A simple strategy for dynamic substructuring: II. Experimental evaluation

This paper is on an extensive experimental evaluation program to explore the robustness of a new strategy dynamic substructuring. This strategy, in contrast to conventional approaches, decouples the substructuring controller from the physical subsystem, and consequently results in a simple, yet robust, implementation. The concept is presented in detail in a companion paper. A configuration consisting of a shake table and an active mass driver is used in the experimental program, and various factors such as dynamics of virtual subsystems used, modeling of the actuator, choice of control gain settings, and nonlinear effects in the actuator are investigated, leading to the conclusion that the proposed strategy results in robust performance.     

Control issues relating to real‐time substructuring experiments using a shaking table

Real‐time substructuring is a method of dynamically testing a structure without experimentally testing a physical model of the entire system. Instead the structure can be split into two linked parts, the region of particular interest, which is tested experimentally, and the remainder which is tested numerically. A transfer system, such as a hydraulic actuator or a shaking table, is used to impose the displacements at the interface between the two parts on the experimental substructure. The corresponding force imposed by the substructure on the transfer system is fed back to the numerical model. Control of the transfer system is critical to the accuracy of the substructuring process. A study of two controllers used in conjunction with the University of Bristol shaking table is presented here. A proof‐of‐concept one degree‐of‐freedom mass–spring–damper system is substructured such that a portion of the mass forms the experimental substructure and the remainder of the mass plus the spring and the damper is modelled numerically. Firstly a linear controller is designed and tested. Following this an adaptive substructuring strategy is considered, based on the minimal control synthesis algorithm. The deleterious effect of oil‐column resonance common to shaking tables is examined and reduced through the use of filters. The controlled response of the experimental specimen is compared for the two control strategies. Copyright © 2005 John Wiley & Sons, Ltd.     

Testing of dynamically substructured,base‐isolated systems using adaptive control techniques

Experimental techniques for testing dynamically substructured systems are currently receiving attention in a wide range of structural, aerospace and automotive engineering environments. Dynamic substructuring enables full‐size, critical components to be physically tested within a laboratory (as physical substructures), while the remaining parts are simulated in real‐time (as numerical substructures). High quality control is required to achieve synchronization of variables at the substructuring interfaces and to compensate for additional actuator system(s) dynamics, nonlinearities, uncertainties and time‐varying parameters within the physical substructures. This paper presents the substructuring approach and associated controller designs for performance testing of an aseismic, base‐isolation system, which is comprised of roller‐pendulum isolators and controllable, nonlinear magnetorheological dampers. Roller‐pendulum isolators are typically mounted between the protected structure and its foundation and have a fundamental period of oscillation far‐removed from the predominant periods of any earthquake. Such semi‐active damper systems can ensure safety and performance requirements, whereas the implementation of purely active systems can be problematic in this respect. A linear inverse dynamics compensation and an adaptive controller are tailored for the resulting nonlinear synchronization problem. Implementation results favourably compare the effectiveness of the adaptive substructuring method against a conventional shaking‐table technique. A 1.32% error resulted compared with the shaking‐table response. Ultimately, the accuracy of the substructuring method compared with the response of the shaking‐table is dependent upon the fidelity of the numerical substructure. Copyright © 2009 John Wiley & Sons, Ltd.     

A comparative study and unification of two methods for controlling dynamically substructured systems

This paper addresses the problem of advanced testing of systems via the principle of dynamic substructuring. Use is made of the hybrid simulation (HS) scheme framework to develop a new method of synthesis for the dynamically substructured system (DSS) scheme of Stoten and Hyde. Principal reasons for doing this are (i) to improve upon the original method of DSS synthesis by adopting the more intuitive framework of HS and (ii) to enable the amalgamation of HS and DSS into a unified substructured system (USS) scheme, so that the significant advantages of DSS can be incorporated into an existing HS scheme as a straightforward retrofit. Having established the common framework for HS/DSS, the paper also illustrates, by way of an example, compensator/controller synthesis for the two schemes, together with their advantages and disadvantages. In doing this, both schemes are retained in their basic forms, that is, there are no additional control embellishments used in this work, such as delay compensation, adaptive control, or other advanced control methods. In order to maintain as much transparency as possible, use is made of well‐known classical control techniques. Common problems associated with the substructure testing technique are also investigated, including the effects of physical parameter uncertainty, pure delays in signals, and a ‘split‐mass’ in the substructure formulation. It is shown that, although the new formulation of controlled DSS requires more design effort than compensated‐HS, the advantages of DSS in terms of stability and robustness significantly outweigh this small disadvantage at the design stage. Copyright © 2016 John Wiley & Sons, Ltd.     

