Predictive Optimal Linear Control of Elastic Structures during Earthquake. Part I

A predictive optimal linear control (POLC) algorithm is proposed for controlling the seismic responses of elastic structures. This algorithm compensates for time delay that occurs in real control application by predicting the structural response in the classical optimal linear control equation. The unique feature of this proposed POLC algorithm is that it compensates for time delay very effectively over a very wide range of time delay magnitudes. Numerical examples of single-degree-of-freedom structures are presented to study the performance of the proposed POLC system for various time delay magnitudes. Results show that a time delay always causes degradation of control efficiency, and POLC can greatly reduce this degradation. The effects of natural periods and damping of the structure, different earthquake characteristics and numerical integration schemes, and choices of control gains on the degradation induced by time delay are carefully studied in the analysis. Results show that using a larger time delay magnitude may give smaller structural responses, and this magnitude is independent of earthquake characteristics but dependent on the control gains. Finally, practical application of POLC is performed on a six-story moment-resisting steel frame. It is demonstrated that POLC maintains stability in multi-degree-of-freedom structures and at the same time it has a satisfactory control performance.     

Predictive Optimal Linear Control of Inelastic Structures during Earthquake. Part II

The predictive optimal linear control (POLC) algorithm derived in the companion paper is extended to analyze the controlled responses of inelastic structures by incorporating the force analogy method (FAM). While POLC is very effective in compensating for the negative effect of time delay for elastic structures, the FAM is very efficient in performing the inelastic analysis. Different from conventional inelastic analysis methods of changing stiffness, the FAM analyzes inelastic structures by varying the structural displacement field, and therefore the state transition matrix needs to be computed only once. This greatly simplifies the computation and makes inelastic analysis readily applicable to the POLC algorithm. Numerical simulation is performed on a single-degree-of-freedom system to demonstrate the applicability of the POLC algorithm. Results show that the proposed control algorithm has feasibility for any inelastic structures for various control gains. Even though the control efficiency deteriorates with increase in time delay magnitudes, POLC maintains structural stability over a relatively wide range of time delay magnitudes. Finally, a computer model of a six-story moment-resisting steel frame is analyzed to show that POLC has a good control result on real inelastic structures, particularly in reducing the structural damages experienced during the earthquake.     

Overturning Stability Criteria for Flexible Structures to Earthquakes

Criteria for overturning stability of flexible structures such as chimneys and towers are developed. To the authors’ knowledge all published studies arrive at overturning stability conclusions and criteria based on rigid body motion of systems. This is the first attempt to develop a simple design criterion that includes flexibility effects of slender structures to their overturning stability. The development is based on expressing the system deformation in terms of generalized coordinates. Examples and parametric studies demonstrate use of the criteria as well as the role that each one of the most significant geometric, inertial, and spectral parameters plays on the overturning stability of towers and chimneys. The procedure could also be useful to address the inverse problem that is to estimate the ground acceleration that caused the overturn of a slender structure.     

Model Predictive Control of Wind-Excited Building: Benchmark Study

In this paper, a “third generation” benchmark problem that focuses on the control of wind excited response of a tall building, using the Model Predictive Control (MPC) scheme, is presented. A 76 story, 306 m tall concrete office tower proposed for the city of Melbourne, Australia, is being used to demonstrate the effectiveness of MPC. The MPC scheme is based on an explicit use of a prediction model of the system response to obtain the control actions by minimizing an objective function. Optimization objectives in MPC include minimization of the difference between the predicted and desired response trajectories, and the control effort subjected to prescribed constraints. By incorporating input/output hard constraints, the MPC scheme provides an optimal control force that satisfies the prescribed constraints.     

Adaptive Feedback–Feedforward Control of Building Structures

This paper proposes a combined feedback–feedforward control algorithm for reducing structural response of buildings to seismic excitations. The controller contains both feedback and feedforward components. The feedback component is assumed to be the same as that found from traditional linear quadratic regulator design. The feedforward component is obtained by estimating the external excitation as a series of step functions at each time increment. This feedforward gain varies with the duration of the step function used for estimation and converges as the time duration increases. Thus, a finite number of precalculated gains can be used to represent the potential feedforward gain profile. At any instant in time, the excitation is measured and by using the past measurements, the most effective feedforward gain for the recorded excitation values can be selected from the set of precalculated gains. This value is used as the feedforward gain for the current time step. Numerical examples are presented to show the effectiveness of this adaptive control scheme. The effects of varying the control objectives, the updating time for the feedforward gain, and the number and location of actuators are studied.     

