Clipped-optimal Control Research Articles

Adaptive semiactive control of structure with magnetorheological dampers using wavelet packet transform

Conventional active controllers generally adopt initial dynamic properties of intact structures to calculate optimal control force for magnetorheological damper, which eventually leads to ideal damping force of the device. Also, they cannot assure trade-off between damping force and response reduction under non-stationary excitations. To this end, an adaptive semiactive control algorithm for magnetorheological damper is proposed. Using wavelet packet transform, an improved control law determines optimal control forces in terms of resonant and non-resonant frequency bands in time interval. Both frequency bands are established based on natural frequency(ies) of structures, making damping force rely on actual structural properties and achieving trade-off under non-stationary disturbances. A refined clipped-optimal control algorithm is then deployed to convert optimal control force to the device’s voltage. A numerical study of a six-degree-of-freedom structure under four near- and far-fault ground accelerations reveals that the scheme outperforms existing controllers while attaining cost-effectiveness of damping force versus response alleviations.

Methodology to minimize the dynamic response of tall buildings under wind load controlled through semi-active magneto-rheological dampers

This paper proposes a methodology to evaluate and optimize the dynamic response of tall buildings under wind loading, controlled through semi-active Magneto-Rheological dampers (MR dampers). For this, a tall building, modeled as a 2D frame, is taken as case study and three structural control configurations are proposed. The original structural configuration of the building is the first configuration analyzed, called Uncontrolled Original (C1). In the second configuration, called Uncontrolled Optimized (C2), the fundamental frequency of the building is optimized via PSO algorithm as a function of its mass. Then, in the third configuration, Controlled Optimized (C3), a set of MR dampers with behavior formulated via the modified Bouc-Wen rheological model and controlled through the Linear Quadratic Regulator associated with the Clipped Optimal control strategy (LQR-CO) is applied to the structure. Finally, the dynamic response of the three scenarios under wind action is analyzed and compared to performance criteria established in the literature. The results demonstrate that the C3 configuration is the only one able of satisfying all the established performance criteria, proving that the proposed methodology y that combines structural optimization with MR dampers is a powerful tool for vibration control.

A New Methodology for Optimal Design of Hybrid Vibration Control Systems (MR + TMD) for Buildings under Seismic Excitation

This study proposes a new methodology, based on the optimization procedure by a metaheuristic algorithm, for designing a hybrid vibration control system to mitigate the dynamic response of buildings under nonstationary artificial earthquakes (NSAEs). For illustration purposes, a 10-story shear building is studied. The hybrid control system involves the use of an MR damper (MR) and a tuned mass damper (TMD) located in different places of the structure. To describe the behavior of the MR, the modified Bouc–Wen model (MBW) was used. To calculate the damping force of the MR, the clipped optimal control associated with linear quadratic regulator (LQR), CO-LQR, was considered. The optimization was performed using the whale optimization algorithm (WOA) and seismic load generated by the Kanai–Tajimi spectrum. Different control scenarios were evaluated: MR-OFF, MR-ON, CO-LQR, STMD, and CO-LQR (MR + TMD) to determine the best control scenario that can effectively control the structure. Overall, the optimized hybrid control scenario (MR + TMD) was the only one able to adapt all story drifts to the control criterion of the consulted normative. Then, CO-LQR (MR + TMD), designed via the methodology proposed in this work, proved to be the best alternative to control the seismic response of this building.

Semi-active control of buildings using different control algorithms considering SSI

In current work, a comprehensive study on control algorithms with the presence of soil-structure interaction (SSI) effects is presented. Algorithms used in this study are Clipped-Optimal Control (COC), Lyapunov, Bang-Bang and Fuzzy with two Passive-On (P-On) and Passive-Off (P-Off) cases. Furthermore, characteristics of soil including four cases of fixed base, dense, medium and soft soil are investigated. In order to evaluate the efficiency of these algorithms in determining the appropriate voltage of the Magneto-rheological Damper (MR) and the corresponding control force, a 5-story linear shear building under 21 ground motions is selected. Earthquake records used in this paper contain 3 sets of 7 ground motions including far-fault and near fault records with fling step and forward directivity. Important effects such as nonlinear behavior of MR damper, actuator dynamics and damper saturation are also considered in this study. Mean and standard deviation of structural responses for the 3 sets of presented records show that the reduction in structural responses increases with reducing the stiffness of the base of the structure. Moreover, COC and Bang-Bang algorithms presented better performances than the other considered control algorithms and provide a robust method for semi-active control of structures equipped with MR dampers.

