Robust integrated actuator control: experimental verification and real-time hybrid-simulation implementation

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1 EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS Earthquake Engng Struct. Dyn. 21; 44: Published online 8 October 214 in Wiley Online Library (wileyonlinelibrary.com). DOI: 1.12/eqe.2479 Robust integrated actuator control: experimental verification and real-time hybrid-simulation implementation Ge Ou 1,, Ali Irmak Ozdagli 1,ShirleyJ.Dyke 1,2 and Bin Wu 3 1 School of Civil Engineering, Purdue University, West Lafayette, IN 4796, U.S.A. 2 School of Mechanical Engineering, Purdue University, West Lafayette, IN 4796, U.S.A. 3 School of Civil Engineering, Harbin Institute of Technology, Harbin 19, China SUMMARY In this paper, we propose a new actuator control algorithm that achieves the design flexibility, robustness, and tracking accuracy to give real-time hybrid-simulation users the power to achieve highly accurate and robust actuator control. The robust integrated actuator control (RIAC) strategy integrates three key control components: loop shaping feedback control based on H 1 optimization, a linear-quadratic-estimation block for minimizing noise effect, and a feed-forward block that reduces small residual delay/lag. The combination of these components provides flexible controller design to accommodate setup limits while preserving the stability of the H 1 algorithm. The efficacy of the proposed strategy is demonstrated through two illustrative case studies: one using large capacity but relatively slow actuator of 2 kn and the second using a smallscale fast actuator. Actuator tracking results in both cases demonstrate that the RIAC algorithm is effective and applicable for different setups. Real-time hybrid-simulation validation is implemented using a three- DOF building frame equipped with a magneto-rheological damper on both setups. Results using the two very different physical setups illustrate that RIAC is efficient and accurate. Copyright 214 John Wiley & Sons, Ltd. Received 13 February 214; Revised 12 August 214; Accepted 18 August 214 KEY WORDS: real-time; hybrid simulation; H 1 control; actuator tracking control; robust control; stability 1. INTRODUCTION Hybrid simulation originated in the 197s in Japan [1]. Also known as pseudo-dynamic testing or substructure testing, this approach integrates numerical simulation and physical experimentation to simulate an entire structural system (building, bridge, etc.) under dynamic loading. It is considered to be a cost/space/time efficient approach compared to traditional shake table testing [2]. For over two decades, hybrid simulation was always performed on an extended time scale, neglecting the effects of rate-dependent behaviors [3 ]. Several promising load-rate-dependent auxiliary devices have been developed recently. These developments, combined with recent innovations in embedded systems and real-time execution, have enabled the earthquake engineering community to embrace this new technology [6]. Therefore, executing a hybrid simulation in real-time scale is necessary and possible. Even though it is technically possible to implement real-time hybrid simulation (RTHS), challenges certainly exist. During RTHS, data acquisition, numerical integration, and experimental application of the numerical response through a loading (transfer) system are restricted within a small time frame (. to 1 ms). To execute the numerical computations and experimental actions simultaneously, high precision tracking control of the transfer system is required. However, tracking performance is normally Correspondence to: Ge Ou, School of Civil Engineering, Purdue University, West Lafayette, IN 4796, U.S.A. gou@purdue.edu Copyright 214 John Wiley & Sons, Ltd.

