Research On Time-delay Control Of Flexible Beam By Using Piezoelectric Patch

With the development of technology,flexible structures such as plates and beams have been widely used in engineering due to their light weight.However,due to the small modal damping of the flexible structural system,the attenuation of vibration amplitude is slow for a long period of time when subjected to external excitation,which seriously jeopardizes the working efficiency of the system and even reduces its service life.Therefore,it has important practical significance for the vibration control of flexible systems.Moreover,in the active control,there have a delay phenomenon due to signal transmission,controller operation,actuator action,etc.,resulting in a time delay in which the control output delays behind the measurement signal.If the delay factor is neglected,it may adversely affect the control effect and even the stability of the system.Therefore,how to deal with the time delay factor has important theoretical and practical value.In this paper,the piezoelectric material is used as the actuator and the mathematical model of the flexible system is established.Subsequently,the control system is simulated and experimentally studied by PSO-PID,LQR optimal control and robust control under time delay.The main contents are as follows:(1)First,the dynamic model of the cantilever flexible system is established,and the output equation of the actuator is obtained based on the piezoelectric properties of the piezoelectric material.By combining the two factors,the vibration differential equation of the cantilever piezoelectric control system is finally obtained.Then the position design of the piezoelectric actuator is studied,and the corresponding performance index is established to find the optimal position of the piezoelectric actuator.(2)Based on the PID control law,and through the particle swarm optimization algorithm,the control parameters of the PID controller are optimized to obtain the control parameters.At the same time,the influence of the sampling period in the computer control system on the stability of the control system is studied,and the control parameter variation range that keeps the control system within the stable interval under the influence of the time delay is given.Various parameters that can make the control system stable are obtained.range.(3)For the state equation with time delay,the standard state equation without time delay is obtained by expanding the state equation.Then the control system is designed using LQR optimal control,and the time delay term is integrated.The corresponding state equation is obtained by transforming,and the control system is designed using robust control.At the same time,the range of the feedback parameter without delay and the influence of the delay on stability is given.(4)A flexible beam active control experimental bench was built.Based on the control law designed above and using Lab VIEW and CompactRIO platform,a controller integrating data acquisition,processing,and output was designed.The numerical control experiments proved the design of various controls.Feasibility and accuracy of the method.The results obtained through the above studies show that the designed control law has significant control effects on flexible systems with different time delays.However,there are still many shortcomings,so at the end of this article,we summarize our work and point out the direction for the next work.