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.     

Experimental implementation and verification of multi‐degrees‐of‐freedom effective force testing

This paper presents an experimental implementation and verification of multi‐degrees‐of‐freedom effective force testing (MDOF‐EFT). An experimental setup that consists of a two‐degrees‐of‐freedom structural system and two hydraulic actuators at the Johns Hopkins University was utilized in this study. First, experimental system identification was performed to develop compatible analytical models for the multi‐input and multi‐output systems. Dynamics of the control plant, that is, the valve‐to‐force relations, were modeled with a rational polynomial transfer function matrix and delay components. By using the analytical model, a centralized decoupling loop‐shaping force feedback controller was designed such that the forces are uncoupled and the loop transfer functions have desirable dynamic characteristics in the frequency domain. Then, a series of harmonic force and earthquake simulation tests were performed to assess capabilities and limitations of MDOF‐EFT. Experimental results showed that the dynamic forces in the two actuators were accurately controlled to provide tracking while the system was stable and robust for the entire period of the experiment. Furthermore, earthquake simulation tests with increased levels of the reference forces demonstrated the feasibility of MDOF‐EFT with highly nonlinear test structures. Copyright © 2013 John Wiley & Sons, Ltd.     

Development of high‐performance shake tables using the hierarchical control strategy and nonlinear control techniques

Conventional shake tables employ linear controllers such as proportional‐integral‐derivative or loop shaping to regulate the movement. However, it is difficult to tune a linear controller to achieve accurate and robust tracking of different reference signals under payloads. The challenges are mainly due to the nonlinearity in hydraulic actuator dynamics and specimen behavior. Moreover, tracking a high‐frequency reference signal using a linear controller tends to cause actuator saturation and instability. In this paper, a hierarchical control strategy is proposed to develop a high‐performance shake table. A unidirectional shake table is constructed at the University of British Columbia to implement and evaluate the proposed control framework, which consists of a high‐level controller and one or multiple low‐level controller(s). The high‐level controller utilizes the sliding mode control (SMC) technique to provide robustness to compensate for model nonlinearity and uncertainties experienced in experimental tests. The performance of the proposed controller is compared with a state‐of‐the‐art loop‐shaping displacement‐based controller. The experimental results show that the proposed hierarchical shake table control system with SMC can provide superior displacement, velocity and acceleration tracking performance and improved robustness against modeling uncertainty and nonlinearities. Copyright © 2015 John Wiley & Sons, Ltd.     

Real‐time force control for servo‐hydraulic actuator systems using adaptive time series compensator and compliance springs

Servo‐hydraulic actuators have been widely used for experimental studies in engineering. They can be controlled in either displacement or force control mode depending on the purpose of a test. It is necessary to control the actuators in real time when the rate‐dependency effect of a test specimen needs to be accounted for under dynamic loads. Real‐time hybrid simulation (RTHS) and effective force testing (EFT) method, which can consider the rate‐dependency effect, have been known as viable alternatives to the shake table testing method. Due to the lack of knowledge in real‐time force control, however, the structures that can be tested with RTHS and EFT are fairly limited. For instance, satisfying the force boundary condition for axially stiff members is a challenging task in RTHS, while EFT has a difficulty to be implemented for nonlinear structures. In order to resolve these issues, this paper introduces new real‐time force control methods utilizing the adaptive time series (ATS) compensator and compliance springs. Unlike existing methods, the proposed force control methods do not require the structural modeling of a test structure, making it easy to be implemented especially for nonlinear structures. The force tracking performance of the proposed methods is evaluated for a small‐scale steel mass block system with a magneto‐rheological damper subjected to various target forces. Accuracy, time delay, and resonance response of these methods are discussed along with their force control performance for an axially stiff member. Overall, a satisfactory force tracking performance was observed by using the proposed force control methods.     

