An online multi-input multi-output (MIMO) random vibration control method is presented for a multi-axis hydraulic shaking table system to replicate the reference acceleration power spectral density (PSD) by the reproduction of the acceleration time domain histories that are proportional to the reference. The offline iterations are implemented using conventional random vibration control to compensate for the changes in the frequency response function (FRF) of the system. The successful test mainly depended on the experience of the operator. In online MIMO random vibration control, the reference PSD is transformed into time domain histories by filtering white noise. The impedance matrix of the shaking table system, which is the inverse of the FRF, is calculated and updated online. The time histories are compensated based on the system impedance matrix and then used as the drive signals to the shaking table. The overlap-save method and fast Fourier transformation are proposed to implement the transformation and compensation online. Two-axis random vibration experimental results obtained with the proposed control method show that both the reference PSD and the time domain histories can be replicated with high precision in the output of the shaking table without operator intervention.
Bart P and Jan D (2001) MIMO random vibration control algorithm and simulations. In Proceedings of the 72nd Shock and Vibration Symposium, San Destin, FL, November, pp. 1–11.
2.
Bart P and Jan D (2003) Multi-axial random vibration testing: a 6 degrees-of-freedom test case. In Proceedings the 21st Aerospace Testing Seminar, Manhattan Beach, CA, 21–23 October, pp. 47–62.
3.
BendatJSPiersolAG (2010) Random Data: Analysis and Measurement Procedures, 4th edn. New York: A John Wiley & Sons, Inc.
4.
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 Symposium on International Automotive Technology, University of Bath, UK, 1 January, pp. 487–494.
7.
Guan GF, Wang HT and Xiong W (2012) Random vibration control of a hydraulic shaking table. Journal of Vibration and Control. Epub ahead of print, 22 October 2012. DOI: 10.1177/1077546312461030.
8.
HarrisCMPiersolAG (2001) Harris’ Shock and Vibration Handbook, 5th edn. New York: McGraw-Hill Inc, pp. 21.2521.30.
9.
IEC-60068-2-64 (2008) Environmental Testing-Part 2-64: Tests- Test Fh: Vibration, Broadband Random and Guidance. Geneva, Switzerland: International Electrotechnical Commission.
10.
Karshenas AM, Dunnigan MW and Williams BW (2000) Adaptive inverse control algorithm for shock testing. In Proceedings of IET Control Theory and Applications, vol. 147(3), pp. 267–276.
11.
Koekebakker SH (2001) Model based control of a flight simulator motion system. Phd thesis, Delft University of Technology, The Netherlands.
12.
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.
13.
LjungLGladT (1994) Modeling of Dynamic Systems, New Jersey: Prentice Hall.
14.
Ma O and Angeles J (1991) Architecture singularities of platform manipulators. In Proceedings of IEEE International Conference on Robotics and Automation, Sacramento, CA, USA, 9–11 April, pp. 1542–1547.
15.
MerletJP (1993) Direct kinematics of parallel manipulators. IEEE Transactions on Robotics and Automation9(6): 842846.
OppenheimAVSchaferRW (1998) Discrete-time Digital Signal Processing, 2nd edn. New Jersey: Prentice Hall.
18.
Plummer AR (2007) Control techniques for structural testing: a review. In Proceedings of IMechE, Part I: Journal of Systems and Control Engineering, vol. 221, pp. 139–169.
19.
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): 7987.
20.
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.
21.
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, pp. 212–221.
22.
SmallwoodDOPaezTL (1993) A frequency domain method for the generation of partially coherent normal stationary time domain signals. Shock and Vibration1(1): 4553.
23.
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.
24.
Spectral Dynamics Inc. (2003) Jaguar systems on-line operating manuals. San Jose, CA (US).
25.
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.
26.
StroudRCHammaGA (1988) Multiexciter and multiaxis vibration exciter control systems. Sound and Vibration22(4): 1828.
27.
StroudRCHammaGAUnderwoodMA (1996) A review of multiaxis/multiexciter vibration technology. Sound and Vibration30(4): 2027.
28.
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 221: 171–181.
Thoen BK and Minn EP (1992) Sinusoidal signal amplitude and phase control for an adaptive feedback control system. US Patent 5,124,626. 1992-6-23.
31.
UnderwoodMAKellerT (2001) Recent system developments for multi-actuator vibration control. Sound and Vibration35(10): 1623.
32.
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: 8086.
33.
UnderwoodMAKellerT (2006) Applying coordinate transformations to multi degree of freedom shaker control. Sound and Vibration40(1): 1427.
34.
United States Department of Defense (2008) Department of Defense Test Method Standard for Environmental Engineering Considerations and Laboratory Tests, MIL-STD-810G. Method 514.6. Available at: http://www.everyspec.com/MIL-STD/MIL-STD-0800-0899/MIL-STD-810G_12306 (accessed 11 April 2012).
35.
Zhang SY, Han JW and Zhao H (2004) RCP and RT control of 6-DOF parallel robot. In Proceedings of 4th International Workshop on Robot Motion and Control, Oulu, Finland, June 17–20, pp. 133–137.
