Self-powered and sensing control system based on MR damper: presentation and application Zhihao Wang a,b, Zhengqing Chen *a, Billie F. Spencer, Jr. b a Wind Engineering Research Center, Hunan University, Changsha, China, 41008 b Dept. of Civil & Environmental Eng., Univ. of Illinois at Urbana-Champaign, IL, USA, 61801 ABSTRACT A new self-powered and sensing semi-active control system based on magnetorheological (MR) damper is presented. The system includes four key parts: a rack and pinion mechanism, a linear permanent magnet DC generator, a current adjustment MR damper, and a control circuit. Numerical simulations for seismic protection of elevated bridges equipped with this system excited by two historical earthquakes are conducted. Linear quadratic regulator (LQR) is used for the design of ideal active control system. LQR-based clipped optimal control as well as skyhook control is used to command a MR damper in both the semi-active control with external power and self-powered semi-active control. It is shown that five strategies (ideal active control, two semi-active controls and two self-powered semi-active controls) have similar control performance in pier response as well as bearing response. It is noticed that only one accelerometer is needed to monitor the response of the deck to realize the self-powered skyhook control, which greatly simplifies the classical semiactive vibration control system based on MR damper. Keywords: MR damper, Energy regeneration, DC motor, Semi-active control, Highway bridge 1. INTRODUCTION Semi-active control devices have received significant attention in recent years because they offer the capability of active control devices without the requirement of large power sources [1]. In particular, MR dampers have attracted extensive attention from the community because of their excellent performance in both lab tests and engineering practice. The first two full scale applications of MR damper in civil engineering are the Tokyo National Museum of Emerging Science and Innovation [] and cable vibration control system of the Dongting Lake bridge [3][4]. However, these systems require external stable power supply, which may be not possible or assured in some extreme events, such as earthquakes and typhoons. To solve this problem, Chen et al. [5] have developed the permanent magnet MR damper, and successfully applied it to a cable vibration control system. However, it can be only optimized in the passive mode and won t make full use of the excellent performance of MR damper. Harvesting energy from structure vibration is quite a new and challenging research field. In civil engineering, the main goal is trying to extract energy from structural vibration that can be used to power wireless sensors. Another potential application of energy harvesting is providing power source for vibration control system. There are already some researches in this area. Kim et al. [6] have presented a new type of vehicle suspension system, which combined the energy regeneration with an ER damper. The generated electromotive force (emf) from AC generator was sent to the ER damper after the voltage amplifier. The performance has been also validated by a simple laboratory test. One research group from Korea [7-8] have proposed the concept of smart passive damping system based on MR damper, and have done a small scale laboratory test. Scruggs et al. [9-11] are the first to suggest the active control with the harvested vibration energy in the area of civil engineering. The most contribution they made is the concept of vibration control with non-local power, which means the harvested energy from the structural system can be rearranged and used as a whole. However, they haven t made any laboratory test. A semi-active vibration control system with MR damper and energy regeneration is presented in this paper. To show its feasibility and effectiveness, one elevated highway bridge with self-powered MR damper is investigated. Linear quadratic regulator (LQR) is used to design the ideal active control system. LQR-based clipped optimal control as well as skyhook control is used to realize the semi-active control based on MR damper in both the semi-active control with external power and self-powered semi-active control.
