the system.The uncertainty mentioned herein means the incomplete understanding of some parts of the system,only some imperfect information of the system is known. The robust control problem is how touse the known incomplete information for system design. In fact, robustness problem has drawnmuch attention in the early classical control theory. For example, making the frequencycharacteristics to have sufficient stability margin is to ensure that stability is not damaged byuncertainty of the system. From the early1980s, in robust control, it has begun to activelyconsider uncertainty in the process of mathematical modeling and controller design, quantitativedescription for the effect of uncertainty is studied. Today robust control has been paid more andmore attention by the researchers, in which the H∞method is a hot topic and is gotten many studies.The theory system of the H∞method has already been established nowadays and this method hasmany applications in practical engineering.However, time delay inevitably exists in active control systems. Sometimes it is inherent incontrol systems such as sensor signals gathering and conveying, controller calculating and processfor actuator to build up the required control force; sometimes it is a voluntary introduction into thesystem such as the using of data filter. Time delay may lead to non-synchronization of controlforces, resulting in actuators inputting energy into the control systems when no energy is needed.This may cause degradation of control efficiency or even the instability of the control systems.Moreover, even original dynamic system is linear, the system may appear many complex nonlineardynamic behaviors when active control is applied and time delay is taken into account. Therefore, the research on time delay is of important theoretical significance and practical value. Today timedelay is also one of the hot topics in mathematics, control, mechanics and structural engineering etc.This dissertation is funded by the Key Project [grant number11132001] and the GeneralProjects [grant numbers11072146,11002087] of Natural Science Foundation of China, and theSpecialized Research Fund for the Doctoral Program of Higher Education of China(20110073110008), and presents theoretical and experimental studies of time-delay robust controlof structural vibration. The main research and achievements are as follows:(1) This dissertation starts theoretical and experimental studies of H∞control for a flexible plate.Firstly, the dynamic equation of the plate with time delay is established with considering externaldisturbance. Then the standard state equation without explicit time delay is deduced and obtainedby a particular integral transformation to the time-delay equation. Finally, a H∞time-delaycontroller is designed based on the standard state equation using the method of linear matrixinequality (LMI). The controller designed contains not only current step of state feedback but alsothe linear combination of some former steps of control. Simulation and experimental results revealthat the time-delay controller can effectively deal with time delay in the system, and is available forsmall time delay and large time delay as well. Furthermore, this delay controller is robust to thevariance of intrinsic parameter of the plate and time delay.(2) This dissertation secondly presents theoretical and experimental studies of H∞control for aflexible plate with uncertain time delay. A matrix inequality for stability of the control system isdeduced and proved using the Lyapunov-Krasovskii function and free-weighting matrix. A H∞controller is designed using the parameter adjustment method and genetic algorithm. Threecontrol design problems are specially discussed:(i) allowable time delay for known controller;(ii)controller design with known maximum time delay of the system;(iii) the biggest time delay forsystem stability with unknown controller. The treating methods for the three cases are discussed indetail. Simulation and experimental results indicate that, for the case of known controller, themaximum time delay for stability determined using the proposed method is closer to the realsituation; for the case of known maximum time delay of the system, the H∞controller designedusing the proposed method in this dissertation may achieve good control effectiveness; for the caseof unknown controller, the maximum time delay determined is the biggest one.(3) This dissertation presents a theoretical and experimental study of H∞control for a flexible plateand flexible beam with uncertain time-delay based on output feedback. Firstly, a memorylessobserver is introduced, and a dimension-expanded system is established. Secondly, a matrixinequality for stability of the dimension-expanded control system is deduced and proved using theLyapunov-Krasovskii function and free-weighting matrix. Finally, H∞controller is designed usingthe parameter adjustment method and genetic algorithm. Three control design problems are alsodiscussed detailedly:(i) allowable time delay for known controller;(ii) controller design withknown maximum time delay of the system;(iii) the biggest time delay for system stability withunknown controller. Numerical simulations and experiments results are given to demonstrate thevalidity and feasibility of the proposed methods in this dissertation.