2 442 G. OU ET AL. limited by time delays and time lags introduced by communication, A/D D/A conversion, dynamics of control device, control structural interaction [7], and noise in the feedback loop. Those limitations require individual examination and careful compensation. In 1996, Horiuchi et al. [8] first drew the conclusion that time lag in RTHS, modeled as a pure time delay, is equivalent to adding negative damping. When the time delay is significant, instability may occur in the closed-loop RTHS. In response to this issue, many researchers have sought to compensate for the time delay. First, Horiuchi et al. used polynomial extrapolation based on displacement to predict and compensate the delay effect [9]. Later, Horiuchi and Konno linearly extrapolated the acceleration instead, to improve stability [1]. Darby et al. introduced the first online estimation of time delay, and the updated time delay is compensated in real time [11]. Ahmadizadeh et al. improved time-delay estimation based on reference and measured signal slope [12]. Nguyen and Dorka also developed phase lag compensation with online system identification, where a black box with recursive estimation is used in online updating for system delay [13]. Wallace extended the work of Horiuchi and Darby, updating the polynomial coefficient by a least-squares algorithm in real time to compensate for actuator dynamics [14]. Recently, Wu et al. proposed an upper-bound delay compensation algorithm [1]. Another important branch in the actuator control literature is the model-based control approach, which was first proposed by Carrion and Spence [16,17]. They introduced a data-based actuator system identification and inverted the identified plant model directly by adding a low-pass filter to ensure that the system is strictly proper. Phillips and Spencer modified feedforward (FF) compensation to eliminate of low-pass filter, and using a time-domain representation to replace the improper inverse of actuator plant, one linear quadratic regulator is added as optimized feedback regulation for uncertainties [18]. Combining the model-based approach with delay/lag compensation, Chen and Ricles assumed that the actuator plant can be modeled as a first-order transfer function and compensated with an inverse controller that uses a single estimation parameter representing the time delay/lag in actuator [19]. They later modified their inverse control algorithm with an adaptive feature to update the delay estimation parameter in real time [2]. In 211, Gao et al. proposed a robust actuator controller for RTHS based on H 1, theory which, for the first time, considered noise, disturbance, and model uncertainty effects in actuator control [21 23]. This H 1 controller is designed by trading off tracking performance and control robustness, giving the user the power to meet the testing needs. However, when the noise/signal ratio in the system is high within the frequency range of interest, the sensor noise may be amplified, possibly resulting in a deterioration in performance. The robust integrated actuator control (RIAC) algorithm proposed herein integrates the most effective features of the methods discussed. To reduce the noise impact, the linear quadratic estimation (LQE) scheme is included. For greater flexibility and higher accuracy during testing, an additional feed-forward block minimizes any small residual time delay/lag. Further, it is proved analytically that RIAC has the same stability characteristics as the H 1 algorithm. A step-by-step design and implementation procedure for RIAC is suggested based on the needs of a particular user. RIAC is implemented on two experimental setups, and both simulation and experimental studies demonstrate the efficacy of the RIAC. RIAC is found to significantly reduce the impact of noise as compared to an H 1 design, and to improve the phase response effectively. To further validate the RIAC method, RTHS is performed using a three-story steel building as the numerical substructure and a magneto-rheological (MR) damper as the physical specimen. Two very different experimental setups are used to demonstrate the versatility of RIAC. The results indicate that the RIAC is a very effective and accurate method for imposing boundary condition in RTHS. 2. PROBLEM FORMULATION 2.1. Hybrid simulation and real-time hybrid-simulation formulation In HS and RTHS, a structure system is divided into numerical and experimental (also known as physical substructure) components. The numerical substructure contains the well-understood components and leaves the hard-to-model components in the physical setup. An illustration of a hybrid simulation Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

3 RIAC EXPERIMENTAL VERIFICATION AND RTHS IMPLEMENTATION 443 Figure 1. RTHS system concept. Figure 2. Numerical experimental interaction in RTHS. is shown in Figure (1). A three-story building equipped with damping device is separated into a three-dof shear model in the numerical portion, and the damping device is physically tested in the lab by attaching it to an actuator. The interaction between experimental substructure and numerical substructure through actuator control is shown in Figure 2. Such interaction has different layers: (i) an inner loop PID control is used in most manufacturer-provided software that stabilized the actuator; (ii) the outer loop control algorithm guarantees that desired response from numerical codes is implemented appropriately; and (iii) the force feedback loop between experimental substructure and numerical substructure. The equation of motion for the numerical substructure is as follows: M N Rx C C N Px C K N x C F E.x; Px/ D M Rx g (1) where M N ;C N,andK N indicate mass, damping, and stiffness matrices in the numerical substructure. F E is the measured force from the experimental substructure, and Rx g is the earthquake acceleration record. A typical RTHS implementation is as follows: Step 1. For initial time step, i D 1: Calculate initial numerical response from Equation (1) and obtain x 1 ; xp 1 given x g;1 and F1 E D Œ. Setx d;1 D x 1. Step 2. For time step i;.i > 1/: Impose desired response x d;i 1 through outer loop control algorithm to transfer system (hydraulic actuator) with command signal x c;i. Step 3. Actuator executes command signal, achieves real response x m;i to attached specimen, and then measures experimental restoring force Fi E due to actuator motion. Step 4. Calculate numerical response x i ; Px i using integration scheme with given x g;ic1 and Fi E. Set x d;i D x i. Step. Set i D i C 1, and then go to step 2. Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

