Active control based on finite element analysis. Li Hongying

Transcription

1 5th International Conference on ucation, Management, Information an Meicine (MIM 5) Active control base on finite element analysis Li Hongying Automotive ngineering institute, Jiangxi University of Technology, Nanchang 98, China Keywors: Intelligent structure; Active control; Finite element analysis; Simulation Abstract. With the evelopment of inustry an avance technology, vibration environment is becoming more an more complex. The traitional structural ynamics esign is har to meet the high reliability of the structure, so it s inevitable to seek new ways of vibration control. Active vibration control is the avance technology in the current vibration engineering fiel, an is the integration of many subjects, such as ynamics, control, computer, testing technology an materials science, etc. This paper aopts finite element metho commonly use in engineering for the analysis on plate structure moeling, an numerical simulation stuy on the active vibration control. Finally, calculation examples of the plate verify the effectiveness of previous work. Brief introuction With the evelopment of inustry an avance technology, the scale of structure is becoming larger, an vibration environment is becoming more an more complex. The traitional structural ynamics esign is har to be applie. Structural vibration control has become one of the major topics of moern engineering technology, the intelligent control on suppression of structure eformation an isturbance has been highly value in the engineering circle an theoretical circle. Base on the nee of external energy, structural vibration control methos are ivie into three categories: passive control, active control an integrate passive an active control (also calle hybri control). assive control is mainly the way that requires no external energy through aing amping materials into the structure, which is calle amping processing. When the structure vibrates, strain of amping layer will transform the vibration energy into strain energy that can be issipate as heat so as to restrain vibration, which is an effective way to solve the structural vibration control. The shortcoming of this metho is limite amping effect to low frequency vibration, weak strain capacity to abrupt environment, an ifficult to aapt to the complex an changing mechanical environment. Active vibration control of structure is to reuce the response of the structure uner environmental loa by the use of external energy for control force, which is consiere to be an effective metho. In recent years, with the rapi evelopment of material science, control, microelectronics an computer technology, especially the breakthrough of the stuy on new sensors an actuators, the new sensing materials an actuation materials are constantly applie to replace traitional sensors an actuators in the active vibration control of structure, which promotes the evelopment of the new technology in structure esign, an generates the bran new intelligent structure. The finite element metho is wiely use in engineering practice at present; the existing mature application software, such as ATRAN/NASTRAN an ANSYS are easy for use an promotion. The finite element moeling an structural response analysis are simple an convenient by making use of existing software, an are free from the self-ivision of finite element an writing teious 5. The authors - ublishe by Atlantis ress 4

2 programs; base on large an common structural finite element analysis software, integrate structure esign, optimization, structure analysis an control esign with simulation, complete in the same environment once for all, an truly realize the integration of structural control. This paper aopts finite element metho commonly use in engineering for the analysis on plate structure moeling, an numerical simulation stuy on the active vibration control. Finally, calculation examples of the plate verify the effectiveness of previous work. Simulation stuy on vibration control The traitional esign metho of structural vibration control has always been to follow the flow shown in chart, in which the esign requirements of controller have a certain mathematical moel; the certain mathematical moel is very effective to simple structure; in the process of moeling for complex structure, simplifie treatment of ignoring a few minor factors such as consiering no higher orer moes effect, reucing orer, nonlinear link linearization an steay time varying parameters, an finally get the mathematical moel suitable for control system esign. The moel is only an approximation of actual system, an ifferent from previous moel. However, the cost will increase through experimental metho for structural vibration control, which apparently oes not conform to the integrate esign thought for moern structural control. Structure Mathematical Simplification Control moel esign Figure. Traitional control flow chart With the evelopment of finite element technology, the above problems have been improve a lot. Structural vibration control esign technology base on finite element metho irectly esigns for finite element moel of structure rather than simplifie mathematical moel, as shown in chart. The basic iea is to make use of the finite element structure analysis technology, conuct control simulation experiments with finite element moels replacing real object, etermine control methos an optimize control parameters. The specific metho is: firstly, buil structural finite element moel an loa conitions; seconly, make structural ynamic response analysis, output feeback signal from analysis results an apply control signal through certain control algorithm in the structure; thirly, analyze structural response, calculate an apply control signal; repeat the above process until the terminal conitions are satisfie. The whole process is just like the signal sensor, acquisition, processing, an actuator in the control experiment except that the actual response of the structure is replace by finite element ynamic response analysis. Structure Finite element moel Control esign Figure. Finite element controls 44

3 Finite element moeling As plate structure is a kin of simple an common structure, its moeling stuy is comparatively typical. Laminate piezoelectric plate is three-layer structure, with both linear elastic materials an nonlinear materials, so its finite element moeling an moal analysis are the key technologies. Generally, there are four kins of piezoelectric formula for linear piezoelectric materials accoring to the ifferent inepenent variables, of which the first an secon formula are mostly use. The first kin of piezoelectric equation expression is as follows, in which the inepenent variables are staning for stress, an staning for electric fiel intensity. {D}=[]{ }+[ ]{} () { }=[S t ]{ }+[ ] {} () In the first kin formula, [] is piezoelectric strain constant matrix; {D} is electric isplacement vector; [ ] is ielectric constant matrix when stress is zero or constant; { } is strain vector; [S ] is flexible flexibility constant matrix when electric fiel intensity is zero or constant. The secon kin of piezoelectric equation expression is as follows, in which the inepenent variables areεstaning for strain, an staning for electric fiel intensity. {D}=[e]{ }+ [ ]{} () { }=[C ]{ }-[e] T {} (4) In the secon kin formula, [e] is piezoelectric stress constant matrix; [ ] is ielectric constant matrix when strain is zero or constant; [C] is flexible stiffness constant matrix when electric fiel intensity is zero or constant. In the above two kin of piezoelectric formula, piezoelectric constant an flexible constant have the following relation: [e]=[][c ] (5) For composite piezoelectric materials, the formula (-) an (-) can be expresse as: D D D 5 4 (6) 45

