Events Calendar

Mahmoud Kamalzare Oral Defense

Speaker: Mahmoud Kamalzare , Astani CEE Ph.D. Candidate

Talk Title: Computationally Efficient Design of Optimal Strategies for Passive and Semiactive Damping Devices in Smart Structures

Abstract: In recent years, significant improvements in memory capacity and processing speed of computers have provided the ability of modeling and analyzing large and complex dynamical systems. These systems usually consist of many elements, of which some have nonlinear properties. Standard nonlinear solvers ignore the localized nature of the nonlinearities when computing responses, which can result in a very time-consuming process. However, since the nonlinearities are often limited to only a few of the many degrees of freedom (DOFs), an alternate method has been developed in which the nonlinear perturbation dynamics are excluded from the nominal linear system and evaluated based on the response of the nominal system. This reduces the high-order system to a much lower-order system of nonlinear Volterra integral equations (NVIEs), which provides a very computationally efficient solution. The total response of the system can be then easily calculated using superposition.
This study adapts the methodology to provide a fast and computationally inexpensive method for designing control strategies implemented in but not limited to smart building structures. The development of control strategies for controllable passive dampers, i.e., semiactive damping devices, is complicated by the nonlinear and dissipative nature of the devices and the nonlinear nature of the closed-loop system with any feedback control. Control design for nonlinear systems is often achieved by designing a control for a linearized model since strategies for linear systems are straightforward. One such approach is clipped optimal control in which the desired damper forces are determined from an optimal controller (e.g., linear quadratic regulator (LQR), linear quadratic Gaussian (LQG), H2, etc.), which is designed assuming that the damping devices are fully linear actuators that can exert any forces (dissipative or non-dissipative), and a secondary bang-bang controller commands the controllable damper to exert forces as close as possible to the desired forces. However, designs using any linearized model generally results in suboptimal (and sometimes lousy) performance because the linear actuator assumption differs from the actual implementation with a dissipative damping device. Thus, one must generally resort to a large-scale parameter study (or performing an optimization algorithm) in which the nonlinear system is simulated many times to determine control strategies that are actually optimal for the nonlinear controlled closed-loop system. Herein, it is demonstrated how the proposed approach can significantly decrease the computational burden of a complex control design study for controllable dampers.

Next, this study expands the applicability of the proposed method by demonstrating that the approach can also be adapted to accommodate the more realistic cases when, instead of full-state feedback, only a limited set of noisy response measurements are available to the controller, which requires incorporating a Kalman filter estimator, which is linear, into the nominal linear model. Furthermore, since the primary controller is rarely designed using a high-order model (because it is impractical due to numerical difficulties, as well as often unnecessary since high-order models, such as complex finite element structure models, have high frequency dynamics that remain mostly unexcited by an external disturbance), to bring the method to full maturity, a reduced-order model for control design is incorporated with the full model to simulate semiactively controlled structural responses using the proposed NVIE approach. Finally, it is explained briefly how the proposed approach can be implemented when uncertainties are involved in the system.

This dissertation provides a broad and comprehensive methodology for designing control strategies for smart structures using the proposed computationally efficient method. Numerical results confirm the accuracy, stability, and computational efficiency of the proposed simulation methodology and specifically show about two orders of magnitude speed up relative to the conventional solvers for the typical semiactive design parameter studies.

Location: 209 Conference Room

Audiences: Everyone Is Invited

Contact: Evangeline Reyes