4 444 G. OU ET AL. Figure 3. Hydraulic actuator with inner control loop. Table I. Servo-hydraulic system parameters. k v Valve flow gain K c Valve pressure gain Servo-valve time delay constant C l Piston leakage coefficient A Piston area V t Fluid volume K p Internal controller proportional gain ˇe Effective bulk modulus K vp Pilot stage valve flow gain m System and piston mass c System and actuator damping k System and actuator stiffness The accuracy between desired boundary condition Œx d ; Px d with the transfer system in steps 2 and 3 dominates the fidelity of the RTHS. Here, the outer loop control algorithm is designed based on the assumption that the plant (the actuator model) contains both the hydraulic actuator and the internal PID loop together and can be considered as a linear-time-invariant system Actuator dynamic model The proportional gain controlled hydraulic actuator transfer function can be linearized between output displacement x m and command x d. The system can be represented in block diagram as shown in Figure 3 [24], notations of each parameter can be found in Table I. Several important assumptions have been made in this mathematical model: (i) fluid properties are constant; (ii) servo-valves are not saturated; (iii) supply pressure is much greater than the load pressure; (iv) friction force can be modeled as viscous damping; and (v) main stage spool opening is proportional to pilot stage flow. These assumptions are typically acceptable owing to the relatively low frequency and small amplitude nature of RTHS. The linearized hydraulic system is derived as a fourth-order transfer function directly from the block diagram in Figure 3: G xm ;x d D X m.s/ X d.s/ D Z K p (2) P 1 s 4 C P 2 s 3 C P 3 s 2 C P 4 s C P where Z D K vp K c K v A (3) K a D V t =4ˇe (4) P 1 D K a m () P 2 D K a c C C l m C K a m (6) P 3 D K a k C C l c C K a c C A 2 C mc l (7) P 4 D C l k C K a k C A 2 C C l c (8) P D Z K p C C l k (9) Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

5 RIAC EXPERIMENTAL VERIFICATION AND RTHS IMPLEMENTATION 44 Table II. Noise sources in hydraulic actuation system. Mechanical vibration Fluid vibration Electrical noise Structural impact and friction Hydraulic impact Power line disturbances Rotary imbalance Hydraulic fluid pump Externally conducted noise Hydraulic valve and cylinder Cavitation induced vibration Transmitted noise Pipeline and tank resonance Turbulent flow and vortex Ground loops Parameters Z ;P 1 ;P 2 ;P 3 ;P 4,andP can be identified through complex function curve fitting and will be fully addressed in Section Noise sources in the hydraulic system Noise in the hydraulic actuation system normally comes from two sources. One is the mechanical and fluid vibration in hydraulic actuation components, and the other is the electrical noise due to power sources, ground loops, and so forth. Table II listed all common sources of hydraulic actuation noise. More detailed information is discussed in [2, 26]. Those noise sources are very hard to distinguish and defeat individually during testing. To achieve control robustness, impact of noise should always be carefully studied [27]. 3. ROBUST-INTEGRATED-ACTUATOR-CONTROL ALGORITHM The RIAC strategy uses H 1 optimization to design the core controller to meet the needs of the user. H 1 allows for a trade-off between system performance and its robustness. To further improve control performance for RTHS applications, an LQE is used to reduce measurement uncertainty. In the final setup, one feed-forward block is used in such a way that it does not affect the stability of the feedback system but does enhance tracking performance. The entire system is shown in Figure 4. The H 1 block is designed in the continuous Laplace domain, and the LQE and feed-forward blocks are designed in the discrete domain H 1 control algorithm Gao et al. [21 23] first introduced robust H 1 control into actuator control for RTHS. The feedback block diagram with the H 1 algorithm is shown in Figure. For a typical feedback-control system, the sensitivity function S and complementary sensitivity function T (same as I/O transfer function) are given as Figure 4. RIAC control block diagram. Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

6 446 G. OU ET AL. Figure. H 1 feedback-control block diagram. S.s/ D.1 C G p.s/k.s// 1 (1) T.s/ D 1 S.s/ D G P.s/K.s/ 1 C G P.s/K.s/ (11) x m.t/ D T.x d.t/ n.t// C S G P d.t/ (12) where n.t/ is system measurement noise and d.t/ is system processing disturbance. s D j! indicates equation in frequency domain (written in upper case), and time domain functions in terms of t are written in lowercase. For the RTHS implementation, the input tracking signal x d.t/ should be imposed on the actuator accurately. Thus, the I/O transfer function T.s/ should be close to unity over the relevant control frequency (low frequency), and close to at high frequency where noise/disturbance signal is dominant. A desired open-loop transfer function W.s/ should be designed according to such requirements. H 1 algorithm is used to design the optimal controller K.s/ that assures that the system open-loop transfer function GK closely meets the target function W.s/. W.s/ can be written in state-space form W.s/ D ssœa w ;B w ;C w ;D w. Controller K.s/ is defined as K.s/ D G c G d, where direct inverse compensation G c.s/ is designed as G c.s/ D W.s/=G xm ;x d. And G d.s/ is obtained from H 1 optimization. Aw B w P 1 Dw C w X C X Aw B w P 1 Dw C w XB w P 1 Bw XC w I D w P 1 Dw Cw D Aw B w T 1 Dw C w Z C Z Aw B w T 1 Dw C w ZC w T 1 Cw ZB w I D w T 1 Dw B w D (13) (14) P D I C D w D w;t D I C D w D w (1) Thus, X and Z can be obtained by solving two generalized algebraic Riccati equations, Equations (13) and (14), where denotes the complex conjugate transpose of one matrix. To obtain G d ;H 1 optimization Gd.I W G d / 1 QL 1.I W G d / 1 QL 1 1 (16) QL D T 1=2 C T 1=2 C w.si A w UC w / 1 U (17) where U D ZCw C B wdw T 1 (18) Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