Decentralized robust control of building structures under seismic excitations

Many of the control algorithms proposed for structures subjected to seismic excitations are based on a centralized design philosophy, such as the linear quadratic regulator (LQR) design. The information of all the states of the system is usually required in these methods to determine the control command. For applications involving large‐scale systems, it may be more convenient to design decentralized controllers that depend only on the information of the local states for control command calculation. In this study, a nonlinear decentralized robust control algorithm is proposed. The structural system is decomposed into several artificially uncoupled subsystems. The interconnections between adjacent subsystems are treated as uncertain but bounded disturbances to the subsystems. The controller associated with one subsystem determines the control command based only on the states of the local subsystem. Numerical examples of linear and nonlinear structural models are presented to demonstrate the effectiveness and robustness of the proposed controller. The traditional LQR design is used as a baseline for comparison. Copyright © 2007 John Wiley & Sons, Ltd.     

Real‐time hybrid experiments with Newmark integration,MCSmd outer‐loop control and multi‐tasking strategies

Real‐time hybrid testing is a promising technique for experimental structural dynamics, in which the structure under consideration is split into a physical test of key components and a numerical model of the remainder. The physical test and numerical analysis proceed in parallel, in real time, enabling testing of critical elements at large scale and at the correct loading rate. To date most real‐time hybrid tests have been restricted to simple configurations and have used approximate delay compensation schemes. This paper describes a real‐time hybrid testing approach in which non‐linearity is permitted in both the physical and numerical models, and in which multiple interfaces between physical and numerical substructures can be accommodated, even when this results in very stiff coupling between actuators. This is achieved using a Newmark explicit numerical solver, an advanced adaptive controller known as MCSmd and a multi‐tasking strategy. The approach is evaluated through a series of experiments on discrete mass–spring systems. Copyright © 2006 John Wiley & Sons, Ltd.     

Pseudo-dynamic testing using conventional testing devices

This paper presents the development of a new type of pseudo-dynamic test system, in which a conventional static jack is utilized for loading. Two of the new hardware devices developed for the system are detailed: a hydraulic pump system that can adjust the rate of oil flow using an inverter motor, and a controller that controls the jack's motion with a displacement feedback signal transmitted from a digital displacement transducer. The unique advantages of the system are summarized as: larger force capacity achieved by the static jack, maximum use of hardware devices available in many existing structural testing laboratories, and flexibility for program development accomplished by separating tasks into multiple PCs. The reliability of the system is calibrated first by a pseudo-dynamic test for an SDOF system and then by a pseudo-dynamic test for a ten-storey building model having hysteretic dampers. For the latter test, substructuring techniques have been incorporated. The accuracy of the results obtained is discussed based upon the capacity of the system to control displacement and comparison with numerical results.     

Tall building vibration control using a TM‐MR damper assembly: Experimental results and implementation

This paper summarizes the relevant results of the design, construction, testing, and implementation of a nominal 120 kN magnetorheological damper developed to control a free‐plan tall building in Santiago, Chile, equipped with two 160‐ton tuned masses. Cyclic as well as hybrid simulation tests were performed on the prototype damper. Global building responses using measured MR properties showed good correlation with analytical estimations. Also, a proposed physical controller for the MR damper was validated through hybrid and building pull‐back tests. Its performance is essentially equivalent to that of an LQR controller, but the information needed in its implementation is considerably less. Pull‐back tests of 10 cm amplitude were performed on one mass along the flexible edge of the building and its response controlled using the passive and controlled modes of the MR damper. The MR damper was capable of controlling the TM displacements very effectively, as well as the simulated building response for different ground motions and harmonic excitation. Copyright © 2010 John Wiley & Sons, Ltd.     