Time-Delayed Positive Velocity Feedback Control Design for Active Control of Structures

In this paper we present and propose a design methodology that uses intentional time delays for the active control of structures. We use here positive velocity-feedback, time-delayed control and show that its performance is, in general, superior to the previously developed methodology of using time delayed, negative velocity-feedback control. A detailed study carried out in this paper of the nonsystem poles and their interaction with the system poles reveals the reasons for this. Analytical results related to performance and stability of the new method are presented. We apply the time delayed positive velocity feedback active control methodology to a multidegree-of-freedom system subjected to the S00E component of ground acceleration recorded during the El Centro 1940 earthquake. The excellent behavior in terms of stability, performance, and control efficiency that is demonstrated by our time-delayed control design as well as its facile implementation makes it attractive for earthquake hazard mitigation in a practical sense.     

Acceleration Feedback-Based Active and Passive Vibration Control of Landing Gear Components

In this paper, a novel methodology is developed to absorb the vibrations of relatively large-scale aircraft structures such as landing gear components. This is accomplished using a combination of active and passive controls. A system equivalent to a Boeing 747 landing gear break rod is selected as a test bed. The expected goal of this study is to dissipate the fundamental vibration mode of the tube. A beam-type dynamic absorber and a constrained layer damping treatment are used for passive vibration control. Simulations and experimental results are provided for the dynamic absorber case. In addition, full-state feedback along with state estimation based on the “reciprocal state space” method is presented. The plant responses and estimates for both the open loop and closed loop systems are shown in simulations. An optimal controller based on acceleration measurements using piezoelectric actuators is implemented using a hardware in the loop protocol for the active vibration control of the system. The integrated controller with passive and active components absorbs the fundamental mode of the system, according to the experimental results.     

Direct Adaptive Neurocontrol of Structures under Earth Vibration

A direct adaptive neurocontroller is proposed to reduce structure response to earth vibrations by actively creating an equal but opposite force to that of the first mode force of the structure. While earthquake forces are generally considered to be unpredictable, the short-term predictions by the proposed neurocontrol architecture significantly reduce structure vibrations. To demonstrate its general applicability and utility to future earthquakes, the proposed adaptation algorithm is also shown to be asymptotically convergent. The approach is validated by several simulations in which actual time series from the Hachino, Northridge, Kobe, and Bam earthquakes are applied against structures of various heights, three-, five-, and seven-story structures. The simulation results are then compared with those of a conventional linear quadratic regulator. Results indicate a significant and consistent improvement in minimal structure displacement.     

Earthquake Response and Energy Evaluation of Inelastic Structures

A computational method is derived to characterize the energy in inelastic structures and the transfer among various energy forms over the duration of an earthquake. This computational method is based on the force analogy method, which uses a change in displacement field to represent the inelastic behavior of structure instead of the traditional method of changing stiffness. The evaluation of plastic energy due to inelastic deformation in the structure becomes very simple using the force analogy method, where the accumulation of plastic energy due to plastic rotations is exactly equal to the elastic moment multiplied by the change in plastic rotations. In addition, this plastic energy formula can be used for any material with predefined stress–strain relationship, and therefore the transfer of energy among various forms can be calculated at any specific time. Once the energy equation is derived, numerical analyses are performed on a single degree of freedom system to study the characteristics of energy transfer. This is then extended to study the transfer of energy among various forms in a multidegree of freedom system. These two studies show that the analytically derived equation for plastic energy is accurate in studying the structural energy response due to earthquake excitations.     

Improved Decentralized Method for Control of Building Structures under Seismic Excitation

A decentralized control method with improved robustness and design flexibility is proposed for reducing vibrations of seismically excited building structures. In a previous study, a control scheme was developed for multistory building models using nonlinear, decentralized control theory. This control method has now been improved in this study in that less information about material properties and geometrical parameters of the building is needed and the selection of control design parameters is more flexible. The nonlinear behavior of the proposed control system is studied and its stability property is proven mathematically. To evaluate the effectiveness and robustness of the proposed method, three illustrative structural models, i.e., an eight-story elastic shear beam model, a two-story nonlinear elastic shear beam model, and a 20-story elastic benchmark model are studied. The 1940 El Centro and the 1995 Kobe earthquakes are used in these examples. The performance of the current control design, as applied to these examples, has shown to be more effective in reducing structural responses and improving robustness.     