7 RIAC EXPERIMENTAL VERIFICATION AND RTHS IMPLEMENTATION 447 Figure 6. H 1 control performance under different open-loop W designs. The constructed controller G d in state-space form is A Gd B Gd C Gd D Gd 3 2 A w B w V C 2 W1 1 ZCw.C 3 w D w V/ 7 D 2 W1 1 ZC w 6 4 Bw X 7 D w (19) where W 1 D I C.XZ 2 I/and V D P 1 D w C w C B w X. The performance of H 1 compensation largely depends on the design of W. Figure 6 shows three different H 1 optimization results, and their corresponding performance under W ;A;B;C for plant G is described by G D 1: s 4 C 282:87s 3 C 6: s 2 C : s C 1: (2) It is illustrated that design A is the most aggressive controller among the three, and tracking can be performed up to 2 Hz. However, high-frequency noise attenuates only slightly even up to 1 khz. Alternatively, design C is effective in depressing noise influence in tracking, but the acceptable tracking performance is only acceptable to 3 Hz. Thus, it is clear that there is a trade-off between performance and sensitivity. In a real-world experiment, those limitations can make it impossible to perform a successful test Linear quadratic estimation Control accuracy is compromised when noise content in the feedback measurement is high. This phenomenon is more difficult to tackle using H 1 optimization when the noise frequency is at or close to the frequency of the control signal. To reduce noise in the actuator displacement measurement, the LQE, also known as Kalman filter method, is implemented to estimate the actuator displacement [28]. Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

8 448 G. OU ET AL. A discrete actuator system with processing disturbance d.t/ and measurement noise n.t/ is written in discrete state-space form: x P.k C 1/ D A d x P.k/ C B d u.k/ C d.k/ (21) y p.k C 1/ D C d x P.k/ C n.k/ (22) where system state-space matrices A d ;B d ;C d are converted to discrete state space from actuator model described in Equation (2), Œx p.k/ is the plant state vector, and y p.k/ is direct measured displacement from the actuator s internal Linear Variable Differential Transformer (LVDT). For each time step k, the LQE is formulated as follows: (i) Time update: Ox P.k C 1/ D A d x P.k/ C B d u.k/ (23) (ii) Measurement update: P K.k C 1/ D A d P K.k/AT d C Q (24) K k.k C 1/ D P K.k C 1/ C d P K.k C 1/C T C R 1 (2) Ox P.k C 1/ DOx P.k C 1/ C K k.k C 1/ y P.k/ C d Ox P.k C 1/ (26) P K.k C 1/ D.I K k.k C 1/C d /PK.k C 1/ (27) Oy P.k C 1/ D C d Ox P.k C 1/ (28) where P K is the Kalman filter error covariance matrix, K k is the Kalman filter gain, Q is the predefined processing disturbance matrix, and R is the predefined measurement noise. Q=R ratio determines the estimator weights on plant output and system measurement. (iii) Set k D k C 1, and then go to step (i) Inverse compensation Because actuator delay/lag is critical for RTHS, when the small residual delay/lag is found in experimental implementation after H 1 controller, an additional block dedicated to small time delay/lag is integrated in RIAC. The inverse compensation algorithm is proposed by Chen [19], where the system delay/lag is assumed to be constant for the entire frequency range. The compensated system after H 1 is modeled as a first-order system: G a. / D. 1/ (29) The open-loop inverse compensation is the direct inverse of G d. /: K a. / D. 1/ (3) Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

9 RIAC EXPERIMENTAL VERIFICATION AND RTHS IMPLEMENTATION 449 Figure 7. Pole positions for RIAC system and H 1 system under the same W. Figure 8. Flow chart for implementing RIAC design and validation test. Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