Semi-active control of nonlinear smart base-isolated structures using MR damper: sensitivity and reliability analyses

Semi-active control of base-isolated structures using magneto-rheological (MR) dampers is well studied in recent years. However, there is a study gap for sensitivity and reliability analyses assessment of the structure in the literature. Besides, the reliability analysis of the structures based on the importance of the building from a user perspective categorized into three groups including very high, high, and medium is an interesting topic that is considered in this study. Extension of the study for the case of uncontrolled base-isolated structures and controlled ones in both passive-off and passive-on modes of the MR dampers and tuning the command voltage of the MR dampers by a multi-objective modified clipped optimal (MOMCO) controller are also addressed in this paper in different seismic hazard regions with different peak ground accelerations. The Monte Carlo simulation-based Sobol’s indices and importance sampling (IS) method are applied for the sensitivity and reliability analyses. Studies are conducted on an eight-story nonlinear base-isolated structure. The sensitivity analyses show the main seismic responses are more influenced by the changing uncertainties of the stochastic ground acceleration; the mass, and stiffness of the structural model; and the yield force of the isolation system. MR dampers can significantly reduce the failure probabilities of the structures in different seismic hazard regions. By increasing seismic hazard, an increment is observed in failure probability. Enhancing the importance of the building from medium to very-high status leads to an increase in the failure probabilities of the structure in all cases. However, the performance of three control cases in reducing the failure probabilities of the structure is often increased. The MOMCO controller and passive-on mode represent fewer failure probabilities than the uncontrolled and passive-off mode in different seismic hazard regions and groups. However, the MOMCO gives the best performance in the reduction of failure probabilities.

Experimental and numerical studies on multiple response optimization‐based control using iterative techniques for magnetorheological damper‐controlled structure

SummaryThe field of semiactive control dampers for structural control has seen a significant advancement in recent years. However, the controllers proposed in recent years have been computationally inefficient, time consuming, and did not allow the designer the flexibility in overall structural control. Consequently, this study presents a sequence of numerical and experimental studies conducted to determine the efficiency and performance of proposed multiple response optimization (MRO)‐based control with iterative technique, using magnetorheological (MR) dampers as a control device in mitigating the structural response. The prime objective of the MRO control strategy is selecting an optimal control gain, obtained by a trade‐off between the gains corresponding to the local minima of structural responses, selected as the performance objective of the controllers. The proposed strategy is numerically compared with H2/LQG with clipped optimal control (COC). Results indicated the efficiency and flexibility of the proposed strategy in mitigating the structural responses. Finally, multiple shake table tests were performed on a five‐story steel frame with MR damper, employing the control strategies to be examined. The corresponding results substantiated the superiority of MRO control over passive control strategies, in mitigating the structural responses.

Broad learning robust semi-active structural control: A nonparametric approach

We propose a novel algorithm for dynamic response suppression via semi-active control devices, which we refer to as broad learning, robust, semi-active control (BLRSAC). To configure the semi-active controller, a nonparametric reliability-based output feedback control strategy is introduced. In particular, an adaptive broad learning network is developed to formulate the control strategy using the clipped-optimal control technique. The learning network is augmented incrementally to adopt additional training data based on the inherited information of the trained learning network. By utilizing a robust failure probability, the training dataset is obtained adaptively to include the training input–output pairs with optimal structural control performance. The robust failure probability we propose incorporates both predicted failure probability and the uncertainty of the underlying structure. Therefore, the resultant control strategy can handle the inevitable uncertainty of the actual control situation to achieve optimal structural control. To examine the efficacy of the proposed BLRSAC algorithm, illustrative examples of a shear building and a three-dimensional braced frame under various external excitation and structural damaging conditions are presented.

Shaking table tests and numerical investigations of a novel response-based adaptive control strategy for multi-story structures with magnetorheological dampers

This study presents a sequence of experimental and numerical studies conducted to determine the performance of a novel response-based adaptive (RA) control strategy. The inter-story displacement-based response adaptive (IDRA) control is developed which encompasses numerically obtaining control model parameters while minimizing the overall inter-story displacement response. A total of 53 shake table tests were performed on a reduced scale five-story steel frame, employing the control strategies to be examined. The results obtained from the shake table tests verified the effectiveness of the IDRA control algorithm in mitigating the seismic response of the structure. Finally, the numerical simulation of the proposed strategy is compared with the clipped optimal control (COC) strategy in Simulink (MATLAB). It was concluded that IDRA control has outperformed the classic COC strategy in alleviating the inter-story response of the structure. However, for acceleration responses, the IDRA control results were comparable to those of COC for high-intensity recordings and marginally higher for low-intensity ground motions.