Wavelet-Hybrid Feedback Linear Mean Squared Algorithm for Robust Control of Cable-Stayed Bridges

Cable-stayed bridges are flexible structures, and control of their vibrations is an important consideration and a challenging problem. In this paper, the wavelet-hybrid feedback least mean squared algorithm recently developed by the writers is used for vibration control of cable-stayed bridges under various seismic excitations. The effectiveness of the algorithm is investigated through numerical simulation using a benchmark control problem created based on an actual semifan-type cable-stayed bridge design. The performance of the algorithm is compared with that of a sample linear quadratic Gaussian (LQG) controller using three different earthquake records: the El Centro (California, 1940), Mexico City (Mexico, 1985), and Gebze (Turkey, 1999) earthquakes. Simulation results demonstrate that the new algorithm is consistently more effective than the sample LQG controller for all three earthquake records. Additional numerical simulations are performed to evaluate the sensitivity of the new control algorithm. It is concluded that the algorithm is robust against the uncertainties existing in modeling structures.     

Experiments on a Full-Scale Building Model using Modified Sliding Mode Control

This paper presents a modified sliding mode control (MSMC) method using acceleration feedback to reduce the response of seismic-excited civil buildings. A pre-filter is introduced prior to the control command so that a systematic trade-off between control and structural responses can be achieved. To demonstrate practical implementation of MSMC controllers, extensive shake table experimental tests have been conducted on a full-scale three-story building equipped with active bracing systems at the National Center for Research on Earthquake Engineering, Taiwan. To improve the effectiveness of active control, a nominal system that incorporates the control–structure interaction effect is used in the MSMC controller design. In addition, existing system uncertainties in the nominal system resulting from system identification are considered in the process of controller design and the robustness of control performance and stability is demonstrated through shake table experiments. Experimental results indicate that the MSMC strategy using acceleration feedback for the full-scale building is robust and its performance is quite remarkable. Furthermore, the numerical simulation based on an analytical model that was identified previously by taking into account the control–structure interaction effect was conducted and comparisons are made with the experimental results. It is shown that the correlation between numerical simulation results and experimental data is quite excellent.     

Detection of Changes in Global Structural Stiffness Coefficients Using Acceleration Feedback

This technical note presents an extension of a previous study where two methods for detecting structural damage have been developed by using displacement and velocity measurements. In this study, acceleration feedback is used in detecting changes in global structural stiffness coefficients of lumped-mass-shear-beam models. The previously developed method relies on the decoupling of effects of changes in stiffness at different locations and the use of displacement or velocity feedback has proven to be effective. Extension to the use of acceleration feedback using existing formulation is not trivial in that the desired decoupling effect cannot be achieved by simple coordinate transformation because the acceleration itself is directly related to the stiffness coefficients. An approach to circumvent this difficulty is presented and it involves increasing the order of time derivatives of the linear system so that the acceleration becomes the “velocity” of the new system. The performance of the proposed method is demonstrated using an illustrative example of a three-story model with stiffness changes at different floors. Numerical studies are also conducted to evaluate the time horizons required to normalize monitor outputs for the effective and efficient detection of stiffness changes.     

Space Structures: Issues in Dynamics and Control

A selective technical overview is presented on the vibration and control of large space structures, the analysis, design, and construction of which will require major technical contributions from the civil∕structural, mechanical, and extended engineering communities. The immediacy of the U.S. space station makes the particular emphasis placed on large space structures and their control appropriate. The space station is but one part of the space program, and includes the lunar base, which the space station is to service. This paper attempts to summarize some of the key technical issues and hence provide a starting point for further involvement. The first half of this paper provides an introduction and overview of large space structures and their dynamics; the latter half discusses structural control, including control‐system design and nonlinearities. A crucial aspect of the large space structures problem is that dynamics and control must be considered simultaneously; the problems cannot be addressed individually and coupled as an afterthought.     

