Optimal Semi-active Control Research Articles

Seismic Response Control for Bridge Piers with Semi-Active MR Damper Based on Displacement Feedback

ABSTRACT This study investigates the semi-active control of railway bridges using an MR damper to reduce the excessive displacement in the bearings of isolated bridges under severe earthquakes. Within the study context, the variable-oval-control (VOC) rule based on structural response displacement feedback is applied to the MR damper and compared with a passive control and clipped optimal semi-active control algorithm. The simulation results show that the dynamic response of railway bridge piers can be effectively reduced, and seismic safety can be significantly improved using MR dampers based on a variable ellipse control strategy. MR damper, based on the VOC rule, directly adopts structural response displacement to perform control force state change. The VOC method only requires the minimum control force to achieve a good displacement control effect, high control efficiency, and stable control effect.

Optimal Semi-Active Control for a Hybrid Wind-Wave Energy System on Motion Reduction

Integration of wave energy converters and floating wind turbine can potentially reduce the levelized cost of energy. The coupling effects between the wave energy converters and the foundation, however, could amplify the foundation motion so that both the efficiency and the fatigue life of wind turbine would be degraded. In this study, wave energy converters are designed as a controlled suspension system for a novel hybrid wind-wave energy system, and an optimal semi-active control method having predictive ability is proposed for reducing the foundation motion. In the controller design, the physical constraints and the passivity of the wave energy converters are also taken into consideration. A full numerical model taking account of aero-hydro-servo-mooring coupled dynamics is proposed for a comprehensive analysis of the controller under various environmental conditions. Numerical results show that the foundation motion can be reduced by 16% even in very rough sea states with the help of the controller.

Grey relation analysis of natural frequency and semi-active robust optimal control of a multi-dimensional isolator based on parallel mechanism and magneto-rheological damper

For isolating multi-dimensional vibrations experienced by precise facilities carried on a vehicle, a novel isolator is proposed based on 2-RPC/2-SPC parallel mechanism with magneto-rheological dampers. Kinematics and dynamics of the isolator are analyzed by geometrics and the Lagrange method. Grey relation analysis approach is conducted to determine the contributions of geometric parameters on natural frequency conveniently. Through analysis, the first order natural frequency of the isolator is affected by the length of the fixed platform most significantly. Due to manufacturing and assembling errors which could not be avoided in the isolator, robust optimal control algorithm is conducted to ensure control effect and robustness of the isolator at the same time. The gain of robust optimal control algorithm is obtained by deducing and solving linear matrix inequality. Compared to passive control, velocity root mean square values of robust optimal semi-active control decreased obviously in horizontal, longitudinal, vertical, and roll directions.

A general synthesis of identification and vibration control of building structures under unknown excitations

The synthesis of structural health monitoring with vibration control is cost-effective and beneficial for developing smart structures. In the last decade, some synthetic algorithms have been proposed for combining system identification and vibration control. Among them, an approach has been developed recently for the synthesis of identification and vibration control under unknown excitation. However, these approaches are only suitable when structural measurement/observation equations contain the unknown excitations, which limits the application of this approach. In this paper, a general approach is proposed to tackle this limitation problem. A generalized extended Kalman filtering with unknown input (GEKF-UI) is proposed to circumvent the limitations of previous EKF-UI approaches. The proposed GEKF-UI can simultaneously identify structural system and unknown excitation when structural measurement/observation equations contain or do not contain the unknown excitations. Moreover, data fusion of measured acceleration and displacement responses is adopted to prohibit the drifts in the identified structural state and unknown excitations. Then, the identified structural state is synthesized in real time with the linear-quadratic-Gaussian (LQG) control strategy for optimal semi-active optimal control provided by magneto-rheological (MR) dampers. Some numerical examples for the synthesis of identification and vibration control of buildings subject to unknown external forces or unknown earthquake ground motion are adopted to verify the feasibilities of the proposed approach.

