RESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL. Yaoqi FENG 1, Hanping QIU 1. China Academy of Space Technology (CAST)

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1 ICSV4 Carns Australa 9- July, 007 RESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL Yaoq FENG, Hanpng QIU Dynamc Test Laboratory, BISEE Chna Academy of Space Technology (CAST) Abstract Ths paper analyses and sums up the exstng problems whch occur n dual-shaker sne vbraton testng of large spacecraft structures by usng the vbraton level controller and the phase controller to control separately the level and phase of two shakers. From ths bass, a new method whch conssts of controllng smultaneously the vbraton level and phase of two shakers s proposed for dual-shaker sne vbraton control. In the paper, the technques used to generate the two drvng sgnals, to acqure and process the response data and phase sgnal, and to control the vbraton level and phase of two shakers are descrbed n detals. Fnally, the paper presents brefly the test results obtaned by usng the new control method to carry out the sne vbraton testng by means of two small shakers, and the test results obtaned llustrate that the proposed method can be used for dual-shaker sne vbraton testng.. INTRODUCTION The vbraton testng of large spacecraft structures has the followng characterstcs: The mass and the sze of the structure are bg, and the centre of gravty s hgh. The structure s very complex, and the modal densty of the structure s very hgh. The test needs to smulate the dynamc nterface condtons for the ant-resonance of the launch vehcle from the spacecraft. The vbraton test system conssts of generally two or more than two synchronous exctaton shakers. Therefore, the test condton s very complex, and t makes the dual-shaker vbraton test control very dffcult []. The sne sweep vbraton test s one of the mportant test tems of spacecraft envronment test. For the tme beng, the dual-shaker vbraton test system, whch conssts of two 0-ton electrc shakers, s used to carry out the large-scale spacecraft s vbraton test n CAST. The accurate

2 ICSV4 9- July 007 Carns Australa vbraton control s always a dffcult ssue n dual-shaker sne vbraton testng for large spacecraft structures. Therefore, t s very mportant to do the research on dual-shaker sne vbraton control n order to meet the requrement of the spacecraft dynamc test and to mprove the test performance.. DESCRIPTION OF EXISTING DUAL-SHAKER CONTROL METHOD. Prncple of Dual-Shaker Control At present, the vbraton level controller and phase controller are used to control separately the level and phase of two shakers n the dual-shaker sne vbraton testng. The prncple of synchronous control conssts of two separate control loop as seen n Fg.. Fgure. The prncple of the dual-shaker s two-closed loop control of ampltude & phase The outsde loop manly controls the vbraton level of two shakers. Normally, the mult-pont average control technque s adopted durng the test. The vbraton level controller calculates the control error n real tme accordng to the dfference between the current response spectrum and the test reference spectrum, and t updates contnuously the drve spectrum to make the response of the control ponts correspond to the test reference. The nsde loop manly controls the vbraton phase of two shakers. In order to make the dual shakers vbrate synchronously, the phase controller adjusts the phase of the two drvng sgnals accordng to the two voltage sgnals, whch are provded by the Hall Effect Sensor and proportonal to the drvng current of two shakers.. Problems of Exstng Dual-Shaker Control Method In the exstng dual-shaker vbraton control system, t s requred that the control speed of the vbraton controller and the phase controller should be matched. The dependence of the control speed of two controllers results n that t s dffcult to update one of them. In consequence, the problem of matchng the two controllers should be resolved n the dual-shaker synchronous control.

