Benchmark Problems in Structural Control: Part I -- Active Mass Driver System

paper (PDF, 181KB); AMD results

Abstract: This paper presents the overview and problem definition for a benchmark structural control problem. The structure considered - chosen because of the widespread interest in this class of systems (Soong 1990; Housner et al. 1994b; Fujino et al. 1996) - is a scale model of a three-story building employing an active mass driver. A model for this structural system, including the actuator and sensors, has been developed directly from experimentally obtained data and will form the basis for the benchmark study. Control constraints and evaluation criteria are presented for the design problem. A simulation program has been developed and made available to facilitate comparison of the efficiency and merit of various control strategies. A sample control design is given to illustrate some of the design challenges.

Benchmark Problems in Structural Control: Part II -- Active Tendon System

paper (PDF, 108KB)

Abstract: In a companion paper (Spencer, et al. 1997), an overview and problem definition was presented for a well-defined benchmark structural control problem for a model building configured with an active mass driver (AMD). A second benchmark problem is posed here based on a high-fidelity analytical model of three-story, tendon-controlled structure at the National Center for Earthquake Engineering Research (NCEER) (Chung et al. 1989; Dyke et al. 1996). The purpose of formulating this problem is to provide another setting in which to evaluate the relative effectiveness and implementability of various structural control algorithms. To achieve a high level of realism, an evaluation model is presented in the problem definition which is derived directly from experimental data obtained for the structure. This model accurately represents the behavior of the laboratory structure and fully incorporates actuator/sensor dynamics. As in the companion paper, the evaluation model will be considered as the real structural system. In general, controllers that are successfully implemented on the evaluation model can be expected to perform similarly in the laboratory setting. Several evaluation criteria are given, along with the associated control design constraints.

Modal Space Sliding Mode Control of Structures

paper (PDF, 710KB); AMD results

Abstract: For dynamical systems expressed in state space form or for systems with nonclassical damping, the reduction of the structural modal ento the modal coordinates involves complex modal anlysis with complex modal coordinates. Sliding mode control (SMC) is formulated herein in terms of such complex modal coordinates and the resulting control scheme is applied to the Benchmark problem (Spencer, Dyke, and Deoskar, 1997) consiting of the buulding-AMD system. Model reduction is achieved on the bases of the spectral analysis as well as wavelet analysis of the response of the system. Suitable provision is then provided to elminate the effects of the neglected higher modes on the control performance. It is seen that the performances of MS-SMC are comparable to those of LQG.

Application of Optimal Polynomial Controller to a Benchmark Problem

paper (PDF, 752KB); TEN results

Abstract: In this paper, we investigate the performance of optimal polynomial control for the vibration suppression of a benchmark problem; namely, the active tendon system. The optimal polynomial controller is a summation of polynomials of different orders, i.e., linear, cubic, quintic, etc., and the gain matrices for different parts of the controller are calculated easily by solving matrix Riccati and Lyapunov equations. A Kalman-Bucy estimator is designed for the on-line estimation of the states of the design model. Hence, the linear quadratic Gaussian (LQG) controller is a special case of the current polynomial controller in which the higher order parts are zero. While the percentage of reduction for displacement response quantities remains constant for the LQG controller, it increases with respect to the earthquake intensity for the polynomial controller. Consequently, if the earthquake intensity exceeds the design one, the polynomial controller is capable of achieving a higher reduction for the displacement response at the expense of control efforts. Such a property is desirable for the protection of civil engineering structures because of the inherent stochastic nature of the earthquake.

Synthesis of Controllers for the Active Mass Driver System in the Presence of Uncertainty

paper (PDF, 775KB); AMD results

Abstract: The structured singular value (µ) synthesis technique is used to design controllers for the Active Mass Damper (AMD) Benchmark problem. The motivation for using µ synthesis is its ability to directly incoporate performance and robustness objectives into a multivariable control design framework. In addition to stated performance objectives, robustness of the controllers to high frequency unmodeled dynamics (the neglected high frequency modes of the evaluation model), modeling error in the actuator dynamics and variations in the first structural natural frequency and damping value are considered in the design. The resulting controller achieves similar performance levels on the nominal evaluation model and the evaluation model with significant variations in its first natural frequency and damping value.

Neural Networks for Structural Control of a Benchmark Problem, Active Tendon System

paper (PDF, 754KB); TEN results

Abstract: Methodology for active structural control using neural networks has been proposed by Ghaboussi and his co-workers in the past several years. The control algorithm in the mathematically formulated methods is replaced by a neural network controller (neuro-controller). Neuro-controllers have been developed and applied in linear and nonlinear structural control. Neuro-controllers are trained with the aid of the emulator neural networks. The emulator neural network is trained to learn the transfer function between the actuator signal and the sensor reading and it uses that past values of these quantities to predict the future values of the sensor readings. In this paper, we apply the previously developed neuro-control method in the benchmark problem of the active tendon system. The emulator neural network is developed and trained using the evaluation model given in the benchmark problem with is considered to be the true representation of the active tendon system. However, a reduced order model has been developed and used, along with the emulator neural network, to train the neuro-controller. The evaluation model represents the three story steel frame structure, including the actuator dynamics. The absolute acceleration of the first floor and the actuator piston displacement are used as feedback. Three neuro-controllers, with different control criteria, have been developed and their performances have been evaluated with the prescribed performance indexes. The robustness of the neuro-controllers in the presence of some severe uncertainties, has also been evaluated.