Synthesize identification and control for smart structures with time‐varying parameters under unknown earthquake excitation

The synthesis of structural identification with vibration control is cost-effective and beneficial for developing smart building structures. In the past several decades, techniques have been put forward for the combination of structural identification and vibration control. However, it is still a challenging task to synthesize identification and vibration control of time-varying structures under unknown earthquake excitation. First, structural dynamic responses collected by a structural health monitoring (SHM) system are absolute responses under unknown earthquake excitation, so existing identification approaches for unknown external excitations are not applicable for this situation. Moreover, it is essential to have an efficient algorithm for accurately tracking the various scenarios of time-varying structural physical parameters with inexpensive computation to ensure the real-time performance requested by structural vibration control. In this paper, an algorithm is put forward to tackle this challenging problem. It is proposed to treat structural time-varying effect as “virtual unknown inputs” to the corresponding time-invariant structure. A generalized extended Kalman filtering with unknown input (GEKF-UI) is proposed to circumvent the limitations of the existing EKF-UI approaches. The proposed GEKF-UI can simultaneously identify structural system, unknown earthquake excitation, and the “virtual unknown inputs” using only partially measured structural absolute responses. Then, the identified structural state is synthesized in real time with the instantaneous optimal control strategy for optimal semiactive control provided by magnetorheological dampers. Therefore, the proposed algorithm can track various structural time-varying with much less computation, which is more suitable for synthesis with structural control compared with other existing approaches. Some numerical cases of synthesizing identification and vibration control of various type time-varying structures under unknown earthquake motion are adopted to investigate the feasibilities of the proposed algorithm.

Integration of identification and vibration control of time-varying structures subject to unknown seismic ground excitation

The synthesis of structural health monitoring and vibration control is important in order to provide facilities for constructing smart structures. In recent years, some techniques have been developed to integrate structural identification and optimal vibration control. However, it is still challenging to integrate the identification and vibration control of time-varying structures subject to unknown earthquake excitation. The main difficulties are that structural dynamic responses collected by a simple harmonic motion system are absolute responses under unknown earthquake ground motion while previous identification approaches for unknown external excitation are not applicable for this situation and the need of an efficient algorithm to accurately track the various scenarios of time-varying structures with inexpensive computation to ensure the real-time performance requested by structural vibration control. In this paper, a novel algorithm is presented, in which structural time-varying parameters are treated as ‘virtual unknown inputs’ to the underlying time-invariant structure, a generalized Kalman filter with unknown inputs is proposed for joint identification of joint structural state, unknown earthquake excitation and ‘virtual unknown inputs’ with only partially measured structural absolute responses, and the identification results are integrated in real-time with the instantaneous optimal control scheme to reach the goal of optimal semi-active control provided by magneto-rheological dampers. Some numerical examples of integrated identification and vibration control of various time-varying structures subject to unknown earthquake excitation are used to demonstrate the performances of the proposed algorithm.

Extension of the Constrained Bilinear Quadratic Regulator to the Excited Multi-input Case

This paper introduces a new method for the computation of an optimal semi-active feedback of a plant, which is controlled by multiple semi-active control dampers and subjected to external, a priori known deterministic disturbance input. The control force is written in bilinear form in equivalent damping gains and a linear combination of the states. This form leads to a bilinear state-space model with corresponding damping gain constraints. An optimal control problem, denoted as constrained bilinear quadratic regulator, is formulated with a performance index, which is quadratic in the states and the equivalent damping gains. The methodology, which is used for solving this problem, is Krotov’s method. In this study, the sequence of improving functions, which enables the use of Krotov’s method in this case, is formulated. Its incorporation in Krotov’s algorithm leads to the suggested novel algorithm for solution of the constrained bilinear quadratic regulator problem for excited optimal semi-active control design. The results are demonstrated numerically by constrained bilinear quadratic regulator control design of controlled structure with seismic disturbance input.

Semi-active bounded optimal control of uncertain nonlinear coupling vehicle system with rotatable inclined supports and MR damper under random road excitation

The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

Optimal Semi-active Structural Control with a Wavelet-Based Cuckoo-Search Fuzzy Logic Controller

An adjustable cuckoo-search wavelet-based fuzzy logic controller (ACSWBFLC) is introduced to mitigate structural responses during seismic motion by using magnetorheological (MR) dampers. The ACSWBFLC incorporates four algorithms: discrete wavelet transform (DWT), fuzzy logic controller (FLC), modified Bouc–Wen model and geometrical nonlinearity algorithm. DWT is applied to acquire the local energy distribution of seismic excitation over the frequency bands. These online data are transmitted to FLC to operate MR damper intelligently based on online excitation frequency. Furthermore, modified Bouc–Wen phenomenological algorithm was utilized to generate the nonlinear behavior of the MR dampers. A wavelet low-pass filter is employed to prevent the stabilization of coefficients and minimize the computational burden. Moreover, geometrical nonlinearities were considered to design a more robust controller. Furthermore, a novel evolutionary algorithm of cuckoo search was used to optimize the placement and the number of MR dampers and sensors in the sense of minimum resultant vibration magnitude. Numerical efforts were considered to validate the efficiency of the proposed FLC. From a designer’s point of view, the proposed ACSWBFLC controller can determine the optimal solutions during a reasonable number of iterations. Finally, numerical examples are utilized to demonstrate the efficiency of ACSWBFLC under several far- and near-fault seismic excitations. The results indicate that ACSWBFLC attenuates the excessive responses of the structural building in real time more efficiently than traditional FLC controllers by using appropriate control force.

