Smart semi-active MR damper to control the structural response


One advanced means of protecting structures against earthquake ground motions is the use of semi-active devices to customise and limit structural response. Thus, the design, modelling and analysis of different semi-active control devices have received increasing research attention. This study presents a method to determine optimal control forces for magneto-rheological (MR) dampers, using three algorithms: a discrete wavelet transform (DWT), a linear quadratic regulator (LQR), and a clipped-optimal control algorithm. DWT is used to obtain the local energy distribution of the motivation over the frequency bands to modify conventional LQR. The clipped-optimal control algorithm is used to get the MR damper control force to approach the desired optimal force obtained from modified LQR. A Bouc-Wen phenomenological model is utilized to capture the observed nonlinear behaviour of MR dampers. Time history analysis for a single degree of freedom (SDOF) with periods of T= 0.2-5.0 sec is utilized to compare the impact of using classic and modified LQR in controlling the MR damper force under 20 design level earthquakes of the SAC (SEAOC-ATC-CUREE) project. Performance is assessed by comparing the maximum displacement (Sd), total base shear (Fb) and the controller energy. This study shows the proposed modified LQR is more effective at reducing displacement response than conventional LQR. The modified LQR method reduces the median value of uncontrolled Sd by approximately 40% to 88%, over all periods to 5.0 seconds. Moreover, the modified LQR uses about 45% less energy than conventional LQR. Overall, these results indicate the robustness of the proposed method to mitigate structural response and damage using MR devices.


Chase JG, Mulligan KJ, Gue A, Alnot T, Rodgers G, Mander JB, Elliott R, Deam B, Cleeve L and Heaton D (2006). "Re-Shaping Hysteretic Behaviour Using Semi-Active Resettable Device Dampers". Engineering Structures. 28(10): 1418-1429. DOI:

Wang D and Liao W (2005). "Modeling and Control of Magnetorheological Fluid Dampers Using Neural Networks". Smart Materials and Structures. 14(1): 111-126. DOI:

Kim Y, Langari R and Hurlebaus S (2009). "Semiactive Nonlinear Control of a Building with a Magnetorheological Damper System". Mechanical Systems and Signal Processing. 23(2): 300-315. DOI:

Lee D-Y and Wereley NM (2000). "Analysis of Electro-and Magneto-Rheological Flow Mode Dampers Using Herschel-Bulkley Model". SPIE's 7th Annual International Symposium on Smart Structures and Materials. 2000. International Society for Optics and Photonics, Newport Beach, CA, April, 244-255.

Kamath GM and Wereley NM (1997). "A Nonlinear Viscoelastic-Plastic Model for Electrorheological Fluids". Smart Materials and Structures. 6(3): 351-359. DOI:

Christenson R, Lin YZ, Emmons A and Bass B (2008). "Large-Scale Experimental Verification of Semiactive Control through Real-Time Hybrid Simulation". Journal of Structural Engineering. 134(4): 522-534. DOI:

Jansen LM and Dyke SJ (2000). "Semiactive Control Strategies for Mr Dampers: Comparative Study". Journal of Engineering Mechanics. 126(8): 795-803. DOI:

Spencer Jr B, Dyke S, Sain M and Carlson J (1997). "Phenomenological Model for Magnetorheological Dampers". Journal of Engineering Mechanics, 123(3): 230-238. DOI:

Chin CS (2012). "Computer-Aided Control Systems Design: Practical Applications Using Matlab® and Simulink®". CRC Press, Broken Sound Parkway NW, 384pp.

Wu W and Nagarajaiah S (1996). "Application of Partitioned Predictor Corrector Approach in Nonlinear Dynamic Structural Analysis and Optimal Control". Report 97-4, Department of Civil Engineering, University of Missouri, Columbia, MO.

Wu W-H, Chase JG and Smith HA (1994). "Inclusion of Forcing Function Effects in Optimal Structural Control". Proceedings of the First World Conference on Structural Control., Los Angeles, CA, 3-5 August, 22-31.

Panariello G, Betti R and Longman R (1997). "Optimal Structural Control via Training on Ensemble of Earthquakes". Journal of Engineering Mechanics. 123(11): 1170-1179. DOI:

Basu B and Nagarajaiah S (2008). "A Wavelet-Based Time-Varying Adaptive Lqr Algorithm for Structural Control". Engineering Structures. 30(9): 2470-2477. DOI:

Amini F, Hazaveh NK and Rad AA (2013). "Wavelet Pso‐ Based Lqr Algorithm for Optimal Structural Control Using Active Tuned Mass Dampers". Computer‐Aided Civil and Infrastructure Engineering. 28(7): 542-557. DOI:

Yang G, Spencer B, Carlson J and Sain M (2002). "Large-Scale Mr Fluid Dampers: Modeling and Dynamic Performance Considerations". Engineering Structures. 24(3): 309-323. DOI:

Dyke S and Spencer Jr B (1996). "Seismic Response Control Using Multiple MR Dampers". Proceedings of the 2nd International Workshop on Structural Control, Notre Dame, December, Vol. 2: 163-173

Dyke S and Spencer Jr B (1997). "A Comparison of Semi-Active Control Strategies for the MR Damper". In the Proceedings of IIS97: Intelligent Information System. IEEE, Grand Bahama Island, December, 580-584. DOI:

Mohajer Rahbari N, Farahmand Azar B, Talatahari S and Safari H (2013). "Semi-Active Direct Control Method for Seismic Alleviation of Structures using MR Dampers". Structural Control and Health Monitoring. 20(6): 1021-1042. DOI:

Sommerville P, Smith N, Punyamurthula S and Sun J (1997). "Development of Ground Motion Time Histories for Phase II of the FEMA/SAC Steel Project". SAC Background Document Report BD-97/04, Sacramento, CA, 44pp.

Limpert E, Stahel WA and Abbt M (2001). "Lognormal Distributions across the Sciences: Keys and Clues on the Charms of Statistics, and How Mechanical Models Resembling Gambling Machines Offer a Link to a Handy Way to Characterize Log-Normal Distributions, Which Can Provide Deeper Insight into Variability and Probability—Normal or Log-Normal: That is the Question". BioScience. 51(5): 341-352. DOI:[0341:LNDATS]2.0.CO;2

How to Cite
Hazaveh, N. K., Chase, J. G., Rodgers, G. W., & Pampanin, S. (2015). Smart semi-active MR damper to control the structural response. Bulletin of the New Zealand Society for Earthquake Engineering, 48(4), 235-244.

Most read articles by the same author(s)

1 2 > >>