DEVELOPMENT AND OPTIMIZATION OF CONTROLLERS FOR MITIGATION OF SEISMIC VIBRATIONS

Abstract

Seismic vibrations induce additional stresses to the structures, which are harmful to their health. During the last three decades especially, since the introduction and unparalleled improvement of deployable computer systems, researchers and practicing engineers have studied the use of control technology to reduce the potential damage caused to these civil structures, particularly tall buildings by earthquakes. The motive of the structural control is to reduce the seismic vibration by supplying adequate counterforce by means of changing the stiffness, and/or altering the damping with the help of external active, passive or semi-active devices. In this study, semi active control scheme is considered due to its advantages over the other schemes. Semi active control schemes use lesser power and yet provide performance at par with the active control schemes and stability of passive control schemes. Magnetorheological dampers (MR damper) are commonly used devices among the various available external semi active control devices. The MR damper can deliver a high level performance in the mitigation of seismic vibrations if an appropriately designed controller is utilized. Therefore, it is an interesting problem to design an efficient and effective controller which can take the advantage of MR damper while implementing the semi-active control scheme. In this thesis, new control algorithms are developed in this direction. Proper selection of a controller dependent on the type of non-linearity present in the semiactive device, the available feedback measurements or the number of devices to be implemented in the structure. To gauge the difficulty level in the selection and development of appropriate controller, some previously used controllers are implemented initially. These controllers are the Passive ON/OFF, Double output feedback polynomial controller (DOFPC), the simple passive controller (SPC), the Lyapunov controller, the clipped-optimal LQR/LQG controller, Quasi bang bang controller, modified Quasi bang bang controller and the classic PID controller. These controllers are formulated for use with MR damper and evaluated for the best performance for a prototype three storey structure. It is observed that the controllers like Passive ON/OFF, Lyapunov, QBB, MQBB, SPC and DoFPC do not consider the feedback from the MR damper. These controllers continuously provide input command signal (electrical signal), based on the structural response, to the MR damper without considering its maximum capability whereas the controllers like clipped optimal LQR/LQG take the feedback from the MR damper and compare it with the desired force calculated by the control algorithm. Based on this comparison, the input signal is provided to the MR damper. Thus, clipped optimal LQR/LQG (CO-LQR/LQG) vi controllers have better control over the actuator`s (MR damper) input and therefore it is further studied in this work. In theory optimal controllers like LQR/LQG have a cost function which is to be minimized for the best performance. This cost function has constant weighting matrices namely state weighting matrix Q and control weighting matrix R. Control weighting matrix R indicates the force to be imparted to the structure. In conventional LQR/LQG theory, it is customary to note that the values of these design parameters are decided at the time of designing the controller and cannot be subsequently altered. During an earthquake event, the response of the structure may increase or decrease, depending the quasi-resonance occurring between the structure and the earthquake. In this case, it is essential to modify the value of the design parameters of the conventional LQR/LQG controller to obtain optimum control force to mitigate the vibrations due to the earthquake. A few studies have been done to sort out this issue but in all these studies it was necessary to maintain a database of the earthquake. To solve this problem and to find the optimized design parameters of the LQR/LQG controllers in real time two approaches namely PSO-FFT and PSO-τp max are proposed to modify the control weighting matrix R for better control action at the quasi resonance. In PSO-FFT based approach, fast Fourier transform (FFT) is utilized to find the quasi resonance where the amplitude of the vibrations will be the maximum and the particle swarm optimization (PSO) is utilized to find the best value of control weighting matrix R to counter the effect of this quasi resonance. Two new controllers are developed based on PSO-FFT approach namely PSO-FFT-modified-LQR and PSO-FFT-modified-LQG. Similarly, in PSO- τp max based approach, the maximum dominant period (τp max) approach is used to find the quasi resonance and PSO is utilized to find the best value of control weighting matrix R to counter the effect of this quasi resonance. Unlike in PSO-FFT approach where dominant frequency is estimated in frequency domain, PSO- τp max approach works totally in time domain and is faster. The controllers developed based on the PSO-τp max approach are PSO- τp max -modified-LQR and PSO- τp max -modified-LQG. These controllers are evaluated on a three storey prototype structure for various conditions. For a robust evaluation of the proposed controllers, many conditions are considered. A detailed study is carried out for each condition. These studies are discussed below. To assess the performance of the developed controllers in the different seismic environment, the prototype structure is subjected to several recorded earthquake time histories. The analysis is carried out for the modified LQR/LQG controllers developed for both PSO-FFT and PSO- τp max approaches. The responses of the structure are analyzed and compared with the vii conventional clipped optimal LQR/LQG. Further, to make the evaluation consistent, the same conditions are considered as in [1]. The author established the supremacy of CO-LQR controller over the other controllers used in their research. Following the same methodology, the result analysis of current study demonstrates that the performance of the proposed modified LQR controller is superior than the CO-LQR controller. Similarly, proposed modified LQG controller performs better than the conventional CO-LQG controller. To find the best location for the placement of MR damper within the structure if only one MR damper is available. The performance analysis of the proposed controllers is carried out keeping the MR damper at first, second and the third floor respectively. Further, an analytical study is presented for the assessment of the performance of the developed controllers if power vanishes at the peak of the seismic event. It is very likely to happen amid the seismic activity. To assess the performance of the developed controller for the structures in different soil conditions, a study is also carried out by subjecting the prototype structure to an earthquake recorded in different soil conditions (i.e. hard, medium and soft soil). Further, to check the suitability of the proposed controllers for higher modes, a similar analysis is carried out for a five-storey structure as carried out for the three storey structure. Based on the analysis carried out in this thesis work, it is shown that the developed controllers based on the proposed two approaches (PSO-FFT and PSO- τp max) deliver better performance for three storey as well as five storey structure as compared to conventional COLQR/ LQG controllers. Apart from these studies, a separate study has been carried out to develop PSO-modified quasi-bang bang controller to improve the performance of the modified quasi bang-bang controller which give command signal to actuator directly without considering the feedback from the MR damper. This controller is evaluated for the three DOF test structure subjected to several near-fault earthquake excitations and earthquake recorded in different soil conditions. It is shown that the PSO-modified quasi bang bnag controller performs better that the modified quasi bang bang controller. Moreover, a prototype hardware is also developed for this controller using ESP series microcontroller and three ADXL-435 accelerometers. For ease of the analysis a GUI is also developed using MATLAB.