4 G G G 5 4 (7) In the above formula,,, an are the elasticity moulus for piezoelectric moulus, is the shear moulus of Athens material are G, G an G. (8) Since the avent of finite element technology in the 7s, many mechanical problems that is not solve or completely solve can be solve with the technology. Finite element technology has been eveloping so well for nearly years that there seems to be no mechanical problems that can t be solve by finite element. Suitable finite element moel shall be establishe for laminate plate unit analysis, an comparative analysis on the same issue aopting ifferent unit when necessary. The weakness of this metho is that the moeling of complex structure is very ifficult, an the more accurate the moel, the more egrees of freeom; the common workstations are har to bear the resources consumption of the machine. For the simple structure of plate, all kins of finite element programs such as Cosmosm, Nastran, Aina an Ansys can easily solve varie finite element analysis. The ynamics equations of system can be written in general form: [M]{u}+[C]{u}+[K]{u}={F} (9) Cantilever (mm*5mm*mm), top an bottom surface with iezoelectric Transucer (ZT) are sensors an actuators, as shown in chart. The material constant of beam: 7.5* N / m elasticity moulus p, oisson ratio k., mass ensity 7kg/ m, supposing the moel of ZT sensors an actuators is the same as the one for physical experiment, the thickness h=mm, mass ensity 6kg/ m 6.* N / m, elasticity moulus p, k. 46

5 Figure. Geometric moel Apply pulse with N, an action time. secon on the point A of beam-en; the total mass matrix an stiffness matrix of the beam can be calculate by NASTRAN analysis. Lea the total mass matrix an stiffness matrix into MATLAB, an make simulating calculation in SIMULINK. Conclusion Vibration control experimental evices aopt xc target real-time system base on MATLAB; the composition of control system is shown in chart 5-, which mainly inclues sensor, preamplifier, A/D converter, computer, D/A converter, riving power an actuators. Overall physical evices shown in chart 5-, inclues sets of C computer, piece of A/D ata collection car of 8-channel CL-88L(integrate D/A conversion car), set of power amplifier of 79 series AVC ((piezoelectric power supply), set of sensing signal regulator of the CI-48A moel. xc target can be operate on one or two machines. For convenience of ebugging program, the experimental evices in the paper aopt the moe of operating on two machines, namely host machine an target machine. In xc target environment, the C installe the software MATLAB, Simulink an Stateflow is the host machine; establish moel with Simulink moel an Stateflow chart an make non real-time simulation. Then make use of coe generator like RTW an Stateflow an the C compiler for generating executable coe an run it on the secon compatible C in real time. When the control system is in real-time control, only the target machine as controller sens control orer; the host machine generates executable coes for the convenience of ebugging program, an ownloas it into the target machine. Base on the research of the piezoelectric plate unit, establish initiative structure moel using commercial finite element software ATRAN/NASTRAN, buil finite element moeling for structure an make varie ynamics analyses. The moeling metho is effective accoring to the results in the paper. On the premise of meeting the engineering accuracy, transform the coorinate of ynamic equation, aopt low orer moe as vector base, truncate an ecouple the high orer moe. Stuy proportional feeback control metho accoring to ecoupling equation an the results of finite element software analysis; base on LQR (quaratic linear optimal control) inepenent moal control metho, etermine the gain of active structural control an control the vibration of the structure. In orer to verify the valiity of the above vibration control metho, combine with a numerical example an experiment, etermine the response of the active structure control before an after an make the curve. Accoring to the simulation results an experimental results, the active control aopting piezoelectric structure is effective to the structural vibration suppression. The paper makes moal analysis on the active structure, an carries numerical simulation an experiment on active vibration suppression. 47

6 Acknowlegements This work was financially supporte by the key subject builing project (vehicle engineering) of Jiangxi University of Technology. Reference []Vlasov Y A, O'Boyle M, Hamann H F, et al. Active control of slow light on a chip with photonic crystal waveguies[j]. Nature, 5, 48(764): []Fuller C C, lliott S, Nelson A. Active control of vibration[m]. Acaemic ress, 996. []Hanforth A, DeGiorgio C M, Schachter S C, et al. Vagus nerve stimulation therapy for partial-onset seizures A ranomize active-control trial[j]. Neurology, 998, 5(): [4]Balas M J. Active control of flexible systems[j]. Journal of Optimization theory an Applications, 978, 5(): [5]Bauer M S, Mitchner L. What is a moo stabilizer? An evience-base response[j]. 4. [6]Li, Lam J, Cheung K C. Multi-objective control for active vehicle suspension with wheelbase preview[j]. Journal of Soun an Vibration, 4, (): [7]Yılız A S, Sivrioğlu S, Zergeroğlu, et al. Nonlinear aaptive control of semi-active MR amper suspension with uncertainties in moel parameters[j]. Nonlinear Dynamics, 4: -4. [8]Kopperahl D L, Aspelun T, Hoffmann F, et al. Assessment of incient spine an hip fractures in women an men using finite element analysis of CT scans[j]. Journal of Bone an Mineral Research, 4, 9(): [9]Karimi A, Navibakhsh M, Razaghi R. Dynamic simulation an finite element analysis of the human manible injury protecte by polyvinyl alcohol sponge[j]. Materials Science an ngineering: C, 4, 4: [] Benazzi S, Grosse I R, Gruppioni G, et al. Comparison of occlusal loaing conitions in a lower secon premolar using three-imensional finite element analysis[j]. Clinical oral investigations, 4, 8():