Dynamic force control with hydraulic actuators using added compliance and displacement compensation

A new approach to dynamic force control of mechanical systems, applicable in particular to frame structures, over frequency ranges spanning their resonant frequencies is presented. This approach is implemented using added compliance and displacement compensation. Hydraulic actuators are inherently velocity sources, that is, an electrical signal regulates their velocity response. Such systems are therefore by nature high‐impedance (mechanically stiff) systems. In contrast, for force control, a force source is required. Such a system logically would have to be a low‐impedance (mechanically compliant) system. This is achieved by intentionally introducing a flexible mechanism between the actuator and the structure to be excited. In addition, in order to obtain force control over frequencies spanning the structure's resonant frequency, a displacement compensation feedback loop is needed. The actuator itself operates in closed‐loop displacement control. The theoretical motivation, as well as the laboratory implementation of the above approach is discussed along with experimental results. Having achieved a means of dynamic force control, it can be applied to various experimental seismic simulation techniques such as the effective force method and the real‐time dynamic hybrid testing method. Copyright © 2008 John Wiley & Sons, Ltd.     

Considerations for the development of real‐time dynamic testing using servo‐hydraulic actuation

This paper presents a study of the use of servo‐hydraulic systems in the implementation of real‐time large‐scale structural testing methods in force control such as effective force testing (EFT) and in displacement control such as real‐time pseudodynamic testing (RPsD). Mathematical models for both types of control systems are presented and used to investigate the influences of servo‐systems on the overall system performance. Parameters investigated include the overall system dynamics, nonlinearities of servo‐systems, actuator damping, system mass including piston mass, and system response delay. Results of both numerical simulations and experiments showed that many of the influences of the servo‐hydraulic system that significantly affect the real‐time dynamic tests can be properly compensated through control schemes identified in this paper. Copyright © 2003 John Wiley & Sons, Ltd.     

Market‐based control of linear structural systems

To limit the response of structures during external disturbances such as strong winds or large seismic events, structural control systems can be used. In the structural engineering field, attention has been shifted from active control to semi‐active control systems. Unlike active control system devices, semi‐active devices are compact, have efficient power consumption characteristics and are less expensive. As a result, an environment of a large number of actuators and sensors will result, rendering a complex large‐scale dynamic system. Such a system is best controlled by a decentralized approach such as market‐based control (MBC). In MBC, the system is modelled as a market place of buyers and sellers that leads to an efficient allocation of control power. The resulting MBC solution is shown to be locally Pareto optimal. This novel control approach is applied to three linear structural systems ranging from a one‐storey structure to a 20‐storey structure, all controlled by semi‐active hydraulic dampers. It is shown that MBC is competitive in the reduction of structural responses during large seismic loadings as compared to the centralized control approach of the linear quadratic regulation controller. Copyright © 2002 John Wiley & Sons, Ltd.     

Theory and implementation of switch‐based hybrid simulation technology for earthquake engineering applications

Hybrid simulation (HS) is a novel technique to combine analytical and experimental sub‐assemblies to examine the dynamic responses of a structure during an earthquake shaking. Traditionally, HS uses displacement‐based control where the finite element program calculates trial displacements and applies them to both the analytical and experimental sub‐assemblies. Displacement‐based HS (DHS) has been proven to work well for most structural sub‐assemblies. However, for specimens with high stiffness, traditional DHS does not work because it is difficult to precisely control hydraulic actuators in small displacement. A small control error in displacement will result in large force response fluctuations for stiff specimens. This paper resolves this challenge by proposing a force‐based HS (FHS) algorithm that directly calculates trial forces instead of trial displacements. The proposed FHS is finite element based and applicable to both linear and nonlinear systems. For specimens with drastic changes in stiffness, such as yielding, a switch‐based HS (SHS) algorithm is proposed. A stiffness‐based switching criterion between the DHS and FHS algorithms is presented in this paper. All the developed algorithms are applied to a simple one‐story one‐bay concentrically braced moment frame. The result shows that SHS outperforms DHS and FHS. SHS is then utilized to validate the seismic performance of an innovative earthquake resilient fused structure. The result shows that SHS works in switching between the DHS and FHS modes for a highly nonlinear and highly indeterminate structural system. Copyright © 2017 John Wiley & Sons, Ltd.     