10 4 G. OU ET AL Stability analysis From Figure 4, it is clear that the feed-forward block does not interact with H 1 feedback loop, and the system after loop shaping control can be written in a discrete transfer function as follows: G ss D K a K. /G x m ;x c. / 1 C K. /G xm ;x c. / D. 1/ K. /G x m ;x c. / 1 C K. /G xm ;x c. / (31) (32) From Equation (32), G ss is determined by H 1 feedback-control design and is irrelevant to the value in feed-forward design. As the H 1 controller is designed based on fitting the desired open-loop target function W of the feedback system, closed-loop stability is guaranteed from Section 3.1. The pole locations for the RIAC control system Figure and the H 1 control system Figure 6 stay the same and are inside of the unit circle Figure 7, indicating that RIAC maintains the stability characteristics of the H 1 design. In this example, G ss is designed W ;A in previous loop shaping illustration case, and it is assumed that the estimator does not affect the system characteristics. As this proof is general and irrelevant to actuator model G or W choice, detailed information of G and W ;A is not presented. 4. EXPERIMENTAL VERIFICATION The design procedure of RIAC is divided into three main stages (Figure 8): system identification, controller design, and experimental tuning. Here, two experimental setups are used to demonstrate the procedure and performance of the controller: setup A, one large-capacity but relatively slow actuator of 2 kn; and setup B, a small-scale fast actuator. RTHS is performed using a three-story steel building as the numerical substructure and an MR damper as the physical specimen. As the capacity of the actuator in setup A is significantly larger than the MR damper maximum force, the nonlinearity of the MR damper is negligible to the hydraulic system during testing. In setup B, an MR damper nonlinearity should also be considered as part of the actuator dynamics during control Control validation on setup A Test setup A, the loading system shown in Figure 9, is located in the School of Civil Engineering, Harbin Institute Technology (HIT), China; and its maximum loading capacity is over 2 kn. The loading system is constrained in the vertical direction, and the MTS Flex GT (Model 793.) system software controls the actuator through an inner PID loop shown in Figure 3. It supports up to eight servo-valves, and the internal LVDT in each actuator can be measured at a maximum rate of 6 Hz using a 16-bit resolution. The hydraulic system is also equipped with two accumulators that supply flow to reach more the short-term velocities, when needed. The saturation velocity limit in this setup is around 9 mm/s. An outer loop control and external command are applied through MATLAB compatible real-time interface hardware dspace 114 (SN ). This system is also used as the data acquisition system, which supports five A/D, D/A channels (one at a 16-bit resolution and four at a 12-bit resolution) to be sampled simultaneously. The sampling frequency in this test is 124 Hz. The MR damper is made by LORD Corporation (RD-1-3). The MR damper is operated with external excitation current. and 1. A for passive-off and passive-on conditions with a maximum force capacity of 2. kn at 1 A. In setup A, the loading capacity of the actuator is very large compared to the MR damper maximum force. The hydraulic system is identified without MR damper attached using a Band Limited White Noise (BLWN) input signal of 1 Hz. The time domain and frequency domain response Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

11 RIAC EXPERIMENTAL VERIFICATION AND RTHS IMPLEMENTATION 41 Figure 9. Experimental setup for a large-scale MTS loading frame with MR damper attached. displacement(mm) 1.. Input Measured time(sec) Figure 1. Open-loop system input and output for system ID. are shown in Figures 1 and 11(a), respectively. The fitted system frequency response is also found in Figure 11(a), and the plant can be written as a fourth-order transfer function given by the following: G xm ;x c ;A D 1: s 4 C 281:79s 3 C 6: s 2 C 6: s C 1: (33) Figure 11(b) indicates noise power spectrum density in the hydraulic system. There is a significant peak around Hz, which is the electric circuit frequency in China. For H 1 design, W is chosen as follows: 1: W.A/ D s 6 C 12s C9:8 1 6 s 4 C8:9 1 9 s 3 C3: s 2 C6: sc4: (34) The desired open-loop transfer functions W, open-loop transfer function after control G xm :x c ;AK and H 1 closed loop are illustrated in Figure 12(a). The noise at Hz is present in the desired tracking frequency (flat region in Figure 12(a)) range; thus, it is necessary to use LQE for noise mitigation in the feedback measurement. A comparison is made between two controllers in simulation considering noise in the feedback loop. Case 1 is the original H 1 design, and case 2 considers LQE (RIAC). In Figure 12(b), for case 1, the noise at Hz is observed, and another peak at 12 Hz is also amplified Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

