An adaptive random control method is presented for a two-axis redundantly actuated electro-hydraulic shaking table system to replicate the reference acceleration power spectral density (PSD). The redundant force controller is developed to reduce the cross-coupling among the actuators. The offline iterations are implemented in conventional random control to compensate for the changes in the frequency response function of the system. Stability and responsiveness of control are determined by operator-selected parameters. In adaptive random control, the reference PSD is transformed into time domain histories by filtering white noise. The adaptive finite impulse response (FIR) filters are used to model and track the inverse system online. The weights of the FIR filters are updated by the forgetting factor recursive least-squares algorithm. The time histories are corrected by the copy of the inverse model. Experimental results obtained in step response and PSD replication demonstrate the effectiveness of the proposed control method.
ChengHYiuYKLiZ (2003) Dynamics and control of redundantly actuated parallel manipulators. IEEE/ASME Transactions on Mechatronics8(4): 483–491.
2.
Clark AJ (1992) Dynamic characteristics of large multiple degree of freedom shaking tables. In: Proceedings of Earthquake Engineering, 10th World Conference, Rotterdam, The Netherlands, July 19–24, pp. 2823–2828.
Dodds CJ and Plummer AR (2001) Laboratory road simulation for full vehicle testing: a review. In: Proceedings of Symposium on International Automotive Technology. University of Bath, UK, 1 January, pp. 487–494.
5.
GuanGFWangHTXiongW (2014a) Random vibration control of a hydraulic shaking table. Journal of Vibration and Control20(2): 204–217.
6.
Guan GF, Wang HT and Xiong W (2014b) Multi-input multi-output random vibration control of a multi-axis electro-hydraulic shaking table. Journal of Vibration and Control. Epub ahead of print 19 February. DOI: 10.1177/1077546314521444.
7.
Guan GF, Xiong W and Wang HT (2010) Random vibration control based on adaptive filter. In: 2010 IEEE International Conference on Mechatronics and Automation. Xi’an, China, August 4–7, pp. 1825–1830.
8.
HarrisCMPiersolAG (2001) Harris’ Shock and Vibration Handbook, 5th edn. New York: McGraw-Hill Inc.
9.
HaykinS (2002) Adaptive Filter Theory, 4th edn. New Jersey: Prentice Hall, Inc.
10.
He JF (2007) Analysis and control of hydraulically driven 6-DOF parallel manipulator. Phd thesis, Harbin Institute of Technology, China.
11.
HeJFJiangHZCongDC (2007) A survey on control of parallel manipulator. Key Engineering Materials339: 307–313.
12.
IEC-60068-2-64 (2008) Environmental testing – Part 2–64: Tests- Test Fh: Vibration, broadband random and guidance, Geneva, Switzerland: International Electrotechnical Commission.
13.
JiangHZHeJFTongZZ (2012) Modal space control for a hydraulically driven Stewart platform. Journal of Control Engineering and Technology2(3): 106–115.
14.
KarshenasAMDunniganMWWilliamsBW (2000) Adaptive inverse control algorithm for shock testing. IEE Proceedings on Control Theory and Applications147(3): 267–276.
15.
Koekebakker SH (2001) Model based control of a flight simulator motion system. Phd thesis, Delft University of Technology, Netherlands.
16.
Kusner DA, Rood JD and Burton GW (1992) Signal reproduction fidelity of servo hydraulic testing equipment. In: Proceedings of Earthquake Engineering, 10th World Conference, Rotterdam, the Netherlands, July 19–24, pp. 2683–2688.
17.
LjungL (1998) System Identification: Theory for the User, 2nd edn. Boston: Birkhäuser.
18.
LucoJEOzcelikOConteJP (2010) Acceleration tracking performance of the UCSD-NEES shake table. Journal of Structural Engineering136(5): 481–490.
19.
Ma O and Angeles J (1991) Architecture singularities of platform manipulators. In: Proceedings of IEEE International Conference on Robotics and Automation, Sacramento, CA, USA, pp. 1542–1547.
20.
MarkiewiczPUhlT (2013) MIMO random control method for vibration testing. Diagnostyka14(2): 3–10.
OppenheimAVSchaferRW (1998) Discrete-time Digital Signal Processing, 2nd edn. New Jersey: Prentice Hall, Inc.