Dual compensation strategy for real‐time hybrid testing

Real‐time hybrid testing is an experimental technique for evaluating the dynamic responses of structural systems under seismic loading. Servo‐hydraulic actuators, by nature, induce inevitable time delay between the command and the achieved displacements. This delay would lead to incorrect test results and even cause instability of the system; therefore, delay compensation is critical for stability and accuracy of hybrid simulations of structural dynamic response. In this paper, a dual delay compensation strategy is proposed by a combination of a phase lead compensator and a restoring force compensator. An outer‐loop feed‐forward phase lead compensator is derived by introducing the inverse model in the z domain. The adaptive law based on the gradient algorithm is used to estimate the system delay in the format of parametric model during the test. It is shown mathematically that the parameter in the delay estimator is guaranteed to converge. The restoring force compensator is adopted to improve the accuracy of experimental results especially when the structure is subjected to high frequency excitations. Finally, analytical simulations of an inelastic SDOF structure are conducted to investigate the feasibility of the proposed strategy. The accuracy of the dual compensation strategy is demonstrated through several shaking table tests. Copyright © 2012 John Wiley & Sons, Ltd.     

Model-based framework for multi-axial real-time hybrid simulation testing

Real-time hybrid simulation is an efficient and cost-effective dynamic testing technique for performance evaluation of structural systems subjected to earthquake loading with rate-dependent behavior. A loading assembly with multiple actuators is required to impose realistic boundary conditions on physical specimens. However, such a testing system is expected to exhibit significant dynamic coupling of the actuators and suffer from time lags that are associated with the dynamics of the servo-hydraulic system, as well as control-structure interaction (CSI). One approach to reducing experimental errors considers a multi-input, multi-output (MIMO) controller design, yielding accurate reference tracking and noise rejection. In this paper, a framework for multi-axial real-time hybrid simulation (maRTHS) testing is presented. The methodology employs a real-time feedback-feedforward controller for multiple actuators commanded in Cartesian coordinates. Kinematic transformations between actuator space and Cartesian space are derived for all six-degrees-offreedom of the moving platform. Then, a frequency domain identification technique is used to develop an accurate MIMO transfer function of the system. Further, a Cartesian-domain model-based feedforward-feedback controller is implemented for time lag compensation and to increase the robustness of the reference tracking for given model uncertainty. The framework is implemented using the 1/5th-scale Load and Boundary Condition Box (LBCB) located at the University of Illinois at Urbana- Champaign. To demonstrate the efficacy of the proposed methodology, a single-story frame subjected to earthquake loading is tested. One of the columns in the frame is represented physically in the laboratory as a cantilevered steel column. For realtime execution, the numerical substructure, kinematic transformations, and controllers are implemented on a digital signal processor. Results show excellent performance of the maRTHS framework when six-degrees-of-freedom are controlled at the interface between substructures.     

Time delayed control of structural systems

Time delays are ubiquitous in control systems. They usually enter because of the sensors and actuators used in them. Traditionally, time delays have been thought to have a deleterious effect on both the stability and the performance of controlled systems, and much research has been done in attempting to eliminate them, compensate for them, or nullify their presence. In this paper we take a different view. We investigate whether purposefully injected time delays can be used to improve both the system's stability and performance. Our analytical, numerical, and experimental investigation shows that this can indeed be done. Analytical results of the effects of time delays on collocated and non‐collocated control of classically damped and non‐classically damped systems are given. Experimental and numerical results confirm the theoretical expectations. Issues of system uncertainties and robustness of time delayed control are addressed. The results are of practical value in improving the performance and stability of controllers because these characteristics (performance and stability) improve dramatically with the intentional injection of small time delays in the control system. The introduction of such time delays constitutes a ‘minimal change’ to a controller already installed in a structural system for active control. Hence, from a practical standpoint, time delays can be implemented in a nearly costless and highly reliable manner to improve control performance and stability, an aspect that cannot be ignored when dealing with the economics and safety of large structural systems subjected to strong earthquake ground shaking. Copyright © 2003 John Wiley & Sons, Ltd.     