12 42 G. OU ET AL. Magnitude (db) Phase (deg) Frequency (Hz) identified model experimental data Frequency (Hz) (a) Frequence Response and Identified Transfer Function of the Open Loop System Power/frequency (db/hz) Frequency (Hz) (b) Noise Power Spectrum Density in Hydraulic System Figure 11. Input output system identification and noise analysis for system A. Figure 12. Controller design and performance for setup A. Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

13 RIAC EXPERIMENTAL VERIFICATION AND RTHS IMPLEMENTATION 43 Figure 13. Experimental setup for a small-scale actuator with MR damper attached. owing to dynamics in the control gain K. However, both the -Hz and 12-Hz peaks have been greatly depressed using RIAC (case 2). An additional small time delay of T d D 1: ms is found during further tuning. The feed-forward compensation parameter is defined as D T d f s,wheref s is sampling frequency during testing. A comparison between the RIAC algorithm and the original H 1 design with the same desired open loop W is shown in Figure 12(c) using a BLWN with a bandwidth of 2 Hz. Further experimental validation is shown in the same figure using bandwidth only up to 12 Hz, which considers the hydraulic fluid velocity limitation. The comparison results show that the experimental result matches that of the RIAC simulation Control validation on setup B The small-scale loading frame shown in Figure 13 is located in Intelligent Infrastructure System Laboratory, Purdue University. This hydraulic system has a maximum loading capacity of 1 kn (velocity limit). The actuator in the loading frame is equipped with an internal LVDT and is controlled by SC6 controller as the inner PID loop. The external command is applied through a high-performance Speedgoat/xPC (Speedgoat GmbH, 211) real-time kernel. High-resolution, high-accuracy, 18-bit analog I/O boards are integrated into this digital control system that supports up to 32 differential simultaneous A/D channels and eight D/A channels, with a minimum I/O latency of less than sfor all channels. The MR damper is made by LORD Corporation (RD-841-1). Specified peak to peak damper force is greater than 2 N when subjected to a velocity of 1.97 in./s ( cm/s) and 1-A current input. The MR damper is operated with external excitation current. and 1. A for passive-off and passiveon conditions. A LORD Wonder Box device provides closed-loop current control that operates as an interface device between data-acquisition-system output and MR damper. The output current with the Wonder Box will be. A when the control input is approximately.4.6 V and is linearly proportional to the aforementioned input voltage. In setup B, the loading capacity of the actuator is at the same order of magnitude as the MR damper maximum force. Thus, the MR damper operating condition affects the response and properties of the hydraulic system. The hydraulic system is identified with MR damper on/off condition [16, 17] using BLWN of 1 Hz, and time domain response is compared in Figure 14. Similarly, the plant can be written in a fourth-order transfer function as Equations (3) (37), and a comparison between Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

14 44 G. OU ET AL. Figure 14. Open-loop system input and output for MR damper on/off condition. Magnitude (db) Phase (deg) Frequency (Hz) 9 4 Passive On Estimated Average TF Estimated Passive Off Estimated 4 Passive On Measured 9 Passive Off Measured Frequency (Hz) (a) Frequence Response and Identified Transfer Fuction of the Open Loop System Power/frequency (db/hz) Frequency (Hz) (b) Noise Power Spectrum Density in Hydraulic System Figure 1. Input output system identification and noise analysis for system A. experimental and estimation frequency response is shown in Figure 1(a). G xm ;x c ;OFF;b D G xm ;x c ;ON;b D 3: s 4 C 17:47s 3 C 3:8 1 s 2 C : s C 3: (3) 4:7 1 9 s 4 C 639:s 3 C 3: 1 s 2 C 7:1 1 7 s C 4: (36) G xm ;x c ;AVG;b D And the loop shaping design for setup B is 3: s 4 C 78:1s 3 C 3:2 1 s 2 C 6: 1 7 s C 3: (37) W.B/ D 1: s 3 C 2s 2 C 1:8 1 s C (38) Similarly, noise content is defined as displacement response (LVDT signal) measured with zero input to the inner loop. The actuator feedback signal is well grounded, and in this case, there is no significant peak shown in noise power spectrum density plot in Figure 1(b). Thus, the desired open loop W is designed to be more aggressive as in Figure 16(a). The efficacy of LQE in RIAC algorithm is Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

15 RIAC EXPERIMENTAL VERIFICATION AND RTHS IMPLEMENTATION 4 Figure 16. Controller design and performance for setup B. First Floor Acceleration Magnitude (db) Second Floor Acceleration Third Floor Acceleration Experimental MCK Model Frequency (Hz) Figure 17. Experimental and identified structural frequency response. Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

