DYNAMIC LOAD SIMULATOR (DLS): STRATEGIES AND APPLICATIONS

Transcription

1 15th ASCE Engineering Mechanics Conference June 2-5, 2002, Columbia University, New York, NY EM 2002 DYNAMIC LOAD SIMULATOR (DLS): STRATEGIES AND APPLICATIONS Swaroop Yalla 1, Associate Member ASCE and Ahsan Kareem 2, Member ASCE ABSTRACT This paper describes the development of a new type of testing facility for simulating dynamic loads referred to as Dynamic Load Simulator (DLS). The DLS employs multiple actuators to simulate dynamic loading environments such as wind, wave and earthquake effects and may be used as an alternative to conventional facilities such as wind tunnels, wave tanks and shaking tables. Control of multiple-actuators is difficult due to the inherent problem of cross-coupling, which implies that each actuator affects the dynamics of other outputs. In order to compensate for these interactions, a new type of coupled control system using the nonlinear control system toolbox in MATLAB TM has been developed in this study. This technique solves the time-domain control parameter-tuning problem as a constrained optimization problem. An application of the DLS system for applying simulated wind loading utilizing two-point correlated signals is presented in this paper. The simulated loading time histories match the target values with high fidelity. Keywords: Dynamic Load Simulator, Natural Hazards, Force-feedback, Nonlinear Control, Structural Testing INTRODUCTION In the face of an increasing vulnerability of the built environment to the devastating forces of nature, the structural engineering community is faced with the major challenge of finding new techniques and devices for testing and validating structural performance under the dynamic load effects. Simulation systems that can mimic the natural environment in the laboratory from a set of field measurements are often very important for gauging the reliability of the structural system. Other applications may include, e.g., for evaluation of motion control devices or the fatigue life of building components. To address these needs, a pilot dynamic load simulator (DLS) was designed and developed by the authors in the NatHaz Modeling Laboratory ( University of Notre Dame for simulating wind, wave or earthquake loads on structures. The pilot DLS was based on a force-feedback control system that could directly mimic dynamic loads (Reinhold and Kareem, 1996; Kareem et al. 1997). The loads generated by a DLS can be introduced to a structure 1 Exponent Failure Analysis Associates, Menlo Park, CA syalla@exponent.com 2 Dept. of Civil Eng. & Geo. Sciences, University of Notre Dame, Notre Dame, IN kareem@nd.edu

2 through a reaction wall or gantry frame. This system is envisioned as a low-cost test simulator, which can be readily assembled using existing equipment in typical structural dynamics laboratories. This paper briefly describes the setup, control system needed to control the actuators and an application for simulating wind loads onto a test structure. DESCRIPTION OF THE SYSTEM The development of a first generation of dynamic load simulator prototype was discussed in Yalla et al The prototype was tested using an aluminum beam with end supports that permitted convenient change in the beam span. This system has been extended to test multi-input multi-output (MIMO) system as shown in Fig.1. A cantilever type structure with two lumped masses is attached to two actuators. The actuator assembly is in turn mounted on a rigid reaction frame. The actuators used in this system are electro-mechanical type with a ball screw couched in two linear motion guide raceways on each side, which provide an extremely rigid and highly accurate actuator transfer function. The actuator is driven by a DC servomotor, which is attached to the motor mounting flanges. The computer-controlled system was implemented using WinCon TM real-time system, which uses MATLAB/SIMULINK TM for control system prototyping. The C-code generation and subsequent download on the DSP chip was performed using Real-time Workshop and Real-time interface from Mathworks, Inc. Data acquisition was accomplished using MultiQ-3 TM board. This board is equipped with 8 single ended analog inputs, 8 analog outputs, 16 bit digital input/output, as well as 8 encoder inputs. A spectrum analyzer from DSPT Technology Inc., SigLab TM was used for obtaining the frequency response functions. actuator Reaction frame F 1 loadcell F 2 Lumped mass FIG. 1. Photograph and schematic of the DLS experimental setup 2

3 A target time history of the desired force is introduced in the computer as an input, which is converted to an analog signal using a DAC (digital-to-analog) converter. This signal is then amplified and fed into the servomotor, which drives the actuator. The stroke of the actuator creates a force on the test specimen/structure while an axial load cell placed in between the actuator and the specimen, measures the actual force imparted to the structure and sends the signal back to the computer using an ADC (analog-to-digital) converter. The error between the measured force and the applied force is corrected using a controller, which is discussed in the next section. CONTROL STRATEGY Since the system under study is a multi-actuator system, the issue of control is not as straightforward as a single actuator system. For optimal control, some prior information of the testing system and the test structure itself (system identification) is required. This is usually obtained before the actual testing or during testing (for on-line adaptive nonlinear type control). In a single-actuator system, the control system can be designed based on judgment or using well-defined rules such as Ziegler-Nichols scheme for PID controllers. However, for multi-actuator systems, this becomes an arduous task since the number of control gains becomes large. Secondly, multiple exciters induce interactions (cross-coupling) between each input-output of a MIMO system. This implies that for an accurate control, the system should have the capability to suppress undesired disturbances induced by other actuators (cross-coupling compensation). In a coupled control system, the objective is to design a MIMO PID controller, which can compensate for the cross-channel coupling. This kind of constrained optimization is automated using the nonlinear control design (NCD) toolbox of MATLAB TM (Potvin, 1993). The main difference between the NCD approach from the conventional optimal control LQG/H 2 type approach is that instead of framing the control design in terms of minimizing various norms of weighted transfer functions and tuning the response by tweaking the weights, i.e., Q and R matrices, the NCD approach utilizes the time domain constraint paradigm. The NCD toolbox essentially transforms the constraints and simulated system output into an optimization problem of the form, min x γ s.t. g ( x) wγ 0 ; xl x xu (1) where x is a vector of tunable variables and x l and x u are the lower and upper bounds on the variables. The vector g(x) is a vector of constraints imposed and w is a vector of weightings on the constraints. This scheme permits inclusion of inherent uncertainties in the various system parameters, which results in a more robust design. The first step was to obtain the transfer function matrix of the open-loop system. These were obtained using band-limited white noise as the excitation to each input of the system and then measuring the system output. These experimentally obtained transfer functions were then curve-fitted using frequency domain system identification techniques. The MIMO PID controller parameter-tuning problem was solved using the NCD toolbox in MATLAB. The control design scheme is shown schematically in Fig. 2. The optimization loop iteratively searches for the optimum set of tuning parameters, which satisfy the time-domain constraints in the output response. The MIMO PID controller for tracking problems involves sequentially stepping the 3