Optimization of structural control via a smart NEURO‐FBG control system

This study improves a NEURO‐FBG active control system to mature the concept of a smart structure. Originally, a system similar to the human brain is created from FBG sensors and neural networks. The system comprises three parts, namely, a structural condition surveillance system, a NEURO‐FBG converter, and a NEURO‐FBG controller. To solve the inherent time‐consuming and reliability problem of the NEURO‐FBG converter, a new technology is first proposed, and the relationship between inter‐story drift and strain data is established. Global indices such as displacement and velocity of the structure are then reconstructed for searching the optimal control force of the actuator. Meanwhile, the soundness of a building with hydraulic actuators is also an important issue to be solved. To make the building sound, the characteristics of earthquakes are considered for enhancing the performance of the NEURO‐FBG controller. Theoretical analysis shows satisfactory improvement to the control efficiency of both displacement and acceleration. To verify the enhanced system, a series of shaking table tests was conducted. Experimental results demonstrated that the new NEURO‐FBG system can effectively manage the structure; and the controller, taking into consideration the ground acceleration effect, is more reliable and robust for practical application than a conventional controller. Copyright © 2007 John Wiley & Sons, Ltd.     

Equivalent force control method for substructure pseudo‐dynamic test of a full‐scale masonry structure

The effectiveness of equivalent force control (EFC) method has been experimentally validated through hybrid tests with simple specimens. In this paper, the EFC method is applied for the MDOF pseudo‐dynamic substructure tests in which a three‐storey frame‐supported reinforced concrete masonry shear wall with full scale is chosen as physical substructure. The effects of equivalent force controller parameters on the response performance are studied. Analytical expressions for the controller parameter ranges are derived to avoid response overshooting or oscillation and are verified by numerical simulation. The controller parameters are determined based on analytical and numerical studies and used in the actual full‐scale pseudo‐dynamic test. The test results show good tracking performance of EFC, which indicates a successful test. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental study of identification and control of structures using neural network. Part 2: control

Experimental verifications of a recently developed active structural control method using neural networks are presented in this paper. The experiments were performed on the earthquake simulator at the University of Illinois at Urbana—Champaign. The test specimen was a 1/4 scale model of a three-storey building. The control system consisted of a tendon/pulley system controlled by a single hydraulic actuator at the base. The control mechanism was implemented through four active pre-tensioned tendons connected to the hydraulic actuator at the first floor. The structure modelling and system identification has been presented in a companion paper. (Earthquake Engng. Struct. Dyn. 28 , 995–1018 (1999)). This paper presents the controller design and implementation. Three controllers were developed and designed: two neurocontrollers, one with a single sensor feedback and the other with three sensor feedback, and one optimal controller with acceleration feedback. The experimental design of the neurocontrollers is accomplished in three steps: system identification, multiple emulator neural networks training and finally the neurocontrollers training with the aid of multiple emulator neural networks. The effectiveness of both neurocontrollers are demonstrated from experimental results. The robustness and the relative stability are presented and discussed. The experimental results of the optimal controller performance is presented and assessed. Comparison between the optimal controller and neurocontrollers is presented and discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

高科技厂房精密仪器工作平台的微振混合控制

车辆运行过程中引起的竖向地面微幅振动是影响高科技厂房精密仪器正常运行的重要因素。本文采用隔振与主动控制相结合的混合控制系统,以高科技厂房及精密仪器工作平台的有限元动力方程为基础,采用子优化控制方法建立了高科技厂房及精密仪器工作平台的分析模型,探讨了车辆运行所引起的高科技厂房精密仪器工作平台竖向微幅振动的混合控制分析方法。一座典型的三层高科技厂房的算例分析表明,采用混合控制方法能够有效地减小高科技厂房精密仪器工作平台的竖向微幅振动。     

Decentralized ℋ︁∞ controller design for large‐scale civil structures

Complexities inherent to large‐scale modern civil structures pose many challenges in the design of feedback structural control systems for dynamic response mitigation. With the emergence of low‐cost sensors and control devices creating technologies from which large‐scale structural control systems can deploy, a future control system may contain hundreds, or even thousands, of such devices. Key issues in such large‐scale structural control systems include reduced system reliability, increasing communication requirements, and longer latencies in the feedback loop. To effectively address these issues, decentralized control strategies provide promising solutions that allow control systems to operate at high nodal counts. This paper examines the feasibility of designing a decentralized controller that minimizes the ??_∞ norm of the closed‐loop system. ??_∞ control is a natural choice for decentralization because imposition of decentralized architectures is easy to achieve when posing the controller design using linear matrix inequalities. Decentralized control solutions are investigated for both continuous‐time and discrete‐time ??_∞ formulations. Numerical simulation results using a 3‐story and a 20‐story structure illustrate the feasibility of the different decentralized control strategies. The results also demonstrate that when realistic semi‐active control devices are used in combination with the decentralized ??_∞ control solution, better performance can be gained over the passive control cases. It is shown that decentralized control strategies may provide equivalent or better control performance, given that their centralized counterparts could suffer from longer sampling periods due to communication and computation constraints. Copyright © 2008 John Wiley & Sons, Ltd.     