16 46 G. OU ET AL. demonstrated through a comparison study similar to that carried out with setup A where measured noise is added to the feedback loop for both H 1 control case and RIAC control case. The power spectrum densities of measured system outputs of both systems are compared in Figure 16(b). Measurement noise impact is significantly depressed by RIAC same as found in setup A. An additional time delay T d D 4 ms is found during tuning. The feed-forward compensation parameter is the same as defined before D T d f s. Figure 16(c) demonstrates the comparison between simulation of a 3-Hz BLWN tracking using RIAC, H 1, and an experimental test of 2-Hz BLWN. The feed-forward block helps mitigate any residual delay in the original H 1 design.. REAL-TIME HYBRID-SIMULATION RESULTS The RTHS application studied for validating RIAC algorithm is shown in Figure 1. The target structure is a three-story steel frame equipped with an MR damper on the first floor for earthquake response Table III. Error indices for all cases. Setup A Setup B Earthquake record J 1 J 2 J 3 J 1 J 2 J 3 El Centro passive on El Centro passive off Morgan passive on Morgan passive off Kobe passive on Kobe passive off velocity (mm/s) measured displacement Time (sec) (a).3 scale Kobe earthquake, passive on measured displacement desired velocity desired velocity time (sec) (c).3 scale Kobe earthquake, passive off, tracking performance and velocity saturation velocity (mm/s) 1 measured displacement Time (sec) (b) Full scale Morgan earthquake, passive on measured displacement desired velocity desired velocity Time (sec) (d) Full scale Morgan earthquake, passive off, tracking performance and velocity saturation Figure 18. RTHS results for setup A. Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

17 47 RIAC EXPERIMENTAL VERIFICATION AND RTHS IMPLEMENTATION mitigation [3]. The numerical component is the three-story frame identified from a physical setup located in HIT, and the MR damper is tested experimentally. The restoring force in Equation (1) is the force produced by the MR damper. Three earthquake records are tested using RTHS. The three-story frame is lightly damped, and the modes of the structure are at 2.89, 8.69, and Hz, respectively, and the experimentally identified mass, stiffness, and damping matrices of the structure are as follows, and the identification results are shown in Figure 17: 2 MN CN KN 3 419: 4:4 2:2 D 4 4:4 364: 1: kg; 2:2 1: 319: :1 4:1 1:8 D 4 4:1 74:3 4: N=.m=s/; 1:8 4: 61: :3 72:1 3:7 D 4 72:1 13:6 6:7 14 N=m 3:7 6:1 4:7 (39) In RTHS validation, three different earthquake records are implemented as the excitation including. scaled El Centro earthquake,.3 scaled Kobe earthquake, and full-scale Morgan earthquake. MR damper is set as on and off modes for each test, respectively. To quantitatively analyze control performance of RIAC algorithm, four error indicators are considered, as follows: 1 1 measured displacement measured displacement Time (sec) (a). scale El-Centro earthquake, passive on (b).3 scale Kobe earthquake, passive off (c) time (sec) Full scale Morgan earthquake, passive off measured displacement 8 1. Time (sec) 1 measured displacement 6 8 (d) Time (sec) Full scale Morgan earthquake, passive on Figure 19. RTHS results for setup B. Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

18 48 G. OU ET AL. r J1 D r J2 D s (4) n Dd2 D RMS.De /=RMS.Dd / n (41) n.dm Dd /2 = max.dd / D RMS.De /= max.dd / n (42) n.dm Dd /2 = n r J3 D n.dm Dd /2 D RMS.De / n tracking error where Dm is measured displacement, Dd is, and De D Dm Dd is the tracking error. Table III lists quantitative errors for each cases under Equations (4) (42). The overall results are good during testing on experimental setup A. However, for MR damper passive-off case, the desired motion of actuator exceeds its velocity limit at 9 mm/s. Therefore, passive-on cases perform significantly better compared to passive-off cases. Figure 18 illustrates displacement tracking performance in passive-on case in setup A (Figure 18(a, b)) and also the displacement tracking and velocity saturation during passive-off tests (Figure 18(c, d)). To demonstrate the RIAC controller performance on another setup, RTHS tests have been implemented on setup B as shown in Figure 19. Tracking results match well (Figure 19(a c)) for all cases, and tracking errors are shown in Figure 2(a d). Quantitative results listed in Table III illustrate the consistency between all six tests on setup B. tracking error time (sec) time (sec) (a). scale El-Centro earthquake, passive on, (b).3 scale Kobe earthquake, passive off, tracking tracking error error tracking error tracking error time (sec) time (sec) (c) Full scale Morgan earthquake, passive off, tracking (d) Full scale Morgan earthquake, passive on, tracking error error Figure 2. RTHS tracking errors for setup B. Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