An inverse TSK model of MR damper for vibration control of nonlinear structures using an improved grasshopper optimization algorithm

This paper aims to present an alternative for modeling an inverse dynamic behaviors of a magneto-rheological (MR) damper using a Takagi-Sugeno-Kang (TSK) fuzzy inference system. The highly nonlinear dynamic nature of this device, however, has proven to be a significant challenge for researchers who try to characterize its behavior. Therefore, in this paper an optimum inverse TSK model of the MR dampers is developed using a meta-heuristic optimization algorithm to optimally emulate the nonlinear behavior of the MR dampers. Recently proposed grasshopper optimization algorithm (GOA) is selected as an optimization algorithm, and it is improved (IGOA) by adding opposition-based learning and merit function methods to boost its exploration and exploitation abilities. Also, IGOA is applied to tune the parameters exist in the TSK model. To investigate the efficiency of the proposed model, a nonlinear benchmark building under different far-field and near-field ground motions are considered, and results are compared with other control strategies such as clipped optimal controller (COC), passive ON, passive OFF and ANFIS. The results show that the proposed inverse TSK model of MR damper can provide very competitive results in comparison with other control algorithms.

Control of the nonlinear building using an optimum inverse TSK model of MR damper based on modified grey wolf optimizer

This paper proposes an inverse model of the magnetorheological (MR) damper, based on a new Takagi-Sugeno-Kang (TSK) model to estimate the required voltage for producing the MR force. Usually, a MATLAB toolbox function, adaptive neuro-fuzzy inference systems (ANFIS), is used to train the TSK models, which uses the gradient-based learning algorithms to tune the weights or membership functions parameters. The main drawback is that, these algorithms most often find themselves trapped in local minima, depending on the initial estimations. To overcome this issue, a grey wolf optimizer (GWO) is selected and modified to achieve the training task and called the model as an optimum modified grey wolf-TSK model (OMGT). Also, the superiority of the modified grey wolf optimizer over its standard one is investigated using some mathematical benchmark test functions. Moreover, the linear quadratic regulator (LQR) controller is designed to estimate the optimal control force of an MR damper. The effectiveness of this optimum inverse model in structural control is illustrated and verified using an eight-story nonlinear benchmark building. The performance of the designed OMGT model is compared with the different control algorithms such on (PON), clipped optimal control (COC), active control, and ANFIS under different earthquakes, which demonstrate an acceptable performance of the OMGT over these control algorithms.

An LQR Approach of Automatic Transmission Upshift Control Including Use of Off-Going Clutch within Inertia Phase

<div class="section abstract"><div class="htmlview paragraph">This paper considers using linear quadratic regulation (LQR) for multi-input control of the Automatic Transmission (AT) upshift inertia phase. The considered control inputs include the transmission input/engine torque, oncoming clutch torque, and traditionally not used off-going clutch torque. Use of the off-going clutch has been motivated by discussed Control Trajectory Optimization (CTO) results demonstrating that employing the off-going clutch during the inertia phase along with the main, oncoming clutch can improve the upshift control performance in terms of the shift duration and/or comfort by trading off the transmission efficiency and control simplicity to some extent. The proposed LQR approach provides setting an optimal trade-off between the conflicting criteria related to driving comfort and clutches thermal energy loss. It ensures tracking a linear-like profile of oncoming clutch slip speed reference, which was found to be nearly optimal based on control trajectory optimization results. A special attention is given on proper implementation of nonlinear energy loss term through LQR cost function cross term and using a clipped optimal control approach to provide that the clutches (described as torque source elements) can only dissipate energy. The LQR approach was applied to a fifth-order powertrain model and different upshift control scenarios ranging from the use of single clutch towards using both clutches and transmission input/engine torque reduction. It is shown that the LQR approach can reproduce Pareto frontiers obtained by multi-objective control parameter optimization demonstrating that apart from being used in closed loop controls, the proposed LQR approach can also be exploited for computationally efficient (off-line) optimization purposes.</div></div>

Semi-active vibration control of structural systems based on linear approximation of switched linear system