Closed‐form solution for seismic response of adjacent buildings with linear quadratic Gaussian controllers

Closed‐form solution for seismic response of adjacent buildings connected by hydraulic actuators with linear quadratic Gaussian (LQG) controllers is presented in this paper. The equations of motion of actively controlled adjacent buildings against earthquake are first established. The complex modal superposition method is then used to determine dynamic characteristics, including modal damping ratio, of actively controlled adjacent buildings. The closed‐form solution for seismic response of the system is finally derived in terms of the complex dynamic characteristics, the pseudo‐excitation method and the residue theorem. By using the closed‐form solution, extensive parametric studies can be carried out for the system of many degrees of freedom. The beneficial parameters of LQG controllers for achieving the maximum response reduction of both buildings using reasonable control forces can be identified. The effectiveness of LQG controllers for this particular application is evaluated in this study. The results show that for the adjacent buildings of different dynamic properties, if the parameters of LQG controllers are selected appropriately, the modal damping ratios of the system can be significantly increased and the seismic responses of both buildings can be considerably reduced. Copyright © 2001 John Wiley & Sons, Ltd.     

地震作用下参数不确定系统的变结构控制

本文对结构参数具有有确定性的变结构控制系统设计方法进行了研究。首先采用摄动方法给出了结构参数具有确定性的控制系统的运动方程,证明了基于层间剪切模型的参数不确定受控系统与其标称系统具有相同的滑动模态,从而解决了系统切换函数的确定问题,并利用到达条件推导了控制律的表示式。算例分析结果表明,本文的控制方法能有效地减小结构的地震响应,对于结构系统建模存在误差或系统本身存在学确定性的情况,控制效果仍十分显著     

Discrete‐time variable structure control of seismically excited building structures

Generally, the active structural control system belongs to the discrete‐time control system, and the sampling period is one of the most important factors that would directly affect the performance of the control system. In this paper, active control approaches by using the discrete‐time variable structure control theory are studied for reducing the dynamic responses of seismically excited building structures. Based on the discrete reaching law method, a feedback controller which includes the sampling period is presented. The controller is extended by introducing the saturated control method to avoid the adverse effect when the actuators are saturated due to unexpected extreme earthquakes. The simulation results are obtained for a single‐degree‐of‐freedom (SDOF) system and a MDOF shear building equipped with active brace system (ABS) under seismic excitations. It is found that the discrete variable structure control approach and its saturated control method presented in this paper are quite effective. Copyright © 2001 John Wiley & Sons, Ltd.     

Optimal PD/PID control of smart base isolated buildings equipped with piezoelectric friction dampers

Long-period pulses in near-field earthquakes lead to large displacements in the base of isolated structures.To dissipate energy in isolated structures using semi-active control,piezoelectric friction dampers(PFD) can be employed.The performance of a PFD is highly dependent on the strategy applied to adjust its contact force.In this paper,the seismic control of a benchmark isolated building equipped with PFD using PD/PID controllers is developed.Using genetic algorithms,these controllers are optimized to create a balance between the performance and robustness of the closed-loop structural system.One advantage of this technique is that the controller forces can easily be estimated.In addition,the structure is equipped with only a single sensor at the base floor to measure the base displacement.Considering seven pairs of earthquakes and nine performance indices,the performance of the closed-loop system is evaluated.Then,the results are compared with those given by two well-known methods:the maximum possive operation of piezoelectric friction dampers and LQG controllers.The simulation results show that the proposed controllers perform better than the others in terms of simultaneous reduction of floor acceleration and maximum displacement of the isolator.Moreover,they are able to reduce the displacement of the isolator systems for different earthquakes without losing the advantages of isolation.