4 command step inputs. When the first channel steps (i.e., a step input is applied), the first output should track the step while the other channels should reject the channel and vice-versa. Before optimization, the system response is coupled and is not meeting the constraints. This means that when the first actuator steps, the second actuator is also producing a response to the excitation. The NCD toolbox effectively tunes the 12 parameters (4 parameters each in P-I-D matrices) under a total of 6012 constraints to provide the solution, which results in an optimum control performance. The details of this scheme are not presented here and will be documented in a full-length paper. Tunable parameters PID gains: K p, K i, K d Nonlinear Optimization loop Fig. 2: Nonlinear Control Design methodology APPLICATIONS For applications, certain limitations of the DLS need to be clearly understood. Unlike conventional test facilities, for e.g., wind tunnels, wave tanks, etc., where continuous space-time variations of aerodynamic and hydrodynamic pressure fields and inertial loads are introduced to model the effects of wind, waves or earthquakes. On the other hand, DLS provides discrete point loads to produce global load characteristics by taking into account the overall spatio-temporal correlation (Fig. 3). A suite of different loading cases: sinusoidal, wind loading with high and low correlations, seismic loading and non-gaussian loading cases were implemented on this system. Due to space constraints, only one of the loafing cases, namely correlated wind loading is presented in this paper. 4

5 F 1 V g (wind) F 2 η (wave) & x& g (earthquake) Continuous loading system Discrete loading system Fig. 3: Comparison between continuous and discrete loading system Time-histories for simulated fluctuating components of wind forces for a 2DOF system are input to the DLS system. Two loading cases are considered: wind loads with high and low correlation. In a typical wind excited structure, the correlation between the wind loads at two points decreases as the distance between the two points increases. The low correlation signals were selected from two well-separated locations whereas the higher correlation case involved two closely spaced locations. The time histories of wind forces were generated using a multi-variate simulation based on prescribed power spectral density matrix with natural correlation structure (Gurley and Kareem, 1998). Figure 4 shows that the two actuators reproduced, with high fidelity the two input signals. Fig. 4: Simulation of Wind Loading with (a) high correlation and (b) low correlation 5

6 CONCLUSIONS The development of new testing facility, namely the Dynamic Load simulator (DLS) is described in this paper. A new type of coupled control system using the nonlinear control system toolbox in MATLAB has been developed in this study. This technique solves the time-domain control parameter-tuning problem as a constrained optimization problem. The demonstrated success in generating a wide range of signals with high repeatability and robustness suggests that the DLS concept will be ideal for fatigue testing of structural components under multiple-correlated loads. The development of a full-scale real-time DLS which utilizes high capacity electro-mechanical actuators with existing support structure in structural testing laboratories will be a valuable tool for testing structures under realistic wind, wave and earthquake loads. ACKNOWLEDGMENTS The authors were supported in part by Grant # CCS by the Lockheed Martin Idaho Technologies and the NSF Grant # CMS This support is gratefully acknowledged. Any opinions, findings, or recommendations expressed in this paper are those of the authors and do not necessarily represent the views of the sponsors. REFERENCES Gurley, K. and Kareem, A. (1998), Simulation of Correlated Non-Gaussian Pressure Fields, MECCANICA, Vol. 33, NO. 3, Kareem, A., Kabat, S., Haan, Jr., F.L., (1997) Dynamic Wind Load Simulator, Proceedings of the 8th U.S. National Conference on Wind Engineering, Baltimore, MD. Potvin, A.F. (1993), Nonlinear Control Design Toolbox, Mathworks Inc., Natick, MA. Reinhold, T.A., and Kareem, A., (1996) Next Generation of Wind Test Facilities: A Feasibility Study, Proceedings of the 2nd International Workshop of Structural Control, Next Generation of Intelligent Structures, Hong Kong, Dec Yalla, S.K., Kareem, A., Kabat, S. and Haan, F.L., Jr. (2001), Dynamic Load Simulator: The development of a prototype, Journal of Engineering Mechanics, ASCE, 127(12),