Rosenbrock‐based algorithms and subcycling strategies for real‐time nonlinear substructure testing

In this paper, Rosenbrock‐based algorithms originally developed for real‐time testing of linear systems with dynamic substructuring are extended for use on nonlinear systems. With this objective in mind and for minimal overhead, both two‐ and three‐stages linearly implicit real‐time compatible algorithms were endowed with the Jacobian matrices requiring only one evaluation at the beginning of each time step. Moreover, these algorithms were improved with subcycling strategies. In detail, the paper briefly introduces Rosenbrock‐based L‐Stable Real‐Time (LSRT) algorithms together with linearly implicit and explicit structural integrators, which are now commonly used to perform real‐time tests. Then, the LSRT algorithms are analysed in terms of linearized stability with reference to an emulated spring pendulum, which was chosen as a nonlinear test problem, because it is able to exhibit a large and relatively slow nonlinear circular motion coupled to an axial motion that can be set to be stiff. The accuracy analysis on this system was performed for all the algorithms described. Following this, a coupled spring‐pendulum example typical of real‐time testing is analysed with respect to both stability and accuracy issues. Finally, the results of representative numerical simulations and real‐time substructure tests, considering nonlinearities both in the numerical and the physical substructure, are explored. These tests were used to demonstrate how the LSRT algorithms can be used for substructuring tests with strongly nonlinear components. Copyright © 2010 John Wiley & Sons, Ltd.     

Pseudo‐dynamic testing with substructuring at the ELSA Laboratory

The paper describes the distinctive features of the pseudo‐dynamic test method as implemented at the ELSA reaction‐wall facility. Both hardware and software aspects are considered. Particular attention is devoted to the digital control system and to a coupled numerical–experimental substructuring technique allowing realistic earthquake testing of very large structures. Mathematical and implementation details corresponding to this testing technique are given for both synchronous and asynchronous input motion. Selected test results illustrate the advantages of the presented features. Copyright © 2000 John Wiley & Sons, Ltd.     

A Rosenbrock‐W method for real‐time dynamic substructuring and pseudo‐dynamic testing

A variant of the Rosenbrock‐W integration method is proposed for real‐time dynamic substructuring and pseudo‐dynamic testing. In this variant, an approximation of the Jacobian matrix that accounts for the properties of both the physical and numerical substructures is used throughout the analysis process. Only an initial estimate of the stiffness and damping properties of the physical components is required. It is demonstrated that the method is unconditionally stable provided that specific conditions are fulfilled and that the order accuracy can be maintained in the nonlinear regime without involving any matrix inversion while testing. The method also features controllable numerical energy dissipation characteristics and explicit expression of the target displacement and velocity vectors. The stability and accuracy of the proposed integration scheme are examined in the paper. The method has also been verified through hybrid testing performed of SDOF and MDOF structures with linear and highly nonlinear physical substructures. The results are compared with those obtained from the operator splitting method. An approach based on the modal decomposition principle is presented to predict the potential effect of experimental errors on the overall response during testing. Copyright © 2009 John Wiley & Sons, Ltd.     

Bond‐graph based substructuring of dynamical systems

A bond graph approach to hybrid simulation of dynamical systems using numerical–experimental real‐time substructuring is presented. The bond graph concepts of a virtual junction and a virtual actuator, hitherto used in the context of physical‐model based control, are used to perform the substructuring in an intuitively appealing way. The approach is illustrated by the reworking of a previously‐published example. The approach is verified experimentally using a bench‐top multiple mass–spring system for the physical substructure and automatically generated real‐time code is used to implement the numerical substructure. Copyright © 2005 John Wiley & Sons, Ltd.     