For vibration control of structural system, semi-active control is expected to show better performance than other control methods in terms of energy efficiency. However, because of the energy dissipation characteristics of the semi-active control devices, the mathematical model of the semi-active control system becomes a hybrid model. Optimal control of hybrid models can be solved by mixed integer quadratic programming. However, this method is computationally expensive because the optimization problem must be solved for every sampling instant. One such computationally inexpensive method is clipped-optimal control, but its performance is not guaranteed because it does not consider the constraints of energy dissipation of the semi-active device. The clipped-optimal control can be expressed as a switching system of three systems under the influence of energy dissipation constraints. In a 1-DOF (degree of freedom) system, the switching conditions of the three systems can be expressed as angles on a phase plane. The 1-DOF vibration system draws an ellipse in the forced vibration and a spiral in an initial response on the phase plane. In the case of a vibration system that draws a circle-like trajectory on the phase plane, unlike other switching systems, the selection of these three systems is performed at a substantially constant rate. In this study, we propose a semi-active control method using a single linear system composed of the above three systems. The linear systems are referred to as the averaged systems in the study. We propose a method to systematically design the clipped-optimal control, which has been conventionally designed by trial and error, with the averaged system. Simulation studies show the effectiveness of the proposed semi-active control approach.

Experimental and numerical studies on pseudo-negative-stiffness control of a base isolated building using magneto-rheological dampers

This article presents a series of experimental and numerical studies on the feasibility and effectiveness of pseudo-negative-stiffness (PNS) control system using magneto-rheological (MR) dampers. First, a MR damper with nominal force capacity of 10 kN was self-developed. A set of experiments was conducted to study the dynamic performance of the MR damper. Then, a PNS control system was established with NI Compact RIO as hardware platform and Labview as software platform. The displacement-based PNS (DPNS) control algorithm was employed to control the MR damper. Dynamic performance tests were performed to investigate the hysteretic behavior of DPNS control force under different excitation conditions and with different control parameters. Next, shaking table tests were conducted on a four-floor steel frame base isolated structure model employing the PNS control system. The seismic responses under uncontrolled case, passive off case, passive on case and DPNS control case were compared. For each control type, the control efficacy was verified for the El Centro, Ji Ji, Kobe_FN and Kobe_FP with increasing peak ground acceleration. The test results show that the DPNS control can further reduce the isolation displacement compared to the passive off case with no accompanying increase of superstructure responses under seismic excitation with different intensities and spectral characteristics. Finally, numerical studies were conducted to compare the effectiveness of DPNS and clipped-optimal control and investigate the effect of time delay of DPNS control. Results indicate that the DPNS control outperforms the clipped-optimal control and the time delay of the DPNS control leads to the adjustment of the DPNS control force at zero displacement, which is beneficial to control efficacy.

Semi-Active Fluid Viscous Dampers for Seismic Mitigation of RC Elevated Liquid Storage Tanks

The effectiveness of the semi-active control strategies using fluid viscous dampers (SAFVDs) for seismic mitigation of reinforced concrete (RC) elevated liquid storage tanks is investigated. Three control algorithms are employed for regulating the damping coefficient of the SAFVDs: (1) Passive-OFF, (2) Passive-ON, and (3) Clipped Optimal Control (COC). The uncontrolled response of the tank is compared with those installed with SAFVD of different control algorithms. Focus is also placed on various positions of the dampers, viz., dampers installed at alternate levels (Configurations I, II, IV, and V) and at all levels (Configurations III and VI) of the staging. A discrete two-mass model for the liquid and multi-degree-of-freedom system for the staging, installed with the dampers, is developed for the RC elevated liquid storage tanks. The response of the broad and slender tanks is studied, for which the ratios of the height of the liquid to the radius of the container are 0.5 and 2.0, respectively. The time-history response of the elevated tank is evaluated for eight different earthquake ground motions, including near- and far-field earthquakes. A MATLAB code was developed to solve the coupled differential equations of motion of the system using the state-space approach. Key parameters, viz., convective displacement, rigid mass displacement, base shear, overturning moment, and damper force, are evaluated. The results show that all the control systems considered herein are beneficial in reducing the seismic responses. The frequency response function for the uncontrolled and semi-actively controlled liquid storage tank in frequency domain exhibits significant response reduction, highlighting the effectiveness of the SAFVDs. The structural response is effectively controlled using the SAFVDs with Passive-OFF (valve closed) and COC algorithms. The COC algorithm employed in this study is a promising candidate for the seismic mitigation of RC elevated liquid storage tanks using the semi-active control.