Fuzzy Control of Structural Vibration. An Active Mass System Driven by a Fuzzy Controller

paper (PDF, 289KB); AMD results

Abstract: The authors are engaged in a long-term research project studying the potential of fuzzy control strategies for active structural control in civil engineering applications. The advantage of this approach is its inherent robustness and its ability to handle the non linear behaviour of the structure. Moreover, the computations for driving the controller are quite simple and can easily be implemented into a fuzzy chip.

In this paper attention is focused on the response of a three-storey frame, subjected to earthquake excitation, controlled by an active mass driver located on the top floor. The design and the implementation of the controller driving the AMD system are discussed.

Design of H_infinity Output Feedback Controllers for the AMD Benchmark Problem

paper (PDF, 283KB); AMD results

Abstract: This paper outlines a general approach for the design of H_infinity dynamic output feedback controllers and applies this method to designing controllers for the active mass driver (AMD) benchmark problem. The example controllers designed for this problem use acceleration output feedback of the structure coupled with the additional actuator sensors and ground motion sensor. Some of the key choices made by a control designer using this method are discussed and evaluated with example controllers. Several sets of controllers are developed to evaluate the sensitivity of controller effectiveness to the choice of regulator response quantities, the choice of feedback quantities, and the choice of when to apply model reduction. Results show that for this design approach, the best controller effectiveness is achieved by chosing to regulate the structural accelerations and displacements with the controller acceleration and command signal. In addition, the sensitivity of the dynamic controllers to the removal of available sensors is investigated, showing that the performance of the dynamic controllers for the nominal AMD model are insensitive to which sensors are available.

Limits of Achievable Performance and Controller Design for the Structural Control Benchmark Problem

paper (PDF, 928KB); AMD results

Abstract: In this work we give a methodology for controller design and analysis which accounts for design criteria such as: (a) optimal system response to external disturbances, (b) robustness to modeling uncertainty, and (c) constraints on the controller order. The methodology is applied to a structural control benchmark problem sponsored by the ASCE Committee on Structural Control. The structural system considered consists of a scale model of a three-story building employing an active mass driver to suppress ground motion disturbances. The methodology proved effective for obtaining a satisfactory low-order controller for this class of problems.

Multiobjective Optimal Structural Control of the Notre Dame Building Model Benchmark

paper (PDF, 360KB); AMD and TEN results

Abstract: Reduced-order, multiobjective optimal controllers are developed for the Notre Dame structural control building model benchmark. Standard H₂/LQG optimal control excels at noise and disturbance rejection, but may have difficulty with actuator saturation and plant uncertainty. The benchmark problem is adapted to a multiobjective optimal control framework, using l₁ and H-infinity constraints to improve controller performance, especially attempting to reduce peak responses, avoid saturation, and improve robustness to unmodelled dynamics. The tradeoffs between H₂ performance, output peak magnitudes, and robust stability are examined. Several optimal controllers and their performance on the benchmark are given.

Controllers for Quadratic Stability and Performance of a Benchmark Problem

paper (PDF, 842KB); AMD results

Abstract: Recently developed quadratic stability and performance control techniques are used to design controllers for the active mass driver (AMD) benchmark problem. Several designs are obtained and analyzed to highlight the utility of the proposed technique. Solution through the use of linear matrix inequalities is presented and extensions to systems with modeling error, actuator/sensor malfunction and saturating controllers are discussed. Simulation results indicate that the performance of the control techniques is quite remarkable.

Covariance Control using Closed Loop Modeling for Structures

paper (PDF, 787KB); AMD results

Abstract: This paper presents a low order controller design method, using closed loop modeling plus covariance control, with application to the benchmark problem in structural control for the active mass driver system at the University of Notre Dame (see Spencer, Dyke and Deoskar, 1997). This method finds a satisfactory controller by iterating between the closed loop modeling and the covariance control. The closed loop modeling implies that the model used for model-based control design is extracted from the feedback system of the last iteration. The covariance control finds the optimal controller to minimize an output variance and at the same time to bound the other output variances.

