Seismic response control of structures using novel adaptive passive and semi-active variable stiffness and negative stiffness devices

Current seismic design practice promotes inelastic response in order to reduce the design forces. By allowing the structure to yield while increasing the ductility of the structure, the global forces can be kept within the limited bounds dictated by the yield strength. However, during severe earthquakes, the structures undergo significant inelastic deformations leading to stiffness and strength degradation, increased interstory drifts, and damage with residual drift. The research presented in this thesis has three components that seek to address these challenges. To prevent the inelastic effects observed in yielding systems, a new concept “apparent weakening” is proposed and verified through shake table studies in this thesis. “Apparent weakening” is introduced in the structural system using a complementary “adaptive negative stiffness device” (NSD) that mimics "yielding” of the global system thus attracting it away from the main structural system. Unlike the concept of weakening and damping, where the main structural system strength is reduced, the new system does not alter the original structural system, but produces effects compatible with an early yielding. Response reduction using NSD is achieved in a two step sequence. First the NSD, which is capable of exhibiting nonlinear elastic stiffness, is developed based on the properties of the structure. This NSD is added to the structure resulting in reduction of the stiffness of the structure and NSD assembly or “apparent weakening”-thereby resulting in the reduction of the base shear of the assembly. Then a passive damper, designed for the assembly to reduce the displacements that are caused due to the “apparent weakening”, is added to the structure-thereby reducing the base shear, acceleration and displacement in a two step process. The primary focus of this thesis is to analyze and experimentally verify the response reduction attributes of NSD in (a) elastic structural systems (b) yielding systems and (3) multistory structures. Experimental studies on 1:3 scale three-story frame structure have confirmed that consistent reductions in displacements, accelerations and base shear can be achieved in an elastic structure and bilinear inelastic structure by adding the NSD and viscous fluid damper. It has also been demonstrated that the stiffening in NSD will prevent the structure from collapsing. Analogous to the inelastic design, the acceleration and base shear and deformation of the structure and NSD assembly can be reduced by more than 20% for moderate ground motions and the collapse of structure can be prevented for severe ground motions. Simulation studies have been carried on an inelastic multistoried shear building to demonstrate the effectiveness of placing NSDs and dampers at multiple locations along the height of the building; referred to as “distributed isolation”. The results reported in this study have demonstrated that by placing a NSD in a particular story the superstructure above that story can be isolated from the effects of ground motion. Since the NSDs in the bottom floors will undergo large deformations, a generalized scheme to incorporate NSDs with different force deformation behavior in each storey is proposed. The properties of NSD are varied to minimize the localized inter-story deformation and distribute it evenly along the height of the building. Additionally, two semi-active approaches have also been proposed to improve the performance of NSD in yielding structures and also adapt to varying structure properties in real time. The second component of this thesis deals with development of a novel device to control the response of structural system using adaptive length pendulum smart tuned mass damper (ALP-STMD). A mechanism to achieve the variable pendulum length is developed using shape memory alloy wire actuator. ALP-STMD acts as a vibration absorber and since the length is tuned to match the instantaneous frequency, using a STFT algorithm, all the vibrations pertaining to the dominant frequency are absorbed. ALP-STMD is capable of absorbing all the energy pertaining to the tuned-frequency of the system; the performance is experimentally verified for forced vibration (stationary and non-stationary) and free vibration. The third component of this thesis covers the development of an adaptive control algorithm to compensate hysteresis in hysteretic systems. Hysteretic system with variable stiffness hysteresis is represented as a quasi-linear parameter varying (LPV) system and a gain scheduled controller is designed for the quasi-LPV system using linear matrix inequalities approach. Designed controller is scheduled based on two parameters: linear time-varying stiffness (slow varying parameter) and the stiffness of friction hysteresis (fast varying parameter). The effectiveness of the proposed controller is demonstrated through numerical studies by comparing the proposed controller with fixed robust H∞ controller. Superior tracking performance of the LPV-GS over the robust H∞ controller in different displacement ranges and various stiffness switching cases is clearly evident from the results presented in this thesis. The LPV-GS controller is capable of adapting to the parameter changes and is effective over the entire range of parameter variations

Repetitive control of hysteretic systems using robust H-infinity controller

Unique properties of smart materials have enabled them to successfully replace conventional actuators and sensors. However, their effectiveness and applicability in control is hindered due to the presence of inherent hysteresis. In this thesis a systematic approach is developed to model this hysteresis in order to design a robust Hinfinity controller for tracking applications in one such smart material based actuator called Thunder actuator. The main objective of this work is to develop a controller to get rid of the delay, caused by the inherent hysteresis of the system, while following a commanded reference signal. To this end a mathematical model of the hysteretic system is developed and robust Hinfinity controller is developed for micro-position tracking control of the Thunder actuator. Tracking performance of compensated system is compared with open loop system for triangular and sinusoidal reference signals. Robustness of the developed Hinfinity controller is demonstrated and validated using experimental results. The first half of the thesis deals with the modeling of the Thunder actuator. Classical Preisach model is used to capture the hysteresis of the Thunder actuator. Congruency property and wiping-out property are verified and a classical Preisach model is developed for Thunder actuator using experimental data from first-order reversal curves. The Preisach model developed has been experimentally validated. Using Preisach model an equivalent time-invariant uncertain second order model is developed for Thunder actuator assuming variable stiffness and damping coefficients. The second half of the thesis involves designing a robust Hinfinity controller for the uncertain Thunder actuator model and validating the designed controller experimentally. Design of the controller is posed as a linear matrix inequality (LMI) problem and a mixed sensitivity optimal controller is calculated by minimizing the Hinfinity norm of the closed-loop system. Minimal tracking error is the performance criteria and noise rejection along with stability of the controller to time-invariant uncertainties are the robustness criteria in mixed sensitivity Hinfinity design. Full state robust controller is calculated for the nominal plant of the Thunder actuator. Robustness of the Hinfinity controller is verified through simulation and experimental studies. Experimental results demonstrate that the hysteresis loop-width of the Thunder actuator, in tracking sinusoidal and triangular signals, can be significantly reduced by using a robust- Hinfinity controller: this clearly demonstrates the effectiveness of the proposed control algorithm