Java-Powered Simulator for Structural Vibration and Control


Table of Contents

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Modified by Yoshinori Satoh and Erik A. Johnson

Go to the Java-Powered Simulation for Structural Vibration and Control



Welcome to the help page for the Java-Powered Simulation for Structural Vibration and Control. This program allows you to compare the effect of using two different control systems to reduce the structural response of an "uncontrolled" structure subjected to earthquake excitation. The two control systems, chosen because of the widespread interest in this class of systems (Soong 1990; Housner et al., 1994; Fujino et al. 1996), are the tuned mass damper (TMD) and the hybrid mass damper (HMD). Note that such controllers can be experimentally verified using the benchscale AMD experiment manufactured by Quanser Consulting, Inc.

This program allows you to vary the control system properties and control objectives and to perform "what if" studies so as to better understand the control design process. The program can calculate and animate the structural responses under the El Centro, Hachinohe, Northridge and Kobe earthquakes, as well as determine the transfer functions of the uncontrolled and controlled systems. Three cases can be considered:

[picture of java page]


How to Use the Program

Structural Parameters

TMD/HMD Parameters

LQR Control Weights

An LQR controller is calculated based on a quadratic performance index (see Technical Background) that weights the structural responses. The parameters q1-q4 weight the following responses:

q1 - structural displacement.
q2 - HMD displacement.
q3 - structural velocity.
q4 - HMD velocity.
The weighting on the control action is taken to be unity.

Radio Buttons

Check the radio buttons to indicate which responses you wish to display.

Response Window Zooming

Width of the excitation/response windows (in seconds) used during the animation. If your computer can't display the animation smoothly, please make this number smaller.

Ground Motion Scaling

Scale used for the motion of the ground in the animation. The ground motion may not be very noticeable in the animation when the same scale is used for both the structural response and the ground motion. The ground displacements are multiplied by the value in this box before they are displayed in the animation. This scale factor does not affect the response calculations nor does it affect the animation when the Relative Motion option is selected in the Animation Frame. An upper limit is set on the value so as to keep the animation within the window boundaries. The default value is 1.

Action Buttons

Animation Frame

The animation frame shows the structural system as it undergoes the earthquake excitation. Each of the three cases mentioned above can be animated by appropriate selection in the left menu associated with this frame. Also, you can choose to animate absolute or relative motion of the structure. Absolute Motion displays the response of the structure from an inertial reference frame. Thus, the motion of the ground is seen here. Relative Motion shows the response of the structure from a reference frame attached to the base of the structure.

Earthquake Signal Frame

The earthquake signal frame shows the current earthquake signal you are now using. There are four earthquake signals you can use:

You can choose to display the displacement or the acceleration corresponding to each earthquake signal. The strong motion data used in the Java program can be download from here.

Bode Plot Frame

The bode plot frame can display the magnitude plot and phase plot for the transfer function from ground acceleration to structural displacement, structural velocity, structural acceleration, TMD/HMD displacement, TMD/HMD velocity, TMD/HMD acceleration or control actuator force. The particular transfer function displayed corresponds to the response shown in the Time Response Frame.

Time Response Frame

The time response frame displays the system's response due to the earthquake signal shown in the Earthquake Signal Frame. It can show the structural displacement, structural velocity, absolute structural acceleration, TMD/HMD displacement, TMD/HMD velocity, absolute TMD/HMD acceleration or control actuator force. Peak response information is displayed in the lower portion of this frame.


Technical Background

Definition of the Primary Parameters

Mathematical Model

Control Design

For the control design, state feedback with noiseless measurements is assumed. By using the LQR optimal algorithm, the optimal gain matrix K is calculated such that the actuator driven signal u = -[K]*z minimizes the quadratic cost function

J = 0.5 * int(z'*[Q]*z+u^2,t=0..infinity)

for the continuous-time state-space model given above where Q is the state weighting matrix with the form:

[Q] = diag([q_1 q_2 q_3 q_4])

Recall that the weighting on the control signal is unity. Here the ground acceleration is treated as an external disturbance for the HMD system.

The optimal gain matrix K is derived from S by K = inv(R)*B'*S, which is the solution of the associated Algebraic Riccati Equation

A'S + SA - SB*inv(R)*B'S + Q = 0

Algorithms for the solution of the Algebraic Riccati Equation are thoroughly discussed in Arnold and Laub (1984).

Closing the feedback loop with an optimal gain matrix K, the system model has the following form:

(dz/dt) = [A-BK]*z + [E]*(d^2x_g/dt^2)

Although the actuator dynamics are not accounted for in the analysis, the role of actuator dynamics and control-structure interaction is important to the design of the protective systems such as the HMD system (Dyke et al., 1995). Future versions of the program will include these phenomena, as well as allow for investigation of output feedback methods.


Experimental Verification

[structure picture]

Experimental verification of structural control strategies is essential for eventual full-scale implementation (Dyke et al., 1996a,b). However, few researchers have facilities readily available to them that are capable of even small-scale structural control experiments. Recently, a bench-scale structural model of a building with an active mass driver has been developed that portrays the salient aspects of full-scale structural control implementations, including: control-structure interaction, actuator and sensor dynamics, actuator saturation effects, limited availability of sensors, output feedback design and digital control implementation (Battaini et al., 1998). This active control experiment, designed and manufatured by Quanser Consulting, Inc., has been shown to be an effective tool for education and for familiarizing practitioners with control system design and the associated challenges.



The support of the National Science Foundation under Grant No. CMS 95-28083 (Dr. S.C. Liu, program director) is gratefully acknowledged. In addition, we would like to thank Prof. Yozo Fujino of the University of Tokyo for his help in securing the Kobe and Hachinohe earthquake records.


Additional References

  1. Arnold W.F., III and Laub A.J. (1984). "Generalized Eigenproblem Algorithms and Software for Algebraic Riccati Equations," Proc. IEEE, 72, pp. 1746-1754.

  2. Battaini, M., Yang, G., Spencer Jr., B.F. (1998). "Bench-Scale Experiment for Structural Control," Journal of Engineering Mechanics, ASCE, in press.

  3. Dyke S.J., Spencer Jr. B.F., Quast P. and Sain M.K. (1995). "The Role of Control Structure Interaction in Protective System Design," Journal of Engineering Mechanics, ASCE, Vol. 121, No. 2, pp. 322-338.

  4. Dyke, S.J., Spencer Jr., Quast P., Kaspari Jr., D.C. and Sain, M.K. (1996a). "Implementation of an Active Mass Driver Using Acceleration Feedback Control," Microcomputers in Civil Engineering: Special Issue on Active and Hybrid Structural Control, Vol. 11, pp. 305-323.

  5. Dyke, S.J., Spencer Jr., B.F., Quast, P., Sain M.K., Kaspari Jr., D.C. and Soong, T.T. (1996b). "Acceleration Feedback Control of MDOF Structures," Journal of Engineering Mechanics, ASCE, Vol. 122, No. 9, pp. 907-918.

  6. Fujino, Y., Soong, T.T. and Spencer Jr., B.F. (1996). "Structural Control: Basic Concepts and Applications," Proceedings of the ASCE Structures Congress XIV, Chicago, Illinois, pp. 1277-1287.

  7. Housner, G.W., Masri, S.F. and Chassiakos, A.G., Eds. (1994). "Proceedings of the 1st World Conf. on Structural Control," Pasadena, CA..

  8. Soong, T.T. (1990). "Active Structural Control, Theory and Practice," Longman Scientific and Technical, Essex, England.