An approach to optimal semi-active control of vibration energy harvesting based on MEMS

Abstract In this paper the energy harvesting problem involving typical MEMS technology is reduced to an optimal control problem, where the objective function is the absorption of the maximum amount of energy in a given time interval from a vibrating environment. The interest here is to identify a physical upper bound for this energy storage. The mathematical tool is a new optimal control called Krotov’s method, that has not yet been applied to engineering problems, except in quantum dynamics. This approach leads to identify new maximum bounds to the energy harvesting performance. Novel MEMS-based device control configurations for vibration energy harvesting are proposed with particular emphasis to piezoelectric, electromagnetic and capacitive circuits.

Online adaptive semi-active vibration damping of slender structures subject to moving loads

The paper deals with the adaptive optimal semi-active control of the slender vibrating structures subjected to the moving loads. The deflection of the structure is governed by Euler-Bernoulli beam equation approximated by the system of bilinear ordinary differential equations. The damping function of the structure support is chosen as the control function. The optimal control problem consists in finding such bang-bang control function to minimize the energy as well as the vibrations of the carrying structure. Although the switched optimal control is a very efficient tool in the reduction of structure vibrations it is very sensitive with respect to changes of the speed of the traveling load. This paper deals with the development of the adaptive descent type algorithm that enables the update of the optimal controls in real time based on the measured speed of the traveling load or structure’s state. The proposed algorithm uses reference optimal controls computed for the constant speeds and the set of functions describing the sensitivity of the system dynamics with respect to the measured parameters. Numerical computations are carried out for different speed scenarios of the moving load. The obtained numerical results indicate that the proposed adaptive controller can significantly outperform the reference optimal solutions.

Online adaptive algorithm for optimal control of structures subjected to travelling loads

SummaryThe problem of adaptive optimal semiactive control of a structure subjected to a moving load is studied. The control is realised by a change of damping of the structure's supports. The results presented in the previous works of the authors demonstrate that switched optimal controls can be very efficient at reducing the vibration levels of the structure. On the other hand, these controls exhibit a high sensitivity to changes of the speed of the travelling load. The aim of this paper is to develop an algorithm that enables real‐time adaptation of the optimal controls according to both the measured speed of the travelling load and the estimated state of the structure. The control objective is to provide smooth passage for the vehicles and reduce the material stresses on the carrying structures. The designed adaptive algorithm uses reference optimal controls computed for constant speeds and a set of functions describing the sensitivity of the system dynamics to the measured parameters. The convergence of the algorithm, as well as aspects of its implementation, is studied. The performance of the proposed method is validated by means of numerical simulations conducted for different travelling speed scenarios. In the assumed objective functional, the proposed adaptive controller can outperform the reference optimal solutions by over 50%. The practicality of the proposed method should attract the attention of practising engineers.

Optimal control of structures subjected to traveling load

The problem of the optimal semi-active control of a structure subjected to a moving load is studied. The control is realized by a change of damping of the structure’s supports. The objective is to provide a smooth passage for vehicles and extend the time needed for the safety service of the carrying structures. In contrast to the previous works of the author, in this paper, the model used takes into account time-varying passage speeds, which allows a broader application, in particular, to robotics. The study of the optimal control problem produces a practical condition that justifies whether, for a given set of parameters, the controlled system can outperform its passively damped equivalent. For the optimization, an efficient method of parametrized switching times is developed and tested via a numerical example. The designed optimal control is examined on a real test stand. The experiments are carried out for three different passage scenarios. In terms of the assumed metrics the proposed method outperforms the passive case by over 40%.