. THE SELF-POWERED AND SENSING VIBRATION CONTROL SYSTEM In general, the proposed vibration control system shown in figure 1 includes four key parts: a rack and pinion mechanism, rack and pinion mechanism a linear permanent magnet DC generator, a current-adjusted MR damper and a control circuit. The rack and pinion mechanism is used to amplify the linear motion of structure vibration. As a result, a bigger emf can be induced by generator, and the generated power is used to drive the MR damper with the management of the control circuit, which is composed of a microprocessor, a capacitor, a variable resistance, diodes and relay switches, etc. As the linear velocity of structure vibration is also proportional to the generated emf, the generator serves to be both the power supply of the MR damper and the sensor of the structure vibration. Excitation MR Damper Linear Motion Rack and Pinion Voltage Input Control Circuit Voltage Generated Amplified Motion DC Motor Figure 1. The flowchart of the control system with energy regeneration We may have several choices for the design of self-powered semi-active MR control system. First, we can design a simple control circuit, which implements a system energy switch according to the control algorithm. When the generated emf is below the threshold, the DC generator charges the capacitor; otherwise the capacitor will be discharged and power the MR damper. The key design parameters are the threshold selection. Secondly, a variable resistance adjusts the input voltage of the MR damper to track the optimum damping force, which is computed by the adopted control algorithm at every time step. Extra sensors to monitor the vibration response are needed. The key issues are the extra sensors placement, the signal processing technology, the control algorithm selection, and the precise mechanical model for the MR damper. The main difference between them is that second strategy is a global control method but the first strategy is to control the system locally. For the specific application to elevated highway bridge, the clipped optimal control based on LQR control as well as skyhook control are used to be as controller to mitigate the vibration of bridge excited by earthquake, which will be explained in detail in the following. 3. CONTROL SYSTEM MODEL OF ELEVATED HIGHWAY BRIDGE 3.1 The elevated highway bridge model Seismic base isolation is one of the most widely implemented and accepted seismic protection systems. The simple idea behind this technology is to separate the structure from the moving ground through flexible mountings so as to reduce the seismic effects on the superstructure [1]. It is well established that base isolation is highly effective in reducing the displacement relative to the base and accelerations of superstructure; but this has been achieved at the expense of a large absolute base displacement, larger than the ground displacement level itself [13]. To enhance the functionality of passive base isolation, the supplemental damping devices are often suggested. However, the addition of passive damping to minimize base displacement may increase both internal deformation and acceleration of the superstructure, thus defeating many of the gains for which base isolation is intended to provide [14]. Seeking to develop isolation systems that can be effective for a wide range of ground excitation, hybrid control strategies, consisting of a passive isolation system and active or semi-active devices, has been investigated by a number of researchers for isolated buildings [15-18] and highway bridges [19-1]. Consider the two-dof model of the highway bridge shown in Figure subjected to the ground excitation x g. The equation of motion of system with external control force between deck and the top of pier is given by:
MX + CX + KX = HU + η (1) where X = [ x1, x] T, and x 1, x represent the displacement of pier and deck relative to the ground, respectively; M, C and K are the mass, damping and stiffness matrices; H is the location vector for control force U ; η is the ground excitation influence vector. In the state representation, the Eq.(1) becomes: x g x g Z = AZ+ BU+ D () Where Z is the state vector; A is a (4 4) system matrix; B is a (4 ) matrix and D is a (4 1) excitation vector, and they are calculated as follows: in which X 0 I Z = X A = 1 1 M K M C 0 B = 1 M H 0 D = 1 M η m 0 c + c c k + k k 1 m 1 1 1 1 M =,,,, 0 m C= c c K = = = k k H 1 η m (4) In the above, m1 and m are the lumped masses of the pier and deck, respectively; c 1 and c are the damping constants of the pier and bearing, respectively; k 1 and k are the stiffness constants of the pier and bearing, respectively. Table 1 shows the values of these parameters, which is assumed as the uncontrolled case with a low damping of bearing. (3) Deck Pier Bearing Figure. The two-dof model of highway bridge Figure 3. The phenomenological model of