Semi-active seismic control of a 9-story benchmark building using adaptive neural-fuzzy inference system and fuzzy cooperative coevolution

Control algorithms are the most important aspects in successful control of structures against earthquakes. In recent years, intelligent control methods rather than classical control methods have been more considered by researchers, due to some specific capabilities such as handling nonlinear and complex systems, adaptability, and robustness to errors and uncertainties. However, due to lack of learning ability of fuzzy controller, it is used in combination with a genetic algorithm, which in turn suffers from some problems like premature convergence around an incorrect target. Therefore in this research, the introduction and design of the Fuzzy Cooperative Coevolution (Fuzzy CoCo) controller and Adaptive Neural-Fuzzy Inference System (ANFIS) have been innovatively presented for semi-active seismic control. In this research, in order to improve the seismic behavior of structures, a semi-active control of building using Magneto Rheological (MR) damper is proposed to determine input voltage of Magneto Rheological (MR) dampers using ANFIS and Fuzzy CoCo. Genetic Algorithm (GA) is used to optimize the performance of controllers. In this paper, the design of controllers is based on the reduction of the Park-Ang damage index. In order to assess the effectiveness of the designed control system, its function is numerically studied on a 9-story benchmark building, and is compared to those of a Wavelet Neural Network (WNN), fuzzy logic controller optimized by genetic algorithm (GAFLC), Linear Quadratic Gaussian (LQG) and Clipped Optimal Control (COC) systems in terms of seismic performance. The results showed desirable performance of the ANFIS and Fuzzy CoCo controllers in considerably reducing the structure responses under different earthquakes; for instance ANFIS and Fuzzy CoCo controllers showed respectively 38 and 46% reductions in peak inter-story drift (J1) compared to the LQG controller; 30 and 39% reductions in J1 compared to the COC controller and 3 and 16% reductions in J1 compared to the GAFLC controller. When compared to other controllers, one can conclude that Fuzzy CoCo controller performs better.

APPROPRIATE BASE STIFFNESS OF SMART BASE ISOLATION SYSTEM

In this paper, the effect of base stiffness on the performance of hybrid control system of base isolation system and magnetorheological (MR) damper has been studied and its appropriate base stiffness has been determined. Many researches have been proposed that in the structure controlled by the single base isolation system without MR damper, the base stiffness should be designed such that the fundamental period of isolated structure is almost triple the fundamental period of fixed-base structure. To determine the appropriate base stiffness of hybrid control system, different values have been considered as base stiffness and MR damper has been also employed in two cases of passive form that voltage and dynamical behaviour of MR damper is constant (hybrid base isolation) and semi-active form that MR damper voltage is applied by H2/linear quadratic Gaussian (LQG) and clipped-optimal control algorithms (smart base isolation). For numerical simulation, a three-story shear frame has been subjected to El Centro, Northridge and Tabas earthquakes. Results show that in the structure controlled by the single base isolation system, the peak responses of structure strongly depend on the base stiffness while the sensitivity of peak responses to the base stiffness is lower when the structure is controlled by hybrid base isolation system. According to results, it can be concluded that the peak base drift of hybrid base isolation system reduces with the increase of the base stiffness while this reduction trend is less considerable in the stiffness that are more than the proposed stiffness for the single base isolation system. Hence the proposed stiffness for single base isolation system is the appropriate stiffness for hybrid base isolation system, too. Results also show that under earthquakes considered in this paper, the smart base isolation system is mostly more effective than hybrid base isolation system in mitigating and controlling both root mean square and maximum of structure responses such as base drift, inter-story drift and acceleration.