3 ICSV4 9- July 007 Carns Australa In addton, there are two control loops durng the vbraton testng, and n both closed loops, the real tme data acquston and processng of feedback sgnal should be carred out, whch makes the system use more tme to fnsh the task of each control cycle. So, the feedback control speed of system s reduced n some degree, and the control precson of vbraton test s affected. 3. NEW IDEA FOR DUAL-SHAKER SYNCHRONOUS CONTROL Based on the analyss of exstng problems descrbed above n two closed loops vbraton control system, a new dea for dual-shaker vbraton test control s proposed. The prncple of new control method s shown n Fg.. Fgure. The prncple of new synchronous control method for dual-shaker vbraton test Compared wth the exstng dual-shaker control system, the new method proposes to control smultaneously the vbraton level and phase of two shakers n one closed loop. That means the new vbraton controller acqures and process not only mult-pont response sgnals, but also two feedback drvng sgnals whch pass through the power amplfer. The ampltude and phase of two drvng sgnals are drectly controlled by the new controller accordng to the response level and the phase dfference of the two feedback drvng sgnals n order to meet the requrement of synchronous control of dual-shaker sne vbraton testng. 4. REALIZATION TECHNIQUES OF NEW CONTROL METHOD The realzaton technques of the new control method for dual shaker sne vbraton testng consst of generatng the two phased drvng sgnals, acqurng and processng the feedback vbraton response sgnal and drvng phase sgnal, and updatng the vbraton level and phase of two shakers. 4. Generaton of Two Phased Drvng Sgnals The new synchronous control method needs to generate two phased sne drvng sgnals. The generaton of the two drvng sgnals s based on the three factors of sne sgnal: frequency, ampltude, and phase. 3

4 ICSV4 9- July 007 Carns Australa Supposng that the frequency and ampltude of the two drvng sgnals are f and ( f ) phase of the two drvng sgnals are ϕ and D k +, the ϕ respectvely, and the converson frequency of dgtal data to analogue sgnal s F s, then the length of sne dgtal data sequence N 0 for one perod can be calculated as followng: Once 0 N = F / 0 s f () N s determned, the value of sne sequence x ( n) and ( n) x are gven by: πn x( n) = Dk + ( f ) sn + ϕ () N πn x( n) = Dk + ( f ) sn + ϕ (3) N Where n=0,, N- N = [ N 0 ] +. The sne dgtal data sequence obtaned by formula () and (3) are loaded nto DA converter buffer n cyclc order, and then wth frequency Fs, the DA converts successvely the dgtal data nto analogue sgnals and generates two contnuous sne drvng sgnals whch are smoothed by the low-pass flter before outputtng to the power amplfer. 4. Acquston & Processng of Response and Phase Sgnals For new control method of dual shaker sne vbraton testng, the feedback sgnal acquston & processng nclude multple control pont response sgnals and two drvng sgnals whch contan the phase nformaton. 4.. Phase Calculaton of Two Feedback Drvng Sgnal For the sne sweep frequency f, the phase of two feedback drvng sgnals can be estmated by trackng flter method. At frst, the coherent functons wth sn( πf n t) and cos ( πf n t) of drvng sgnals should be calculated. R R I R N = N ( 0) d cos( πf n t) n= N = N ( 0) d sn( πf n t) n= n n (4) (5) Where d n s the nth sample value of drvng sgnal dgtal sequence. N s the number of samples n dgtal sequence of calculaton duraton. The ampltude and phase of two drvng sgnals can then be calculated as followng: [ R ( ) R ( 0) ] / D = + (6) R 0 I 4

5 ICSV4 9- July 007 Carns Australa ( 0) ( ) 0 RI ϕ = arctg (7) RR 4.. Ampltude Calculaton of Multple Response Sgnals For the ampltude calculaton of multple response sgnal, besdes the trackng flter method descrbed above for the phase calculaton of drvng sgnals, three other methods can also be used to obtan the ampltude of the mult-pont response sgnals. Peak-value method: A max( ) = = (,,... N), a s the sample value p a = N avg a N = Mean value method: A = ( ) π = (,,... N) = N RMS a N = RMS value method: A = ( ) 4.3 Vbraton Level and Phase Control = (,,... N) For the new control method, the control process should complete two tasks: one task s the ampltude updatng of the drvng sgnals, and the other s the phase correcton of the two drvng sgnals. If the ampltude of the two drvng sgnals s D k ( f ) under the exctng frequency f, the phase of two drvng sgnals are 0 and ϕ respectvely (the drvng sgnal whose phase s zero s the reference sgnal). Then the two drvng sgnals can be expressed as follows: x () t D ( f ) sn( πf t) x = k (8) () t = D ( f ) sn( π f t + ϕ ) k (9) Durng the test, the phases of the two feedback drvng sgnals are calculated n real tme: y y () t = D ( f ) sn( π f t + ϕ ) ' k (0) ' () t = D ( f ) sn( π f t + ϕ ) k () Then the phase dfference between the two drvng sgnals can be obtaned by: ϕ = () ' ' ϕ ϕ The ampltude of two drvng sgnals can be updated accordng to the system s transfer functon H ( f ) and the mult-pont control response error E k ( f ). Due to the system s non-lnearty and the nfluence of other errors, the ampltude of drvng sgnal s updated durng the test as follows [] : 5