MR dampers [1] Table 1. The parameters of bridge model 3. Characterization of MR damper m 1 100 ton m 500 ton c 1 15.7 KN s/m k 1 15,791 KN/m c 196.0 KN s/m k 7685 KN/m To develop control algorithms that take the maximum advantages of the unique features for the MR damper, one mechanical model of the MR damper must be developed adequately and considered with the characteristics of the intrinsic nonlinear behavior. There are a lot of mechanical models for MR damper [1], such as Bingham Model, Bouc- Wen Model, and etc. The phenomenological model shown in above figure 3 described the RD-1005 type MR damper, which is fabricated by the LORD Corporation and used in this study. This model is able to behave both the forcedisplacement and force-velocity relationships. The model is governed by the following equations:
1 y = [ αz+ k0( x y) + c0x ] (5) ( c + c ) 0 1 n 1 z = γ x y z z μ( x y ) z + A( x y ) 1 1 0 n F = c y + k ( x x ) (7) α = au ( ) = aa + au b (8) c = c ( u) = c a + c bu (9) 1 1 1 1 c = c ( u) = c a + c bu (10) 0 1 0 0 u = η ( u v) (11) where v is the voltage applied to the current driver. In this model, there are a total of 14 parameters c, c, k, c, c, k, x, α, α, γ, u, A, n, η ) to characterize the MR damper. ( 0a 0b 0 1a 1b 1 0 a b As mentioned earlier, the model defined above and identified parameter is based on a prototype model of the MR damper. Multiplying the damping, stiffness and hysteretic constants of the model by a modification factor (MF) is needed to magnify the damping force of the MR damper, so that it can be used in the bridge model described in the last section. According to the research of Erkus et al. [19], MF is set as 410.3. The mechanical parameters of MR damper can refer to Erkus et al. [19] directly. 3.3 DC motor model If the velocity amplification of gear mechanism is represented by β, assume that the linear DC motor is ideal and has the following energy conversion property: e= ϕβ ( x x ) (1) 1 Where e is the generated emf, ϕ is a motor constant. The current i in the circuit is: i = e ( r+ R + R ) (13) M where r is the internal resistance of DC motor, R M is the internal resistance of MR damper, and R V is the external variable resistance. The voltage input v of the MR damper can be further obtained as: V v = R e ( r+ R + R ) (14) M M V For the specific application of this paper, R V have only two states: one is nearly zero, and the other is more than 10000Ω. Finally, the control switches can be realized based on the control strategies in the next chapter. 4. CONTROL STRATEGIES 4.1 LQR active control Assume that an active device is equipped between deck and the top of pier, by using the LQR control method, control force u is determined by minimizing the following quadratic objective function: (6) J T T ( ) = ZQZ + ru dt (15) 0
The linear optimal control law is then obtained as: ut () = GZ () t (16) T where the matrices Q and r are positive semi definite matrix and positive scalar, respectively. G= B P / r is the control gain, and P is the Ricatti matrix obtained from the following Ricatti equation: T T AP+ PA PBBP/r+ Q= 0 (17) The optimal value of Q and r can be determined by extensive parametric study. As the research of Erkus et al. [19], Q matrix is represented by a parameter q, based on the energy of system defined as: T 1 1 1 1 ZQZ= q k1( x1) + m1( x 1) + k( x x1) + m( x x 1) (18) In the above equation, q represents the relative importance of pier and bearing response. A smaller value q leads to decrease the bearing response and vice versa. From the equation 18, the Q matrix can be obtained as 1 1 ( qk1+ k) k 0 0 1 1 k k 0 0 Q = 1 1 (19) 0 0 ( qm1+ m) m 1 1 0 0 m m To decide the optimal value of q, r and compare the efficiency of the control strategies, a performance criterion is defined based on the maximum drifts as follows: { } J = ( x ) + ( x x ) (0) max max 1 1 4. Semi-active control of classical MR damper The clipped optimal control based on LQR control [] is used as the first semi-active control strategy. The voltage v i applied to the MR damper changes as: { } vi = vmax H ( fc f) f (1) where v max is the voltage to the current driver associated with saturation of the magnetic field in the MR damper, and it is defined 10V here; H () is the Heaviside step function; fc, f represent the desired active control force and the MR damper force, respectively. The second semi-active control strategy is skyhook control [3], which is defined here as: vi = vmax x ( x x 1 ) > 0 () vi = 0 x ( x x 1) < 0