APPROPRIATE BASE STIFFNESS OF SMART BASE ISOLATION SYSTEM

In this paper, the effect of base stiffness on the performance of hybrid control system of base isolation system and magnetorheological (MR) damper has been studied and its appropriate base stiffness has been determined. Many researches have been proposed that in the structure controlled by the single base isolation system without MR damper, the base stiffness should be designed such that the fundamental period of isolated structure is almost triple the fundamental period of fixed-base structure. To determine the appropriate base stiffness of hybrid control system, different values have been considered as base stiffness and MR damper has been also employed in two cases of passive form that voltage and dynamical behaviour of MR damper is constant (hybrid base isolation) and semi-active form that MR damper voltage is applied by H2/linear quadratic Gaussian (LQG) and clipped-optimal control algorithms (smart base isolation). For numerical simulation, a three-story shear frame has been subjected to El Centro, Northridge and Tabas earthquakes. Results show that in the structure controlled by the single base isolation system, the peak responses of structure strongly depend on the base stiffness while the sensitivity of peak responses to the base stiffness is lower when the structure is controlled by hybrid base isolation system. According to results, it can be concluded that the peak base drift of hybrid base isolation system reduces with the increase of the base stiffness while this reduction trend is less considerable in the stiffness that are more than the proposed stiffness for the single base isolation system. Hence the proposed stiffness for single base isolation system is the appropriate stiffness for hybrid base isolation system, too. Results also show that under earthquakes considered in this paper, the smart base isolation system is mostly more effective than hybrid base isolation system in mitigating and controlling both root mean square and maximum of structure responses such as base drift, inter-story drift and acceleration.

A novel nonlinear road profile classification approach for controllable suspension system: Simulation and experimental validation

Driven by the increasing requirement for road conditions in the field of the controllable suspension system, this paper presents a novel nonlinear road-excitation classification procedure for arbitrary suspension control strategy. The proposed procedure includes four steps: the definition of controller parameters, selection of insensitive frequency ranges, calculation of superior features, and generation of the classifier. To better illustrate the proposed procedure, the clipped optimal control strategy is taken as an example in the simulation part. Simulation results reveal that the proposed method can accurately estimate road excitation level for various controller parameters, vehicle speeds, and vehicle models. Three contributions have been made in this paper: (1) A road classification procedure that can be used for road adaptive suspension control with any control algorithm is developed; (2) In order to improve classification accuracy, the concept of insensitive index which is based on the time-frequency analysis is proposed; (3) Experimental validation with a quarter vehicle test rig is performed, which has verified the effectiveness of the proposed method for the adaptive controllable suspension system.

Semi-active seismic control of buildings using MR damper and adaptive neural-fuzzy intelligent controller optimized with genetic algorithm

This research presents designing a control system to reduce seismic responses of structures. Semi-active control of a magnetorheological (MR) damper is used to improve seismic behavior of a 3-story building implementing neural-fuzzy controller made of adaptive neuro-fuzzy inference system (ANFIS) to determine damper input voltage. Both premise and consequent parameters of fuzzy membership and output functions of ANFIS have the ability for training and improvement but most researchers have focused on just consequent parameters. In order to optimize the controller performance, an approach is proposed in this paper where both premise and consequent parameters of fuzzy functions in an ANFIS network are adjusted simultaneously by genetic algorithm (GA). In order to assess the effectiveness of the designed control system, its function is numerically studied on a benchmark 3-story building and is compared to those of a neural network predictive control (NNPC) algorithm, linear quadratic Gaussian (LQG) and clipped optimal control (COC) systems in terms of seismic performance. The results showed desirable performance of the (ANFIS +GA + membership functions + result function) ANFIS–GA–MFR controller in considerably reducing the structure responses under different earthquakes. The proposed controller showed 30 and 39% reductions in peak story drift (J1) and normed story drift (J4) respectively compared to the NNPC controller, 32 and 44% reductions in J1 and J4 respectively compared to the LQG controller, and 27 and 38% reductions in J1 and J4 respectively compared to the COC controller. The proposed controller effectively reduced acceleration and base shear level compared to the uncontrolled state and had a performance relatively similar to those of three other controllers – for instance, it reduced the maximum level acceleration (J2) 10% higher than COC. Also, the results showed that the ANFIS–GA–MFR controller has more efficiency than the basic ANFIS controller, on average about 20%.

Seismic vibration control of offshore jacket platforms using decentralized sliding mode algorithm

A semi active control algorithm, using MR dampers, is developed for reduction of responses of offshore jacket platforms induced by earthquake ground motions and the responses are obtained for both nonlinear and linearized drag forces. The MR dampers are placed at different levels of the jacket structure and the coupled structure-damper system is modelled in Simulink. Decentralized sliding mode controllers are designed to drive the response trajectories into the sliding surfaces and the command voltage to the MR dampers are generated with the help of clipped-optimal control algorithm. The results of the numerical simulations show that the designed semi active sliding mode controller is effective in reducing the structural vibrations caused by earthquake ground motions. As a result of linearization of the drag force, the effectiveness of the controllers is reduced and responses obtained are conservative in nature, i.e., the increase in controlled responses are more when linearized drag force is considered. The control system is found to be stable and robust; however, the positions and the number of MR dampers have quite significant impact on the performance of the controller.