23.
Peeters B and Debille J (2001) MIMO random vibration control algorithm and simulations. In: Proceedings of the 72nd Shock and Vibration Symposium, San Destin, FL, November, pp. 1–11.
24.
Peeters B and Debille J (2003) Multi-axial random vibration testing: a 6 degrees-of-freedom test case. In: Proceedings of the 21st Aerospace Testing Seminar, Manhattan Beach, CA, pp. 47–62.
25.
Plummer AR (2007a) Control techniques for structural testing: a review. In: Proceedings of IMechE, Part I: Journal of Systems and Control Engineering, vol. 221, pp. 139–169.
26.
Plummer AR (2007b) Motion control for overconstrained parallel servohydraulic mechanisms. In: The 10th Scandinavian International Conference on Fluid Power, Tampere, Finland, May 21–23, pp. 1–13.
27.
PlummerAR (2007c) A general co-ordinate transformation framework for multi-axis motion control with applications in the testing industry. Control Engineering Practice18(6): 598–607.
28.
ShenGZhengSTYeZM (2011) Adaptive inverse control of time waveform replication for electrohydraulic shaking table. Journal of Vibration and Control17(11): 1611–1633.
29.
ShiakolasPSPiyabongkarnD (2003) Development of a real-time digital control system with a hardware-in-the-loop magnetic levitation device for reinforcement of controls education. IEEE Transactions on Education46(1): 79–87.
30.
Smallwood DO (1982) Random vibration testing of a single test item with a multiple input control system. In: Proceedings of the Institute of Environmental Sciences’ 28th Annual Technical Meeting, Dallas, TX, April 21–23, pp. 55–61.
31.
Smallwood DO (1999) Multiple shaker random vibration control – an update. In: Proceedings of the Institute of Environmental Sciences’ 28th Annual Technical Meeting, Sandia National Laboratories, Livermore, CA, US, 18 February 1999, pp. 212–221.
32.
SmallwoodDO (2013) Minimum input trace for multiple input multiple output linear systems. Journal of the Institute of Environmental Sciences and Technology (IEST)56(2): 57–67.
33.
SmallwoodDOPaezTL (1993) A frequency domain method for the generation of partially coherent normal stationary time domain signals. Shock and Vibration1(1): 45–53.
34.
Soderling S, Sharp M and Leser C (1999) Servo controller compensation methods selection of the correct technique for test applications. SAE Technical Paper 1999-01-3000.
35.
Spectral Dynamics Inc. (2003) Jaguar systems on-line operating manuals, San Jose, CA (US).
36.
Stoten DP and Shimizu N (2007) The feedforward minimal control synthesis algorithm and its application to the control of shaking-tables. In: Proceedings of IMechE Part I: Journal of Systems and Control Engineering, vol. 221, pp. 423–444.
37.
StroudRCHammaGA (1988) Multiexciter and multiaxis vibration exciter control systems. Sound and Vibration22(4): 18–28.
38.
StroudRCHammaGAUnderwoodMA (1996) A review of multiaxis/multiexciter vibration technology. Sound and Vibration30(4): 20–27.
39.
Tagawa Y and Kajiwara K (2007) Controller development for the E-Defense shaking table. In: Proceedings of IMechE, Part I: Journal of Systems and Control Engineering, vol. 221, pp. 171–181.
UnderwoodMAKellerT (2004) Rectangular control of multi-shaker systems: theory and some practical results. Journal of the Institute of Environmental Sciences and Technology (IEST)47.1: 80–86.
42.
UnderwoodMAKellerT (2006) Applying coordinate transformations to multi degree of freedom shaker control. Sound and Vibration40(1): 14–27.
43.
United States Department of Defense (2008) Department of Defense test method standard for environmental engineering considerations and laboratory tests, MIL-STD-810G. Method 514 & 527. Available at: http://www.everyspec.com/MIL-STD/MIL-STD-0800-0899/MIL-STD-810G_12306 (accessed: 11 April 2012).
44.
WidrowBWalachE (2008) Adaptive Inverse Control – A Signal Processing Approach, Reissue edition. New Jersey: John Wiley & Sons, Inc.