6 ICSV4 9- July 007 Carns Australa D k + ( f ) = D ( f ) + H ( f ) E ( f ) α ( 0 α ) (3) k Where α s the level correcton coeffcent, t should be carefully chosen because t s drectly related to the control precson and the control stablty of vbraton level. After the updated ampltude and phase of the two drvng sgnals are obtaned, the two drvng sgnals for next sne exctaton frequency can be calculated by: x x () t D ( f ) ( f t) ' k + sn + k = π (4) () t D ( f ) sn( πf t + ϕ + γ ϕ) k ( 0 γ ) (5) ' = + + Whereγ s the phase correcton coeffcent, t s drectly related to the synchronous control of two shakers. Durng the dual-shaker sne vbraton testng, by means of the method descrbed above, the ampltude and the phase of two drvng sgnals are corrected and updated n real tme. In consequence, the synchronous control of dual-shaker sne vbraton testng s realzed. 5. VALIDATION TEST OF NEW CONTROL METHOD 5. Valdaton Test System To valdate the new control method, a vbraton test system wth two small shakers s establshed. Fgure 3 s the schematc dagram of valdaton test system. The two small shakers and power amplfer used n valdaton test system are shown n Fgure 4. Fgure 3. The schematc dagram of valdaton test system 6

7 ICSV4 9- July 007 Carns Australa Fgure 4. Two small shakers and power amplfer 5. Valdaton Test 5.. Test Reference Table. Reference spectrum Frequency (Hz) Level (g) Tolerance (db) ± ± ±6 Sweep Rate (oct/mn) 5.. Test Curves Fgure 5. Level control curve (non-phase control) Fgure 6. Phase dfference (non-phase control) 7

8 ICSV4 9- July 007 Carns Australa Fgure 7. Level control curve (wth phase control) Fgure 8. Phase dfference (wth phase control) 5..3 Analyss of the Test Results Fgure 5 and Fgure 6 show respectvely the vbraton level control curve and the vbraton phase dfference curve of the two shakers obtaned n non-phase control test. The maxmum vbraton phase dfference of two shakers durng the sne sweep test reaches 4º n ths case. Fgure 7 and Fgure 8 show respectvely the vbraton level control curve and the vbraton phase dfference of the two shakers obtaned wth the phase control test. In ths case, the maxmum vbraton phase dfference of two shakers durng the test s reduced to 6.4º. The valdaton test results llustrate that the new control method s able not only to control the vbraton level, but also to compensate the phase dfference of two shakers. So, ths control method can meet the requrement of synchronous control of dual-shaker sne vbraton testng. 6. CONCLUSION The control method proposed n ths paper can realze synchronous control of dual-shaker sne vbraton testng. The applcaton of ths method to the vbraton envronment test of large spacecraft structures can resolve the matchng problem of the vbraton level controller and the phase controller n dual-shaker sne vbraton testng, and can also mprove the control precson of dual-shaker sne vbraton testng. REFERENCES [] S. Q. Ke, et al., Satellte envronment engneerng and smulaton test, (Vol.), Bejng, Space Press, 996. [] T. Keller, M. Underwood. AN APPLICATION OF MIMO TECHNIQUES TO SATELLITE TESTING In: Artcles of MIMO Vbraton Control Technques Applcaton-Theory and Practce. [3] G. A. Hamma etc. A Revew of Multaxs/Multexctater Vbraton Technology. SOUND AND VIBRATION/APRIL

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