Stability of nonlinear signal‐based control for nonlinear structural systems with a pure time delay

Struct Control Health Monit

2020

Self Cite

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.

({, \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: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Basic examination of two substructuring schemes for shake table tests

Struct Control Health Monit

2020

Self Cite

“…Thus, the stability analysis here is discussed for { K r , K σ }. The stability analysis for { K r , K σ , K e } can be found in the study …”

Section: Nsbc For Shake Table Testsmentioning

confidence: 99%

“…Based on the equivalent system in Equation and the linear model in Equation , the unmodelled dynamics, which can be applied in stability analysis, can be estimated to be

normalΔ G_{0} ((), s) = G_{0}^{*} ((), s) - {\overset{true¯}{G}}_{0} ((), s) .

Because maintaining stability becomes more difficult as the unmodelled dynamics become larger, the worst possible parameter variations of the controlled system should be reflected in the stability analysis …”

Section: Numerical Examinationsmentioning

confidence: 99%

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

Struct Control Health Monit

Kajiwara

2019

Self Cite

Summary Nonlinear signal‐based control (NSBC) is very powerful for controlling structural systems with parameter variations and has the advantage that the controllers can be designed using classical control theory and expressed by transfer functions. This report describes the first application of NSBC to shake table tests with nonlinear specimens and compares the performance of NSBC with that of a basic control approach that relies on the inverse transfer function of the controlled system. NSBC and the basic approach were numerically applied to shake table tests to excite a nonlinear single‐degree‐of‐freedom system with earthquake acceleration motion, considering the nonlinear specimen characteristics and estimation errors associated with the table dynamics. NSBC achieved excellent control with near 100% accuracy, whereas the basic approach provided insufficient control. Although inaccurate estimation of the pure time delay in the controlled system causes instability at the practice of NSBC, proper design of the nonlinear signal feedback controller prevented instability. In experimental examinations, controllers for the two approaches were designed on the basis of the table dynamics with/without a specimen, which were preliminarily identified by performing tests using a random wave with small amplitude excitations. With no specimen present, both approaches yielded the expected acceleration motion on the table with high accuracy. However, with the specimen present, only NSBC successfully achieved excellent control of the shake table with near 100% accuracy, whereas the basic approach did not because of the specimen nonlinearity. These results numerically and experimentally demonstrate the efficiency and practicality of NSBC for shake tables supporting nonlinear structures.

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

Earthq Engng Struct Dyn

Ikago

Guo

et al. 2023

Self Cite

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.