Adaptive Control For Flexible Structures With Time Delay

In recent years,many active control methods have gained rapid development.With fast increase of the demand on the control efficiency and system performance,time delay that occurs in controller and actuator inevitably has been an important problem.Time delay exists during those processes like data collecting from sensors,signal transmitting and actuating process of actuators.On the one hand,it may cause decline of effectiveness of control force and even instability of a system.On the other hand,appropriate control law design for time delay can even improve the performance of the dynamic system.For instance,time-delay state feedback has been used in dynamic vibration absorber,linearization of nonlinear system,control of chaos oscillator and so on.Besides,it is difficult to build a model the same as the real system.There may be some errors of uncertain parameters between model and real system.Therefore,it is necessary to take care of those uncertain parameters as well as time delay.Flexible structures are usually typical dynamic systems,which are nonlinear and time-varying.Thus,the modeling of flexible structures has errors inevitably.It is necessary to consider those facts when modeling and designing control law.This inspires us to consider how to handle those uncertain parameters as well as time delay,including the problems of large and minor time delay,uncertainty of structures and nonlinearity of the system.This dissertation is funded by the Natural Science Foundation of China[11472171]and the Specialized Research of Shanghai[14ZR1421000],and presents theoretical and experimental studies of time delay control of uncertain system.The main researches are as follows:(1)Theoretical and experimental studies of model reference adaptive control of linear system with time delay and uncertain parameters are presented in this part,where time delay is uncertain bounded delay.Firstly,the continuous time approximation method is used to handle the input-delay in the system.By means of the difference equation of control input with time-delay,the dynamic equation of the system with delay is changed to augmented state equation without delay in the form.Then,the state equation of a reference model is established based on the time-delay system and known variables,and the corresponding controller for the state equation of the reference model is designed using linear quadratic regulator method.At last,model reference adaptive controller with like-observer is carried out based on the linear quadratic regulator controller.Simulations and experiments on a flexible cantilever beam are carried out to demonstrate the effectiveness of the designed controller.Uncertainty of the first natural frequency of the beam and the uncertain time delay are both considered.The results show that the proposed method can effectively suppress the vibration of the cantilever beam,and the simulation and experiment results are in well agreement with each other(2)Theoretical and experimental studies of model reference adaptive control of linear system with time delay and uncertain parameters are presented in this paper.Simulations and experiments on a rotating flexible beam are carried out to demonstrate the effectiveness of designed controller.Firstly,by means of augmented state variables of differential equation with input-delay,the dynamic equation of the system with delay is changed to augmented state equation without delay in the form.Then,the reference model is established based on the dynamic equation of the delayed system and known variables,and the control law for reference model is derived by using optimal track control to keep the closed-loop system of reference model stable.At last,model reference adaptive control law is carried out based on optimal track control method.Numerical and experimental examples are presented.A rotating flexible beam is chosen as an experimental object to investigate the utility of above method.Uncertainty of the first natural frequency of the beam is considered.Moreover,the system is assumed to have uncertain time delay with upper bounds.The results from the simulations and experiments are in well agreement Under different conditions of uncertain parameters and time delay,the results show the utility of the proposed method(3)Considering time delay and uncertain parameters,the adaptive fuzzy backstepping control for a flexible manipulator is studied.Firstly,the dynamic equation of the flexible manipulator with time delay is established and written into a state space form.To handle the input delay,the state variable is augmented by differential equation with control input,and the standard state equation without explicit time delay is deduced and obtained.In the backstepping design,we use fuzzy logic systems directly to approach unknown nonlinear functions existing in the system.Based on the adaptive backstepping control approach,a fuzzy adaptive backstepping controller with adaptive parameters is constructed.The stability of the close-loop control system is guaranteed by Lyapunov stability theory Finally,Simulation results indicate that the time-delay controller presented in this paper can effectively deal with time delay in the nonlinear system.