19 RIAC EXPERIMENTAL VERIFICATION AND RTHS IMPLEMENTATION CONCLUSIONS The need to achieve accurate boundary condition synchronization is strongly linked to the success of RTHS test. Most of the recent research has focused on time-delay compensation and hydraulic system dynamics. Model uncertainties and noise present in the hydraulic system have not been carefully considered in the design of the actuator controller previously. A new algorithm for actuator control is proposed in this paper. By integrating the most effective feature to develop a flexible and versatile closed-loop control system, the new RIAC algorithm meets the needs of the RTHS user. The limitations of the original H 1 design are overcame, while the robust stability is preserved. In both simulation and experimental results, the RIAC significantly reduced noise impact on the closed-loop system, especially when the noise peak is in the desired control frequency range. RIAC enables the user to fully consider the system dynamics as well as the uncertainty (error or measurement noise) and still establish a design yielding highly accurate tracking. Test results discussed in the paper indicated that RIAC is appropriate and effective for controlling both large and small, and slow and fast systems and that it is very accurate and effective for RTHS. The tracking results achieved in both setups demonstrate feasibility and accuracy of RIAC. ACKNOWLEDGEMENTS The authors would like to acknowledge the support of the National Science Foundation under award 11134, CMMI ; National Natural Science Foundation of China under award and ; and the Sohmen Fund established by Purdue alumnus Anna Pao Sohmen. Data used in this paper are available on Network of Earthquake Engineering Simulation (NEES) website nees.org/warehouse/project/176. REFERENCES 1. Takanashi M, Udagawa K, Okada M, Seki T, Tanaka H. Nonlinear earthquake response and analysis of structures by a computer-actuator on-line system. Bulletin of Earthquake Resistant Structure Research Center, University of Tokyo: Tokyo, Japan, 197; 8: Nakashima M. Development, potential, and limitation of real-time on-line (pseudo-dynamic) testing. Mathematical, Physical and Engineering Sciences 21; 39: Mahin SA, Shing PB. Pseudodynamic method for seismic testing. Journal of Structural Engineering, ASCE 198; 111(7): Takanashi K, Nakashima M. Japanese activities on on-line testing. Journal of Engineering Mechanics, ASCE 1987; 113(7): Shing PB, Nakashima M, Bursi OS. Application of pseudodynamic test method to structural research. Earthquake Spectra, EERI 1996; 12(1): Christenson RE, Lin YZ, Emmons AT, Bass B. Large-scale experimental verification of semiactive control through real-time hybrid simulation. Journal of Structural Engineering, ASCE 28; 134(4): Dyke SJ, Spencer BF, Quast P, Sain MK. The role of control structure interaction in protective system design. Journal of Engineering Mechanics 199; 121(2): Horiuchi T, Nakagawa M. Development of a real time hybrid experimental system with actuator delay compensation, Proceedings of the 11th World Conference on Earthquake Engineering: Acapulco, Mexico, June 23 28, Paper No Horiuchi T, Nakagawa M. Real time hybrid experimental system with actuator delay compensation and its application to a piping system with energy absorber. Earthquake Engineering and Structural Dynamics 1999; 28(1): Horiuchi T, Nakagawa T. A new method for compensating actuator delay in real-time hybrid experiments. Proceedings of the Royal Society A 21; 39(1786): Darby AP, Williams MS, Blakeborough A. Stability and delay compensation for real-time substructure testing. Journal of Engineering Mechanics 22; 128(12): Ahmadizadeh A, Mosqueda G, Reinhorn AM. Compensation of actuator dynamics for real-time hybrid simulation. Earthquake Engineering and Structural Dynamics 28; 37(1): Nguyen VT, Dorka UE. Phase lag compensation in real-time substructure testing based on online system identification, Proceedings of the 14th World Conference of Earthquake Engineering: Beijing, China, 28; (8pp). 14. Wallace MI, Wagg DJ, Neild SA. An adaptive polynomial based forward prediction algorithm for multi-actuator real-time dynamic substructuring. Proceedings of the Royal Society A 2; 461: Wu B, Wang Z, Bursi OS. Actuator dynamics compensation based on upper bound delay for realřtime hybrid simulation. Journal of Earthquake Engineering and Structural Dynamics 213; 42(12): Copyright 214 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 21; 44: DOI: 1.12/eqe

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