Research On Active Vibration Control Of Cantilever Beam Base On Piezoelectric Self-Sensing Actuator

The active vibration control is high-tech in the area of vibration engineering, for its remarkable advantages, it is becoming an effective mean to solve the vibration control problems of the aerospace and other fields. For its light and swift response, piezoelectric material occupies an important position of vibration engineering. In the areas and measurement and control technology of mechanical and electrical systems, actuator and sensors are both needed when implementing measurement and control generally.A transducer device, when it has two functions as a sensor and an actuator can be termed as self-sensing actuator(SSA).Self-sensing actuator has advantage in implementing the same bit configuration of between sensor and actuator, improving the stability of control,reducing the size and quality of system.It has a broad application prospects in active vibration control of structure,demage diagnosis,system identification and MEMS.In the dissertation, we analyse the implementation principles of the space-sharing piezoelectric self-sensing actuator at first, and then make the modal analysis of cantilever beam with ANSYS software. At the basis of these theories, we set up mathematical model of piezoelectric Self-Sensing Cantilever beam, finds the way of control with the theory of quadratic optimal control and controls the first stage of vibration of cantilever beam by means of inputting the energy into the system with the implementation electrode of piezoelectric Self-Sensing Actuator, proposes space-sharing decoupling approach, sets up active vibration control system of cantilever beam based on the piezoelectric Self-Sensing Actuator. The main contents of this dissertation are as follows:1. Raised and implementation principles of the space-sharing piezoelectric self-sensing actuatorBased on the electric bridge method is very difficult in regulating to balance and is necessary to regulate repeatedly, and observe method exists model deviation, which also requires standard sensor to demarcate the deficiencies of secondary deviation, this paper carries out a systematic study to space-sharing approach proposed, and applies in research of active vibration control of cantilever beam. The main implementation principles is based on bilateral transducer theory, the entire electrode of a surface of piezoelectric ceramic is divided into two zones, the first zone for implementation area, the second zone for sensing area, the entire electrode of the other side as to topographic electrode, in this way, energy conversion which is carried out simultaneously in both directions of forward and inverse on a transducer materials are equal to carrying out independently, as a result, the piezoelectric self-sensing is implemented.2. Vibration modal analysis of piezoelectric self-sensing cantilever beamExperimental subjects of this paper is cantilever beam structure, which is a more basic structure, with the horizontal bending vibration, in the dissertation, basing on the basic theory of cantilever beam vibration, differential equations of the cantilever beam horizontal vibration is deduced, and natural frequencies and vibration mode function of the beam is obtained.Make an analysis on optimal allocation of the pasting location of piezoelectric element and an experiment studies on the impact of the structure natural frequencies which is cansed by different pasting location of piezoelectric element,and then identify the optimal distribution of piezoelectric element.Set up a finite element model of cantilever beam using of ANSYS software, and then make its modal analysis, obtained the first three natural frequency and inherent vibration of the piezoelectric self-sensing cantilever beam.3. Set up of the mathematical model of piezoelectric self-sensing cantilever beamThe first step of active vibration control system design is setting up the mathematical model of the system, this paper has set up a dynamic model of cantilever beam vibration, structure system equations of Space-sharing piezoelectric self-sensing actuator and state space dynamic equation of the piezoelectric cantilever beam, identify mass matrix stiffness matrix and damping matrix of the piezoelectric self-sensing cantilever beam. Set up the finite element equation of the piezoelectric self-sensing cantilever beam and obtaine the motion equation of the piezoelectric self-sensing cantilever beam.4. The design of active vibration control rule based on piezoelectric self-sensing actuatorAfter the system model is set up we can make a design of control rule according to the request of system.In this paper, at first,we make an analysis on active vibration control theory of piezoelectric self-sensing actuator and a disturbance control using contingency velocity feedback, the vibration speed of piezoelectric self-sensing cantilever which is disturbed is perceived out by self-sensing actuator,and then based on the optimization control we make use of linear quadratic control algorithm in this paper. Introduce the characteristic of linear quadratic and the describing way of aim function and the engineering meaning of each index in the capability index. On the base of it, it introduces infinite time condition regulator status, gives expression of aim function and solution of the optimization control, makes a design of vibration control rule of cantilever beam, get the quadratic optimization control and deduce the expression of it.5. The design of the main program of control system and the signal generator control proceduresThe relationship between input voltage of piezoelectric actuator and tip displacement is linear relationship which is measured by experiment, tip control force and tip displacement also showed a linear relationship,so input voltage of piezoelectric actuator and equivalent tip control force have a linear relationship,and identified the relationship between the two. We introduce the main design steps and the main compiler process of the main program, on the base of it, we design the control system main program and signal generator control procedures and theirs control panel with LabVIEW, implementation of the control rule in the form of software.6. The experiment research of active vibration control of piezoelectric self-sensing cantilever beamWe build up the active vibration control system of cantilever beam based on space-sharing approach piezoelectric self-sensing actuator. With the control system, we control the freedom vibration of cantilever beam which is disturbed by an initial disturbance, and get the displacement respond curves with and without control which is measured by laser micrometer and piezoelectric self-sensing actuator respectively.Through the experimental situation confirmed that the sensors and actuators integrated in a PZT have two functions which are piezoelectric sensor and implementation. In the optimal control rule, the coefficientρin the weighting matrix Q choose different values have an impact to control effect though experimental research, when the weighting matrix R=1, different values ofρcorresponding to different decay time and damping ratio.Takeρ=0.1 for example, comparing the ratio of damp and the attenuation time under the condition of control and uncontrol.Ratio of damp increase to 8.9 multiple and attenuation time is reducted to 30.8% of uncontrol condition,getting the back of equilibrium position in 2.4 senconds of the system, reducing the vibration attenuation time at a certain extent,proving that the effective of the active control system designed in this paper to vibration suppression.