飞机航电设备的半主动磁流变控制

本文提出一种新的航电设备减振控制策略,采用半主动磁流变阻尼器与小阻尼柔性橡胶支座来取代目前采用高阻尼刚性橡胶支座的方法,以降低对航电设备的耐振要求,增强飞机飞行的安全性。本文建立了航电设备减振控制的两自由度刚体平-扭耦联模型,荷载激励考虑了基底平动与转动加速度。磁流变阻尼器的半主动控制算法选用限幅最优控制算法,主控制器为H2/LQG控制器,并采用一种加速度反馈的控制策略。针对目前的被动控制方案,本文研究了支座阻尼对减振控制效果的影响。为了得到最优的半主动控制效果,本文对控制器的权矩阵进行了参数优化分析。文中针对一系列工况详细比较了本文所提出的半主动控制策略与目前被动控制策略的减振控制效果。仿真分析结果表明,磁流变阻尼器可以非常有效地减小航电设备的动力反应,新的减振控制策略远优于现有的被动控制方案。     

Substructuring of dynamical systems via the adaptive minimal control synthesis algorithm

In this paper we consider the concept of modelling dynamical systems using numerical–experimental substructuring. This type of modelling is applicable to large or complex systems, where some part of the system is difficult to model numerically. The substructured model is formed via the adaptive minimal control synthesis (MCS) algorithm. The aim of this paper is to demonstrate that substructuring can be carried out in real time, using the MCS algorithm. Thus, we reformulate the MCS algorithm into a substructuring form. We introduce the concepts of a transfer system, and carry out numerical simulations of the substructuring process using a coupled three mass example. These simulations are compared with direct simulations of a three mass system. In addition we consider the stability of the substructuring algorithm, which we discuss in detail for a class of second‐order transfer systems. A numerical–experimental system is considered, using a small‐scale experimental system, for which the substructuring algorithm is implemented in real time. Finally we discuss these results, with particular reference to the future application of this method to modelling large‐scale structures subject to earthquake excitation. Copyright © 2001 John Wiley & Sons, Ltd.     

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

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_∞ 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_∞ algorithm. The efficacy of the proposed strategy is demonstrated through two illustrative case studies: one using large capacity but relatively slow actuator of 2500 kN and the second using a small‐scale 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 © 2014 John Wiley & Sons, Ltd.     

Innovative substructuring technique for hybrid simulation of multistory buildings through collapse

Hybrid simulation combines numerical and experimental methods for cost‐effective, large‐scale testing of structures under simulated dynamic earthquake loads. Particularly for experimental seismic collapse simulation of structures, hybrid testing can be an attractive alternative to earthquake simulators due to the limited capacity of most facilities and the difficulties and risks associated with a collapsing structure on a shaking table. The benefits of hybrid simulation through collapse can be further enhanced through accurate and practical substructuring techniques that do not require testing the entire structure. An innovative substructuring technique for hybrid simulation of structures subjected to large deformations is proposed to simplify the boundary conditions by overlapping the domains between the numerical and experimental subassemblies. The advantages of this substructuring technique are the following: it requires only critical components of the structure to be tested experimentally; it reduces the number of actuators at the interface of the experimental subassemblies; and it can be implemented using typically available equipment in laboratories. Compared with previous overlapping methods that have been applied in hybrid simulation, this approach requires additional sensing in the hybrid simulation feedback loop to obtain internal member forces, but provides significantly better accuracy in the highly nonlinear range. The proposed substructuring technique is verified numerically and validated experimentally, using the response of a four‐story moment‐resisting frame that was previously tested to collapse on an earthquake simulator. Copyright © 2014 John Wiley & Sons, Ltd.     