Probabilistic Control for the Active Mass Driver Benchmark Structural Model

paper (PDF, 386KB); AMD results

Abstract: A probability-based robust control design methodology is presented that is applied to the "benchmark system," which is a high-fidelity model of an active-mass-driver laboratory structure. For the controller design, the objective is to maximize the probability that the uncertain structure/controller system achieves satisfactory performance when subject to uncertain excitation. The controller's robust performance is computed for a set of possible models by weighting the conditional performance probability for a particular model with the probability of that model, then integrating over the set of possible models. This is accomplished in an efficient manner using an asymptotic approximation. The probable performance is then maximized over the class of constant-gain acceleration-feedback controllers to find the optimal controller. This control design method is applied to a reduced-order model of the benchmark system to obtain four controllers, two that are designed on the basis of a "nominal" system model and two "robust" ones that consider model uncertainty. The performance is evaluated for the closed-loop systems that are subject to various excitations.

Application of Ensemble Training of a Structural Controller to the AMD Benchmark Problem

paper (PDF, 1060KB); AMD results

Abstract: A benchmark structural control problem has been proposed in an attempt to evaluate the effectiveness of various control algorithms. The problem encompasses the design of an active mass damper (AMD) control system for a multi-degree-of-freedom (MDOF) building type structure subjected to earthquake-type excitation.

In vibration control for civil structures, linear quadratic optimal control is among the most popular techniques. Normally, this approach ignores the external excitation in the time-domain design process. In addition, this technique requires a full-order dynamic observer which is often unattainable. This paper focuses on the development of a new optimal control algorithm which includes the earthquake-type excitation explicitly in the design of control systems and the use of prescribed-order, output feedback controllers. In addition, this approach allows the inclusion of open-loop (feedforward) as well as closed-loop (feedback) control terms in the controller design.

The authors have previously designed an algorithm for full state feedback controllers trained on an ensemble of earthquakes. A cost functional is minimized on an ensemble of "known" earthquakes, using analytical gradient information, in order to determine constant control gains. The gradients are obtained in explicit form. The control system is then validated by testing on 'unknown' earthquakes.

The algorithm is now modified to develop a prescribed-order, output feedback controller for a specific MDOF system model.

A Study of Fixed Order Mixed Norm Designs for a Benchmark Problem in Structural Control

paper (PDF, 454KB); TEN results

Abstract: This study investigates the use of H₂, µ-synthesis, and mixed H₂/µ methods to construct full order controllers and optimized controllers of fixed dimensions. The benchmark problem definition is first extended to include uncertainty within the controller bandwidth in the form of parametric uncertainty representative of uncertainty in the natural frequencies of the design model. The sensitivity of H₂ design to unmodeled dynamics and parametric uncertainty is evaluated for a range of controller levels of authority. Next, µ-synthesis methods are applied to design full order compensators that are robust to both unmodeled dynamics and to parametric uncertainty. Finally, a set of mixed H₂/µ compensators are designed which are optimized for a fixed compensator dimension. These mixed norm designs recover the H₂ design performance levels while providing the same levels of robust stability as the µ designs. It is shown that designing with the mixed norm approach permits higher levels of controller authority for which the H₂ designs are destabilizing. The benchmark problem is that of an active tendon system. The controller designs are all based on the use of acceleration feedback.

Applications of Sliding Mode Control to Benchmark Problems

paper (PDF, 1087KB); AMD and TEN results

Abstract: In this paper, both the methods of continuous sliding mode control (CSMC) and continuous sliding mode control with compensators (CSMC&C) have been applied to two benchmark structures; namely, a building model equipped with an active mass driver system, and a building model equipped with an active tendon system. The CSMC&C strategy is a modification of CSMC to facilitate the design of static output feedback controllers and to provide a systematic tuning of the control effort. Due to the structural identification scheme used in the benchmark problems, in which the state variables are fictitious, one can not take the full advantages of static output feedback controllers. As a result, an observers is used in CSMC whereas a low-pass filter is incorporated for each measurement in CSMC&C. The purpose of using low-pass filters in CSMC&C is to transform the benchmark problems into strictly proper systems. The main advantage of the CSMC&C method is that the on-line computational effort is reduced since the dimension of filters and compensator is much smaller than that of an observer. Simulation results based on the CSMC and CSMC&C methods are presented and compared with that of the LQG method. Robustness of stability and noise rejection for each controller design are also illustrated by examining the loop transfer function. Simulation results for the benchmark problems indicate that the control performances for LQG, CSMC and >CSMC&C are quite comparable.

Robust Controller Design for the Active Mass Driver Benchmark Problem

paper (PDF, 347KB); AMD results

Abstract: In this paper we develop a robust controller design for the active mass driver (AMD) benchmark problem. The design process is based around the D-K iteration procedure for (complex) µ synthesis, together with a balanced truncation procedure to reduce the controller order. The final design is a third order linear controller, which utilizes only four accelerometer measurements, and has desirable rolloff properties (i.e., small required bandwidth, and a high degree of robustness). Despite the simplicity of the controller, it is able to yield quite good performance, while using only modest control authority.

Page designed by Erik A. Johnson (JohnsonE@usc.edu).