4.3 Self-powered control of MR damper The clipped optimal control based on LQR control is also used as the first self-powered semi-active control strategy. The voltage applied to the MR damper changes as follows: i {( ) } v = vh f f f (3) c where v i is the voltage added on the MR damper from the generated voltage v. This control can be realized as follows: when when external power is needed, R V = 0, otherwise R V =. Skyhook control is also changed to realize the self-powered semi-active control, and the control algorithm can be expressed as: vi = v x ( x x 1) > 0 (4) vi = 0 x ( x x 1) < 0 Since the direction of term ( x x 1) can be easily calculated from Eq.(1), only one accelerator is needed to monitor the absolute velocity of deck x and realize the self-powered skyhook control. In this way, the DC motor acts as both the vibration sensor and the power supply of the MR damper. Comparatively speaking, the self-powered skyhook control greatly simplifies the classical semi-active control system based on MR damper. 5. SIMULATION RESULTS AND DISCUSSION Assume that the inductance effect of motor can be ignored. Also, the MR damper is assumed to respond very fast with no time delay. ϕ is chosen as 10 (Vs/m), and its internal resistance r is 4.7Ω. The EI Centro and Kobe earthquake are chosen as the external ground excitation to evaluate the control performance, and their maximum acceleration is 3.417(m/s ), 5.783(m/s ), respectively. For the sake of illuminating the feasibility and effectiveness of this new selfpowered control system, the responses under the self-powered semi-active MR control methods are in comparing with those in the semi-active MR control and ideal LQR control. q is set as 10, which is the same as Erkus [19], and r is taken as 1 10-7 after some trial runs. The velocity amplification ratio β is optimized based on performance indices defined as Eq.(0), and its final optimum value is 3. The Table has shown the performance indices of all the control strategies. Table. The performance indices of the controlled system EI Centro (cm) Kobe (cm) Uncontrolled Active Clipped control Skyhook control Self-powered clipped control Self-powered skyhook control 15.8 8.86 7.78 8.34 8.0 7.7 34.5 16.51 19.93 3.3 1.08 19.56 From the table, it can be seen that: 1) all the control strategies have a great improvement on bridge performance compared with the uncontrolled case; ) both skyhook control and LQR based clipped optimal control can nearly reach the performance of that of ideal LQR active control; 3) the two self-powered control strategy can get close performance with its corresponding semi-active control with external power supply; 4) the self-powered skyhook control can get the best performance among the four semi-active control methods, and what is more, as pointed out above, this controller only needs one accelerometer to monitor the response of the deck. Figure 4 has shown the time histories of displacement response of highway bridge subjected to EI Centro and Northbridge earthquake. To clearly show the performance of different control, both semi-active and self-powered semiactive take active control as a reference in the figure 4. Except the time histories of bridge response, the comparisons between active control force and MR damper force of semi-active control as well as self-powered semi-active control
will be helpful to further understand the control behavior. The force-displacement relationship of every control strategy is also shown in the figure 5 and 6. Figure 4. The time histories of displacement response of highway bridge with different control stategy
From the figure 5, it can be concluded that both clipped optimal control and self-powered clipped optimal control can effectively track the active control force. As a whole, it seems that energy dissipation capability of self-powered skyhook control is a little smaller than skyhook control with external power supply as shown in the figure 6. However, it is still competitive due to its simplicity and reliability. Figure 5. The force-displacement for LQR control, LQR clipped control and self-powered LQR clipped control Figure 6. The force-displacement for skyhook control and self-powered skyhook control
6. CONCLUSIONS AND FURTHER RESEARCH The framework of a semi-active MR damper vibration control system with the energy regeneration is presented in this paper. The DC motor harvests the vibration energy of the structure as electricity, then powers MR damper with the management of a control circuit, and therefore an adjustable damping force is realized. As an example, it is applied to an elevated highway bridge. Numerical simulation has been conducted to illustrate the feasibility and effectiveness of hybrid control system. Some main conclusions are drawn as follows: 1. Both skyhook control and LQR based clipped optimal control can nearly reach the control performance of that of ideal LQR active control;. The two self-powered control strategy can get close performance with its corresponding semi-active control with external power supply; 3. The self-powered skyhook control can get the best performance among the four semi-active control methods, and moreover, this strategy only needs one accelerometer to monitor the response of the deck, since the DC motor can act as sensor