Nonlinear signal‐based control for single‐axis shake tables supporting nonlinear structural systems

Enokida, Ryuta; Kajiwara, Koichi

doi:10.1002/stc.2376

Cited by 14 publications

(36 citation statements)

References 45 publications

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“…In this study, the reliability of a substructuring test will be quantified by the similarity between the emulate responses and the outputs of the substructures . The similarities in the frequency and time domains are given by

({, \begin{array}{l} S_{t} ((),, y_{e}, y) = {(1 + \frac{\sum {((), y_{e} ((), t) - y ((), t))}^{2}}{\sum y_{e} {((), t)}^{2}})}^{- 1} \times 100 % \\ S_{f} ((),, y_{e}, y) = {(1 + \frac{\sum {((), A_{ye} ((), f) - A_{y} ((), f))}^{2}}{\sum A_{italicye} {((), f)}^{2}})}^{- 1} \times 100 % \end{array}),

where A ye and A y are the Fourier amplitude spectra of the emulate response signal y e and the output signal y , respectively.…”

Section: Numerical Simulations For a Linear Emulate Systemmentioning

confidence: 99%

“…Thus, the performance of the HS and DSS schemes needs to be assessed on the basis of the similarity between the true hysteretic loop and what is obtained in the substructuring tests. For this purpose, the similarity of two hysteretic loops is quantified by

S_{hi} = {(1 + \frac{\sum \sqrt{{((), 1 - {\overset{false^}{f}}_{i} ((), t))}^{2} + {((), 1 - {\overset{false^}{δ}}_{i} ((), t))}^{2}}}{\sum \sqrt{{\overset{f}{true}}_{italicri} {((), t)}^{2} + {\overset{δ}{true}}_{italicri} {((), t)}^{2}}})}^{- 1} \times 100 %,

where

{\overset{false^}{f}}_{i} ((), t)

and

{\overset{false^}{δ}}_{i} ((), t)

(

{\overset{false^}{f}}_{ri} ((), t)

and

{\overset{false^}{δ}}_{ri} ((), t)

) are the force and inter‐storey drift on the i th storey of the substructure (emulate system) that are standardised by the maximum values on the same storey of the emulate system. In general, the evaluation with S hi is stricter than visual evaluation from the figure for f i − δ i , because it reflects the difference in the time series.…”

Section: Numerical Simulations For Nonlinear Emulate Systemsmentioning

confidence: 99%

“…In this study, the reliability of a substructuring test will be quantified by the similarity between the emulate responses and the outputs of the substructures. 34,35 The similarities in the frequency and time domains are given by…”

Section: Numerical Conditionsmentioning

confidence: 99%

“…Such nonlinearity degrades the control accuracy of the shake table, and substructuring experimental techniques should be sufficiently robust against such nonlinearity. To address this issue, an innovative approach was recently developed to achieve accurate control of a shake table with a nonlinear specimen . Further studies are currently expected to apply this approach to shake table substructuring experiments.…”

Section: Introductionmentioning

confidence: 99%

“…To address this issue, an innovative approach was recently developed to achieve accurate control of a shake table with a nonlinear specimen. 34,35 Further studies are currently expected to apply this approach to shake table substructuring experiments.…”

Section: Introductionmentioning

confidence: 99%

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Basic examination of two substructuring schemes for shake table tests

Enokida

2020

Struct Control Health Monit

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Summary This study examines two basic substructuring schemes for shake table tests where the dynamics of the table is significantly affected by a specimen. The hybrid simulation (HS) scheme, commonly adopted in substructuring experiments, directly uses the output of a numerical substructure as an input signal to a physical substructure. The dynamical substructuring system (DSS) scheme, developed long after HS, uses feedforward and feedback controllers to minimise the control error produced by the outputs of numerical and physical substructures. Before examining these two schemes, this study introduces a systematic formulation for dividing a multi‐degree‐of‐freedom emulate system into a numerical substructure and a physical substructure with a shake table. Then, controller designs for HS and DSS are discussed for the substructures. The two schemes with basic control approaches were numerically examined through substructuring tests for a linear 3DOF emulate system. DSS with stability was powerful even under a control condition with a pure time delay and inaccurate estimation of the table dynamics, whereas these factors degraded the HS performance. In additional simulations in which nonlinear characteristics were considered, the performance of DSS (HS) was degraded mainly by the nonlinear (inaccurate estimation of the table dynamics). It was found that the stability of substructures with nonlinear characteristics could be roughly assessed by the Nyquist stability criterion. These simulations with/without nonlinear characteristics clarified the performances of the HS and DSS schemes through basic control approaches and stability analysis under practical conditions.

