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MEL 417 Dr. Navin KumarVIBRATION SENSING Submitted by : Vivek DharniaAND CONTROL FOR A (P2009ME1089) Ajeet CANTILEVER BEAM (P2009ME1090) Lalit Aggrawal USING LABVIEW. (P2009ME1088)
` AcknowledgementWe express our sincere thanks to Dr. Navin Kumar to award us with a wonderfulopportunity to do a project on Experimental analysis of a cantilever beam and itsvibration control using Labview. Our project supervisors were instrumental in theprocess of bringing this project to its present form. Without their key support,knowledge and experience, procurement of set-up, our project and its analysiswould not have been possible.Executive SummaryWhenever a cantilever beam gets any impulse or experiences any net externalforce, it starts vibrating. In this project, the main objective is to control thevibrations of a cantilever beam. A cantilever beam made of mild steel is mountedat one end. It consists of a piezoelectric transducer and a piezoelectric actuatorplaced at the root of the cantilever beam. The Vibrations can be caused by varioussources including human activity and harmonic exciter. The piezoelectric sensorsare used to detect the vibrations. Simultaneously, feedback controller sendscorrection signal to the actuator to minimize the vibrations. A Proportionalderivative (PD) controller is used to control the vibrations. The controller as wellas the whole system is designed in Labview.
`Table of contents List of figures Introduction Experimental Set up Procedure Experimental Results Discussion Conclusions and Recommendation ReferenceList of figures Following are the figures of our setup of a cantilever beam and the PZT crystals attached to it. Figure-1 : Cantilever beam with PZT crystals mounted at top and bottom surface
`IntroductionActive vibration control is defined as a technique in which the vibration of astructure is reduced or controlled by applying counter force to the structure that isapproximately out of phase but equal in amplitude to the original vibration. As aresult two opposite forces cancel each other and dampen the vibration. Techniqueslike the use of spring, dampers and pads are known as passive vibrationscontrolled. These techniques were previously used but now a days, these havebecome obsolete as they are incompatible with modern machines. These are veryheavy, large and thus not suitable for controlling vibrations in new modern, smalland sophisticated machines. Moreover, these techniques could work for a verysmall range of vibrations.Active vibrations controller has more life expectancy. They use sensors, actuators,controllers, feedbacks for controlling the vibrations. Piezoelectric sensors operateusing the direct effect, i.e., electric charge is generated when a piezoelectricmaterial is stressed causing deformation. These sensors are extremely sensitive andhave superior signal to noise ratio. In this case, the sensor is bonded to the bottomsurface of the beam by means of soldering.Typical piezoelectric actuators operate using the converse effect of piezoelectricmaterials. Whenever a voltage is applied across its electrodes, a strain is induced inthe material. PZT is commonly used for actuation. PZT is ideal because of itsrespectable maximum actuation strain, reasonable cost, and high accessibility.They are bonded at the surface of the beam by soldering it.Experimental Set upTo identify the dynamics of the beam, the beam needs to be stimulated via theactuator. We give input signal (excitations) at the free end of the beam manually orusing a harmonic exciter. The impulse excites the beam and thus producesvibrations in the beam. These vibration signals are sensed by the sensor andgenerated, along with some noise, in Labview through the input port (ai0) of aData Acquisition system (DAQ). These signals are then passed on to a Proportional
`Derivative (PD) controller designed in Labview. The output of the controller isthen passed through the output port (ao0) of the Data Acquisition system (DAQ).The output signals are fed to the actuator which transforms the electrical signalsinto mechanical vibrations to the beam and corresponding out of phase vibrationswith equal magnitude will be produced to nullify the impact of the vibrationswhich was produced due to the excitations. The following figure shows the basicblock diagram implemented in Labview. Figure -4 : Block Diagram in Labview.
`Theory and Controller designIn the experiment, a beam (mild steel) was made and mounted it in a fixed placewith one end hanging. A piezoelectric transducer was placed at the fixed end. Thebeam is then connected with the Labview system. The impulse is given at the freeend of the beam to produce vibrations. These vibrations are imparted into thecomputer having Labview with the help of piezoelectric transducer. Thesevibrations are analysed in the Labview and controlled with the help of PIDcontroller by producing out of phase vibrations of equal magnitude.A proportional–integral–derivative controller (PID controller) is a control loopfeedback mechanism (controller) extensively used in control systems. It calculatesan "error" value as the difference between a measured process variable and adesired set point which is given as input initially. It attempts to minimize the errorby adjusting the process control inputs.The PID controller calculation involves three separate constant parameters: theproportional, the integral and derivative values, denoted by P, I, and D.Heuristically, these values can be interpreted in terms of time: P depends on thepresent error, I on the accumulation of past errors, and D is a prediction of futureerrors, based on current rate of change. The weighted sum of these three actions isused to adjust the process via a control element such as the position of a controlvalve, or the power supplied to a heating element.In the absence of knowledge of the underlying process, a PID controller hashistorically been considered to be the best controller. By tuning the threeparameters in the PID controller algorithm, the controller can provide controlaction designed for specific process requirements. The response of the controllercan be described in terms of the responsiveness of the controller to an error, thedegree to which the controller overshoots the set point and the degree of systemoscillation. Note that the use of the PID algorithm for control does not guaranteeoptimal control of the system or system stability.In our experiment PD was used because we don’t need the accumulation of thepast error which is represented by I.
`Experimental ResultsUsing the procedure described above, the controller was implemented on thesystem. The vibrations on the cantilever beam were successfully controlled withthe help of piezoelectric actuator and PD controller designed in the Labview.Though we were unable to actuate the cantilever beam because the output signalsproduced by the controller were too weak to produce mechanical vibrations andhence cannot be implemented without an amplifier, nevertheless we observed theoutput signals on Labview. Following figures show the input signal as well as theoutput signal out of the controller. Figure -5 : Input Signal
`Figure 6 : Input signal (Black wave) as well as output signal from controller(red wave)DiscussionThrough this project, we carried out vibration sensing of a cantilever beam anddesigned a controller to dampen the vibrations in Labview. Following observationscan be made during the analysis: The cantilever beam is an under damped system with a natural frequency of approximately 9 Hz. During controller design, the proportional gain was set to 1. Increasing the Proportional gain to more than 1 increase the amplitude of the output signal. During controller design, the derivative time Td was set to a value of 0.001.
`Conclusions and RecommendationA smart beam is constructed using mild steel, PZT sensor and a PZT actuator. Acontroller is designed in Labview and is used to control the vibrations of the beam.It can be concluded that a Proportional Derivative (PD) controller can be used tocontrol the vibrations and it further depends on the Proportional gain andderivative time of the controller. An out of phase vibrations are produced to nullifythe impact of the actual vibrations and depends on the gain, differential time of thePD controller. It is recommended that an amplifier is used with the actuator toamplify the output signals from the controller and is able to actuate the beam. Reference 1. K. B. Waghulde et al. /International Journal of Engineering and Technology Vol.2(4), 2010, 259-262. 2. Journal of Vibration and Control March 2012 vol. 18 no. 3 366-372. 3. http://www.kyu.edu.tw/93/epaperv6/93-033.pdf 4. Wikipedia – The free encyclopaedia.. 5. National Instruments (NI) manual. 6. Tutorials on Controller design by National Instruments (NI).