Cantilever beam robustness self-adaptation control method

Abstract

The invention discloses a cantilever beam robustness self-adaptation control method. An ideal cantilever beam dynamic model is designed and contains frequency signals rich enough to serve as a reference trajectory of a system, it is guaranteed that the actual cantilever beam trajectory can track the reference trajectory for the whole self-adaptation control system, an ideal dynamic property is realized, and compensation of manufacturing errors and environment disturbance is achieved. The parameters of a cantilever beam are taken as unknown system parameters, a parameter error vector theta is formed, a slip form function is designed, the derivative of the slip form function is made to be zero, an equivalent controller is obtained, a feedback term and a robustness term serve as an input signal on this basis, the self-adaptation rule of the parameter theta of the controller is designed based on the Lyapunov method, the stability of the system is guaranteed, tracking error is converged to zero, and all the parameters are converged to true values.

Description

technical field [0001] The invention relates to a robust adaptive control method for a cantilever beam. Background technique [0002] A cantilever beam means that one end of the beam is a fixed support that does not produce axial, vertical displacement and rotation, and the other end is a free end (which can generate forces parallel to and perpendicular to the axial direction). In the force analysis of engineering mechanics, it is a typical simplified model. In actual engineering analysis, most of the actual engineering stress components can be simplified as cantilever beams. [0003] In 1985, Bailey et al. attached a whole piece of piezoelectric film PVDF to the entire beam as an actuator, and conducted experimental research on the vibration control of the cantilever beam by using constant gain (CGC) and constant amplitude (CAC) feedback. In 1991, Lee et al. proposed a design method for piezoelectric modal sensors and piezoelectric modal drivers. This method designs the m...

AI Technical Summary

Problems solved by technology

[0004] However, for example, for the modeling of piezoelectric cantilever beams, the changes in the stiffness and quality of the beam structure caused by pasting piezoelectric materials or embedding piezoelectric materials are usually ignored, and due to the inevitable processing errors and environmental The influence of temperature will cause the difference between the characteristics of the original and the design, resulting in the uncertainty of the parameters of the cantilever beam, and it is difficult to establish an accurate mathematical model and other problems

In addition, the external disturbance in the working environment cannot be ignored, which makes the trajectory tracking control of the cantilever beam difficult to realize, and the robustness is low

The traditional control method is completely based on the design of the nominal value parameters of the cantilever beam, and ignores the effects of orthogonality error and external disturbance. Although the system is still stable in most cases, the tracking effect is far from ideal. This design for a single environment The controller has great limitations

The cantilever beam based on the traditional control method still has inconvenience and defects in use, and further improvement is urgently needed

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