Research On Multi-stage Optimal Arbitrary Time-delay Filter

The flexibility in the flexible manipulators, recoverable satellites, flexible aircraft wings, cranes and hard driver head locators will cause residual vibration when they moved and worked. This problem will degrade the control accuracy and control stability of system. So, vibration control of flexible system is a hot spot of research.Input shaping is a simple, effective method for suppressing the residual vibration of the flexible system.The physical properties and the vibration properties of system are considered in command shaping method, and the reference signal is reshaped so that the vibratory modes of the system are canceled, system oscillations are eliminated. Over the past two decades, there are many researchers have examined the command shaping method for reducing endpoint vibration and verified the effectiveness of the proposed algorithm.Firstly, this paper gives a brief overview of the development process and research status of the input shaping method. Based on the theory of input shaping technique, the design processes of the typical input shaper, such as Zero Vibration (ZV), Zero Vibration and Derivative(ZVD) and Extra-Insensitive(EI) shapers are given in detail. The essence of robust input shaper is shaping the reference inputs repeatedly,the price for greater robustness, however, is an increase in shaper duration. In order to characterize the input shaper’s sensitiveness to the modeling errors, parameter uncertainties and nonlinearities, the sensitive curve is plotted.Secondly, based on the principle of design of robust shaper, the Multi-stage Optimal Arbitrary Time-delay Filter (MOATF) is obtained by the convolution of two Optimal Arbitrary Time-delay Filters (OATF). The prominent advantage of this approach is that the value of time-delay is arbitrarily selected and regardless of the system parameters. The simulation of MOATF and ZVDD,MOATF and OATF with the different time-delay are researched. Simulation results prove its effectiveness and robustness.Finally, based on the principle of pole/zero cancellation, the algorithm called Adaptive Input Shaping(AIS) is proposed in the time domain. And the proposed method is implemented on the second-order harmonic oscillation system with parameter uncertainties. Simulation results show that AIS algorithm combines both advantages of adaptive control and input shaping, can effectively track changes in system parameters, adjusting the parameters of Adaptive Input Shaper in real-time and vibration suppression is effective.