A nonlinear signal-based control method and its applications to input identification for nonlinear SIMO problems

2020

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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.

Section: Introductionmentioning

confidence: 99%

Basic examination of two substructuring schemes for shake table tests

2020

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“…NSBC has recently been developed for controlling nonlinear systems, without requiring detailed information about the nonlinearities in the systems. This control approach is literally based on the feedback action of the nonlinear signal σ , which is generated as the difference between the two outputs of the controlled system and its linear model under the same input signal.…”

Section: Introductionmentioning

confidence: 99%

“…Following the introduction of NSBC and its application to substructuring experiments using a hydraulic actuator, this report describes the first application of NSBC to shake table control. The innovative features of this study are as follows: NSBC controller design is addressed for shake tables supporting nonlinear multiple‐degree‐of‐freedom (MDOF) systems.…”

Section: Introductionmentioning

confidence: 99%

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

Kajiwara

2019

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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.

“…43,44 Nonlinear signal-based control (NSBC) has recently been proposed to control nonlinear structural systems. 45 The key feature of NSBC is the feedback action of the nonlinear signal σ, which is obtained as the difference between the two outputs of the controlled system and its linear model under the same input. NSBC using the feedback action for σ, together with the controllers for reference signal r and error signal e, can achieve accurate control of nonlinear controlled systems without adaptations of the controller gains or accurate information concerning the controlled systems.…”

Section: Introductionmentioning

confidence: 99%

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

2019

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Nonlinear signal-based control (NSBC) has recently been developed for nonlinear structural systems. NSBC shows high tracking performance in structural systems that display parameter variations during control practice. This control approach is also efficient for substructuring experimentation, an advanced technique based on real-time interaction between physical experiments and numerical simulations. NSBC allows controller design to be based on classical control theory, with the controllers expressed by transfer functions. Without losing this benefit, this study proposes to analyse the stability of NSBC for nonlinear structural systems and a pure time delay by employing the Nyquist stability criterion, which is also classified into classical stability theory.Then stability analysis that regards the nonlinearity as a parameter variation associated with the linear model of the controlled system has been established in this study. The efficiency and practicality of the stability analysis are examined via numerical control practices for various nonlinear single-and multiple-degree-of-freedom (S/MDOF) systems having pure time delay. In the examination, the controlled systems are nonlinear SDOF and 2DOF systems with different types of nonlinear springs. In the numerical simulations, two control practices for NSBC (i.e., the nonlinear signal feedback action with or without the error feedback action) have offered excellent control with near 100% accuracy. Stability analysis of NSBC has accurately provided the stability conditions for the nonlinear controlled systems with a pure time delay.