of the deck velocity relative to the top of the pier. Therefore, skyhook control is quite suitable for application in the self-powered semi-active MR control system. Since the main purpose of this paper is to demonstrate the feasibility of the new self-powered MR damper system, this study may not have an optimum design on MR dampers, motors, as well as control strategy, but the control system is still able to implement effectively and comparably. Although the numerical simulation has shown the good performance, further real time hybrid simulation test or real laboratory test is still required to validate the new control system. ACKNOWLEDGEMENTS The authors greatly appreciate the support from the National Science Foundation of China under Grant No. 5073800. The first author also would like to thank the support from Chinese Scholarship Council. REFERENCES [1] Spencer, B. F., Dyke, S. J., Sain, M. K. and Carlson, J. D., Phenomenological model of a magnetorheological damper, ASCE Journal of Engineering Mechanics, 3, 30-38 (1997). [] Spencer, B. F. and Nagarajaiah S., State of the art of structural control, ASCE Journal of Structural Engineering, 19(7), 845-856 (003). [3] Chen, Z. Q., Wang, X. Y., Ko, J. M. and Ni, Y. Q., Field measurements on wind-rain-induced vibration of bridge cables with and without MR dampers, Proceedings of the Third World Conference on Structural Control, 00. [4] Chen, Z. Q., Wang, X. Y., Ko, J. M. et al., MR damping system for mitigating wind-rain induced vibration on Dongting Lake Cable-Stayed Bridge, Wind and Structures, 7(5), 93-304 (004). [5] Chen, Z. Q., Wang, X. Y., Yu, J. D., et al., Field measurements of wind-rain-induced cable vibration with MR dampers, Proceedings of the 4 th World Conference on Structural Control and Monitoring, 006. [6] Kim, K. S., Kim, S. H., Choi, S. B. and Cheong C. C., ER Suspension System with Energy Generation, Journal of Intelligent Material Systems and Structures, 10, 738-74 (1999). [7] Cho, S. W, Jung, H. J and Lee, I. W., Smart passive system based on magnetorheological damper, Smart Materials and Structures, 14, 707-714 (005). [8] Choi, K. M, Jung, H. J, Lee, H.J and Cho, S.W., Feasibility study of an MR damper-based smart passive control system employing an electromagnetic induction device, Smart Materials and Structures, 16, 33-39 (007). [9] Scruggs, J. T and Lindner, D., Active energy control in civil structure, Proceedings of SPIE Conference on Smart systems for Bridges, Structures, and Highways, 1999. [10] Scruggs, J. T and Iwan, W. D., Control of a civil structure using an electric machine with semi-active capability, ASCE Journal of Structural Engineering, 19(7), 951-959 (003). [11] Scruggs, J. T and Iwan, W. D., Optimal non-local and asymmetric structural damping using regenerative force actuation networks, ASCE Journal of Engineering Mechanics, 13, 93-940 (006). [1] Morales, C. A., Transmissibility concept to control base motion in isolated structures, Engineering Structures,
5(10), 135-1331 (003). [13] Kelly, J. M, Leitmann, G., Soldatos, A. G., Robust control of base-isolated structures under earthquake excitation, Journal of Optimization Theory Application, 53(), 159 180 (1987). [14] Naeim, F., and Kelly, J. M., Design of seismic isolated structures: From theory to practice, Wiley, Chichester, England, 1999. [15] Ramallo, J. C, Johnson, E. A, Spencer, B.F., Smart base-isolation systems, ASCE Journal of Engineering Mechanics, 18(10), 1088-1100 (00). [16] Yoshioka, H., Ramallo, J. C., and Spencer, B. F., Smart base-isolation strategies employing magnetorheological dampers, ASCE Journal of Engineering Mechanics, 18(5), 540-551 (00). [17] Walsh, K. K. and Abdullah, M. M., Adaptive base-isolation of civil structures using variable amplification, Earthquake Engineering and Engineering Vibration, 5(), 3-33 (006). [18] Li, H., and Ou, J. P., A design approach for semi-active and smart base-isolated building, Structural control and health monitoring, 13, 660-681 (006). [19] Erkus, B., Abe, M. and Fujino, Y., investigation of semi-active control for seismic protection of elevated highway bridge, Engineering Structure, 4, 81-93 (00). [0] Hwang, J. S. and Tseng, Y. S., Design formulations for supplemental viscous dampers to highway bridges, Earthquake Engineering and Structural Dynamics, 34, 167-164 (005). [1] Kori, J. G. and Jangid, R. S., Semiactive control of seismically isolated bridges, International Journal of Structural Stability and Dynamics, 8(4), 547-568 (008). [] Dyke, S. J., Spencer, B. F., Sain, M. K. and Carlson, J. D., Modeling and control of magnetorheological dampers for seismic response reduction, Smart Materials and Structures, 5, 565-575 (1996). [3] Nagarajaiah, S. and Narasimhan S., Smart base-isolated benchmark building. Part II: Phase I sample controllers for linear isolation systems, Structural Control and Health Monitoring, 13, 589-604 (006)