Adaptive Vibration Suppression Research Of Smart Cantilevered Beam Based On Hysteresis Property And Time Delay Phenomenon

Smart structure is consisted of main structure, sensor, actuator and controller, and it is usually used in the aerospace equipment, ships, bridges and various devices of the mechanical processing field. However, some smart structures have hysteresis phenomena in the smart actuators. Moreover, the nonlinear phenomenon of smart structure will reduce control accuracy in the control system and limit the broader range of applications in the high accuracy field. Especially for the smart flexible space structure, it has high requirements for location precision, its modal damping is rather small and it is easily affected by the external environment. When it suffers from an external disturbance, its free vibration has slow attenuation property because of the structure’s small damping. If these structures work for long time in an unstable, complex and fast-changing environment, their normal working properties and service lives will be influenced. Meanwhile, the control signal transmissions in the sensor, the filter and the computer processor will cost a certain period of time, which cause the time delay in the control signal. This time delay will be slowly getting larger and larger when the devices have long-period working experiences. Therefore, the time delay may have negative or positive effect on the control result and the stability of the smart system.The time delay phenomenon appears because the signal transmission costs some time, then the output signal lags behind the input signal in a system. Furthermore, from the view of the phenomenology, the time-lag effect is similar to the hysteresis nonlinearity to some extent, but the two phenomena are different properties, even the two properties have influences on each other. Therefore, in the paper, the hysteresis property and the time delay effect will be investigated through their dynamical mathematical model to analyze their relevances and irrevances and their influences on each other.The time delay must exist in the control system, only the time delay may be small or large. However, the time delay is not always bad factor. When the time delay is overlarge in the control system, the control effect of control system may be negatively affected. When the time delay is small enough, the control result of smart system will be improved, the stability of system will be enhanced, and the control performance of control system will be improved. In the paper, the conclusion, that the small enough time delay will be beneficial to improve the ability of control system’s suppressing vibration, is verified through some simulations and some experiments.The main contexts and conclusions in the paper are as follows:1. Through analyzing the motion of electric domain in the piezoelectric material when it is applied with an electric field, the generation principle of hysteresis property in the piezoelectric material is informed. Based on the linear constitutive equation of piezoelectric material and Bouc-Wen hysteresis model, the nonlinear constitutive equation describing the hysteresis property between the electric field and the electric displacement is attained. Then combing the nonlinear constitutive equation and Hamilton Principle with the assuming modal method, the dynamic mathematic model of smart cantilevered beam is constructed. Through some simulations and some experiments, the hysteresis effect between the strain in the root part of smart beam and the applied voltage on the piezoelectric actuator is described effectively by the nonlinear model. Moreover, it is studied that the amplitude and frequency of the actuating voltage have much influence on the hysteresis property.2. Through analyzing the relevances and irrevances between the hysteresis property and time delay phenomenon of smart cantilevered beam and based on the nonlinear model for the hysteresis phenomenon, the mathematic model for the two phenomena is proposed. Meanwhile, from the mathematic model, the time delay affects not only the area but also the direction of the hysteresis loop, and this effect is periodic(it is the natural period of system). Moreover, for the smart cantilevered beam hysteresis-time delay system, the stability of smart beam is analyzed. It is informed that the stability of the smart system with one piezoelectric actuator is affected by the time delay of control system.3. For the adaptive controller design to the smart system, the ARMAX model with RELS identification algorithm is adopted to identify the hysteresis property, and the effect on the hysteresis by time delay is also identified and verified by experimental results. Based on the online identifying ARMAX model, the Minimum Variance Self-Tuning Direct Regulator is employed to suppress free vibration of the smart beam. Meanwhile the simulation results testify that the small enough time delay is beneficial to enhance the control performance of the smart control system.4. To filter the measure noise of sensing data in the experiments and improve the control effect of the smart control system, it is a necessary task to design a filter for the smart beam. In the paper, based on the filtering property of the high speed Tracking-Differentiator, a filter is designed to remove effectively the measure noise of sensing data during the experimental process.5. Based on the simulation results of vibration suppression for the smart cantilevered beam with the Minimum Variance Self-tuning Direct Regulator, an experimental platform is constructed to verify the theoretical simulation results. Through the experimental verification, the vibration suppression results with small enough time delay is better than that without time delay. Furthermore, the hysteresis property between the free vibration and control voltage in the experiments is influenced by the time delay and the effect is periodic, which are consistent with simulation results.In conclusion, based on the theoretical analyses of vibration suppression for the smart beam with hysteresis property, the control performance of the smart cantilevered beam with the Minimum Variance Self-Tuning Direct Regulator is improved with a small enough time delay.