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({, \begin{array}{l} S_{t} ((),, y_{e}, y) = {(1 + \frac{\sum {((), y_{e} ((), t) - y ((), t))}^{2}}{\sum y_{e} {((), t)}^{2}})}^{- 1} \times 100 % \\ S_{f} ((),, y_{e}, y) = {(1 + \frac{\sum {((), A_{ye} ((), f) - A_{y} ((), f))}^{2}}{\sum A_{italicye} {((), f)}^{2}})}^{- 1} \times 100 % \end{array}),

where A ye and A y are the Fourier amplitude spectra of the emulate response signal y e and the output signal y , respectively.…”

Section: Numerical Simulations For a Linear Emulate Systemmentioning

confidence: 99%

S_{hi} = {(1 + \frac{\sum \sqrt{{((), 1 - {\overset{false^}{f}}_{i} ((), t))}^{2} + {((), 1 - {\overset{false^}{δ}}_{i} ((), t))}^{2}}}{\sum \sqrt{{\overset{f}{true}}_{italicri} {((), t)}^{2} + {\overset{δ}{true}}_{italicri} {((), t)}^{2}}})}^{- 1} \times 100 %,

where

{\overset{false^}{f}}_{i} ((), t)

and

{\overset{false^}{δ}}_{i} ((), t)

(

{\overset{false^}{f}}_{ri} ((), t)

and

{\overset{false^}{δ}}_{ri} ((), t)

Section: Numerical Simulations For Nonlinear Emulate Systemsmentioning

confidence: 99%

Section: Numerical Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Basic examination of two substructuring schemes for shake table tests

Enokida

2020

Struct Control Health Monit

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Nonlinear backstepping hierarchical control of shake table using high‐gain observer

Xiao

Pan

Yang

2022

Earthq Engng Struct Dyn

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Shake table testing is a common technique used to examine the responses of structures under dynamic loads. Shake table is often regulated using linear controller, such as proportional‐integral‐derivative (PID) controller. However, traditional PID control cannot consider inherent nonlinearities in the structural and control systems. In this paper, a series of novel backstepping control methods, which consider the nonlinearities in the structural and control systems, have been developed. In addition, high‐gain observers, which can provide highly accurate estimation of the shake table displacement, velocity and acceleration, are also developed. The proposed backstepping control methods and high‐gain observers are implemented in a hierarchical framework, where the high‐level backstepping controller generates the command signal for the low‐level controller to execute. A total of four hierarchical backstepping control methods, including the acceleration‐based backstepping hierarchical control (ABHC), the ABHC with high‐gain observer (ABHCO), the displacement‐based backstepping hierarchical control (DBHC) and the DBHC with high‐gain observer (DBHCO), have been implemented. Detailed parameter studies have been conducted to identify the optimized parameters for the proposed hierarchical backstepping control methods. The proposed control method is verified through a series of shake table tests. The experimental results show the ABHC, ABHCO, DBHC and DBHCO can all achieve high‐performance shake table control, especially with superior acceleration tracking over the traditional PID control. Overall, ABHCO achieves the best tracking performance for displacement, velocity and acceleration.

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Nonlinear signal‐based control for shake table experiments with sliding masses

Enokida

Ikago

Guo

et al. 2023

Earthq Engng Struct Dyn

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This study introduces the first application of nonlinear signal‐based control (NSBC) to shake table experiments with sliding masses. NSBC utilising a nonlinear signal was specifically developed for nonlinear system control. In shake table experiments with a steel structure, it realised a seismic acceleration record on the table with near 100% accuracy even when the structure displayed nonlinear characteristics due to yielding of its components. Regarding the severity, sliding is stronger than yielding because of the rapid shifts of stick and slip states. Sliding is utilised for structural damage mitigation in seismic isolation systems, which are prominent devices in earthquake engineering. However, when sliding occurs on a shake table, it significantly jeopardises the table control. Thus, this study investigates the performance of NSBC to shake table experiments involving the phenomenon. First, this study examines the effectiveness of NSBC via numerical simulations on a shake table with a sliding interface, demonstrated by the Karnopp model, with a friction coefficient of 0.2. Subsequently, a linear model is designed based on the stability analysis of NSBC to assess stability margins obtained from different models. Experiments are performed by placing masses weighing approximately twice the table weight on sliding interfaces with friction coefficients of 0.2–0.4. In these experiments, NSBC with a reasonable linear model design realised expected acceleration records with sufficiently high accuracies, whereas inversion‐based control failed. This study verifies the effectiveness of NSBC for shake table experiments with sliding masses.

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Nonlinear signal‐based control for single‐axis shake tables supporting nonlinear structural systems

Cited by 14 publications

References 45 publications

Basic examination of two substructuring schemes for shake table tests

Basic examination of two substructuring schemes for shake table tests

Nonlinear backstepping hierarchical control of shake table using high‐gain observer

Nonlinear signal‐based control for shake table experiments with sliding masses

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