General Approach for Training Back-Propagation Neural Networks in Vibration Control of Multidegree-of-Freedom Structures

A general approach is proposed for back-propagation training of multilayer feed-forward (MLFF) neural networks for active control of earthquake-induced vibrations in multidegree-of-freedom structures. The training functions for adjustment of connection weights of the neural network controller are formulated in the proposed approach by minimizing a general cost function using the steepest gradient descent scheme. The proposed method can be applied for training an MLFF neural network controller in vibration control of building structures both in the pattern (online) and batch (off-line) mode. The method can be implemented in structural control systems with more than one control action. Case studies are presented to demonstrate the feasibility of implementing the training approach for effective vibration control of structures subjected to earthquake ground motions.     

冷轧机机架间张力预测函数控制器的设计

由于常规PID控制器的参数往往针对一种情况进行整定,很难保持冷连轧张力始终处于一个好的控制状态。在分析了张力控制原理的基础上,应用预测函数控制设计了辊缝式调张法张力控制系统,用预测函数控制,其控制量计算方程简单,实时控制计算量小,达到了张力控制的精度要求,仿真结果证明了该控制器显著提高了系统的动态响应性能,其控制效果优于常规PID控制器。     

Implementation of Modal Control for Seismically Excited Structures using Magnetorheological Dampers

This paper proposes an implementation of modal control for seismically excited structures using magnetorheological (MR) dampers. Many control algorithms such as clipped-optimal control, decentralized bang-bang control, and the control algorithms based on Lyapunov stability theory have been adopted for semiactive systems including MR dampers. In spite of good features, some algorithms have drawbacks such as poor performance or difficulties in designing the weighting matrix of the controller. However, modal control reshapes the motion of a structure by merely controlling a few selected vibration modes. Hence a modal control scheme is more convenient to design the controller than other control algorithms. Although modal control has been investigated for several decades, its potential for semiactive control, especially for the MR damper, has not been exploited. Thus, in order to study the effectiveness for a MR damper system, a modal control scheme is implemented to seismically excited structures. A Kalman filter is included in a control scheme to estimate modal states from measurements by sensors. Three cases of the structural measurement are considered by a Kalman filter to verify the effect of each measurement; displacement, velocity, and acceleration, respectively. Moreover, a low-pass filter is applied to eliminate the spillover problem. In a numerical example, a six-story building model with the MR dampers on the bottom two floors is used to verify the proposed modal control scheme. The El Centro earthquake is used to excite the system, and the reduction in the drifts, accelerations, and relative displacements throughout the structure is examined. The performance of the proposed modal control scheme is compared with that of other control algorithms previously studied. The numerical results indicate that the motion of the structure is effectively suppressed by merely controlling a few lowest modes, although resulting responses varied greatly depending on the choice of measurements available and weightings.     

Performance of Masonry Stone Buildings during the March 25 and 28, 2004 A?kale (Erzurum) Earthquakes in Turkey

This paper reviews the performance of stone masonry buildings during the March 25 and 28, 2004, A?kale (Erzurum) earthquakes. A?kale is a township located 35?km from Erzurum city in Turkey. A majority of the buildings in the affected region are built in masonry. Most of the masonry buildings were formed with random or coursed stone walls without any reinforcement supporting heavy clay tile roofing over wooden logs. A large number of such buildings were heavily damaged or collapsed. The cracking and failure patterns of the buildings are examined and interpreted relative to current provisions for earthquake resistance of masonry structures. The damages are due to several reasons such as site effect, location, and length of the fault, and the poor construction quality of the buildings. In addition to these reasons, the two earthquakes hit the buildings within three days, causing progressive damage. Low strength stone masonry buildings with mud mortar are weak against earthquakes, and should be avoided in high seismic zones.     

Robust Control for Structural Systems with Unstructured Uncertainties

Natural hazards, such as earthquakes and strong wind events, place large forces on tall, slender structures and on long-span bridges. In view of the numerous uncertainties due to model errors, stress calculations, material properties, and environmental loads, the structural system is uncertain. Here, the Lagrangian representation is modeled as an uncertain state-space model. The paper develops a robust active control approach with uncertainties in not only the system and control input matrices, but also the disturbance input matrices. Robust active control provides both robust relative stability and H∞ disturbance attenuation. The H∞ norm of the transfer function from the external disturbance forces (e.g., earthquake, wind, etc.) to the observed system states is restricted by a prescribed attenuation index. The uncertainties considered herein are norm-bounded unstructured uncertainties. Preservation of H2 optimality of robust structural control is also revealed. The results may be further extended to structured uncertainties. A numerical example illustrates that the approach may be applied to robust control of structural systems under earthquake excitation.