Probabilistic approach for active control based on structural energy

This paper presents an active control algorithm using the probability density function of structural energy. It is assumed that structural energy under excitation has a Rayleigh probability distribution. This assumption is based on the fact that the Rayleigh distribution satisfies the condition that the structural energy is always positive and the occurrence probability of minimum energy is zero. The magnitude of the control force is determined by the probability that the structural energy exceeds the specified target critical energy, and the sign of the control force is determined by the Lyapunov controller design method. The proposed control algorithm shows much reduction of peak responses under seismic excitation compared with the LQR controller, and it can consider the control force limit in the controller design. Also, the chattering problem which sometimes occurs in the Lyapunov controller can be avoided. Copyright © 2003 John Wiley & Sons, Ltd.     

An off-and-towards-equilibrium strategy for vibrational control of structures

Traditional control strategies have difficulty handling nonlinear behavior of structures, time variable features and parameter uncertainties of structural control systems under seismic excitation. An off-and-towardsequilibrium （OTE） strategy combined with fuzzy control is presented in this paper to overcome these difficulties. According to the OTE strategy, the control force is designed from the viewpoint of a mechanical relationship between the motions of the structure, the exciting force and the control force. The advantage of the OTE strategy is that it can be used for a variety of control systems. In order to evaluate the performance of the proposed strategy, the seismic performance of a three-story shear building with an Active Tendon System （ATS） using a Fuzzy Logic Controller （FLC） is studied. The main advantage of the fuzzy controller is its inherent robustness and ability to handle any nonlinear behavior of structures. However, there are no design guidelines to set up the corresponding control rule table for a FLC. Based on the proposed strategy for the FLC, a control rule table associated with the building under study is developed, which then allows formation of a detailed algorithm. The results obtained in this study show that the proposed strategy performs slightly better than the linear quadratic regulator （LQR） strategy, while possessing several advantages over the LQR controller. Consequently, the feasibility and validity of the proposed strategy are verified.     

Neuro-fuzzy control strategy for earthquake-excited nonlinear magnetorheological structures

Magnetorheological (MR) damper is a prominent semi-active control device for earthquake responses mitigation of structures. The most important topic for the intelligent MR structures is choosing the control current of MR dampers quickly and accurately. The typical control strategy is on–off control strategy, i.e. bi-state control strategy, while inherent time-delay and coarse control precision lie in this strategy. This paper proposes neuro-fuzzy control strategy, in which the neural-network technique is adopted to solve time-delay problem and the fuzzy controller is used to determine the control current of MR dampers quickly and accurately. Through comparison between the bi-state control and the neuro-fuzzy control strategies and a numerical example about a three-story reinforced concrete structure, it can be concluded that the control strategy is very important for semi-active control, the neuro-fuzzy control strategy can determine currents of MR dampers quickly and accurately, and the control effect of the neuro-fuzzy control strategy is better than that of the bi-state control strategy.     

Multidegrees‐of‐freedom effective force testing: a feasibility study and robust stability assessment

This paper presents a feasibility study of multidegrees‐of‐freedom effective force testing (MDOF‐EFT). The study is intended to facilitate the development of a force feedback controller and investigation of performance as well as robustness of MDOF‐EFT. First, the dynamics of MDOF‐EFT systems are analytically investigated. Analytical transfer functions of the control plant, the valve‐to‐force relations, showed that the plant is dynamically coupled and the natural frequencies of test structures are the transmission zeros of the plant. Using a set of model parameters from a previous study, a case study that includes controller design, numerical simulations and robust stability assessment is performed. A decoupling loop shaping (DLS) controller consisting of a pseudo inverse of the plant and second‐order loop shaping controllers is adopted as the force feedback controller. It is shown that the DLS controller provides a stable control system while successfully decoupling the control loops and compensating the control‐structure interaction. Numerical simulations demonstrate that the DLS controller enables tracking of static and dynamic forces for multiple actuators. Robust stability of MDOF‐EFT with the DLS controller is assessed using Monte Carlo simulation. The stochastic simulation results show that the DLS controller is stable and robust, providing sufficient stability margins for uncertain models with maximum 50% errors in the estimated system parameters. This paper demonstrates that MDOF‐EFT is feasible with the DLS controller and can be implemented in experimental laboratories. Copyright © 2013 John Wiley & Sons, Ltd.