Optimal semi-active control of seismically excited MR-equipped nonlinear buildings using FLC and multi-objective NSGAII algorithms considering ground excitations

Among the variety of control algorithms, fuzzy logic control (FLC) strategies have the advantage of not depending on the system model behavior, of being simple, and intrinsically robust, and therefore they have recently been used to control the dynamic response of multi-story buildings equipped with semi-active supplemental damping devices. However, their tuning has shown to be a difficult task, especially when they use a multi-objective strategy. Introducing several FLC-based control strategies, an optimal semi-active control strategy using an advanced multi-objective optimization procedure called Non-dominated Sorting Genetic Algorithm II (NSGAII) has been proposed in this paper to mitigate the nonlinear structural response of a new generation of benchmark buildings. Besides peak inter-story drift ratio and peak floor acceleration, the base shear force as an extra objective has been used as the three-objective function for the multi-objective optimal design problem. The robustness of the optimized semi-active algorithms which were produced using binary tournament-based parents has been assessed for 3-story and 20-story nonlinear benchmark buildings experiencing nonlinear behavior during a wide range of earthquake records. The results showed that the performance of optimized semi-active control systems is acceptable and in some cases work much better than the non-optimized controllers taken in previous studies.

Optimal Control via Integrating the Dynamics of Magnetorheological Dampers and Structures

Magnetorheological (MR) dampers have the advantage of being tuned by low voltages. This has attracted many researchers to develop semi-active control of structures in theory and practice. Most of the control strategies first obtain the desired forces of dampers without taking their dynamics into consideration and then determine the input voltages according to those forces. As a result, these strategies may face situations where the desired forces cannot be produced by the dampers. In this article, by integrating the equations of the dynamics of MR dampers and the structural motion, and solving them in one set, a more concise semi-active optimal control strategy is presented, so as to bypass the aforementioned drawback. Next, a strong database that can be utilized to form a controller for more realistic implementations is produced. As an illustrative example, the optimal voltages of the dampers of a six-storey shear building are obtained under the scaled El-Centro earthquake and used to train a set of integrated analysis-adaptive neuro-fuzzy inference systems (ANFISs) as a controller. Results show that the overall performance of the proposed strategy is higher than most of the other conventional methods.

Computationally efficient design of optimal strategies for controllable damping devices

SUMMARY The development of control strategies for controllable passive dampers — ‘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 form of parametric 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, linear quadratic Gaussian, H2 and H∞), which is designed assuming that the damping devices are fully linear actuators that can exert any forces (dissipative or nondissipative), 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 result in suboptimal (and sometimes very poor) 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 in which the nonlinear system is simulated many times to determine control strategies that are actually optimal for the nonlinear controlled closed-loop system. This paper demonstrates how an approach developed by the authors, which can reduce the model of a system with local modifications to a lower order set of Volterra integral equations in the modification forces, can significantly decrease the computational burden of a complex control design study for controllable dampers. The approach is first adapted to use a state feedback control with a bang–bang on–off secondary controller. Then, the structural and damping device models are detailed. The optimal semiactive control design is demonstrated via both a parameter study and an optimization algorithm. Numerical examples demonstrate that the approach is effective and, compared with a conventional simulation approach, can reduce computation time by two orders of magnitude. Copyright © 2014 John Wiley & Sons, Ltd.

Feedforward and Feedback Vibration Control and Algorithm Design for Cable-Bridge Structure Nonlinear Systems

Technique of feedforward and feedback optimal vibration control and simulation for long-span cable-bridge coupled systems is developed. Buffeting loading systems of long-span cable-bridge structure are constructed by weighted amplitude wave superposition method. Nonlinear model of cable-bridge coupled vibration control system is established and the corresponding system of state space form is described. In order to reduce buffeting loading influence of the wind-induced vibration for the structure and improve the robust performance of the vibration control, based on semiactive vibration control devices and optimal control approach, a feedforward and feedback optimal vibration controller is designed, and an algorithm is presented for the vibration controller. Numerical simulation results are presented to illustrate the effectiveness of the proposed technique.

Optimal passive and semi-active control of a wind excited suspension bridge

Herein, a model of an existing suspension bridge is developed at the numerical level in the ANSYS finite element code starting from original data, and it is used (a) to simulate the structural response under strong wind excitation; (b) to assess the efficacy for the bridge protection of passive and on/off Skyhook semi-active control laws, here presented in a modified version, with due attention on their feasibility and reliability. Their efficacy is shown and the factors contributing to their positive performance are highlighted. Wind loading, corresponding to the extreme event, derives from generated 3D turbulent wind fields, non-homogeneous in space to consider the atmospheric boundary layer.

MR ダンパーの最適制御によるセミアクティブ制御効果の評価

This study elucidates a method to ascertain control variables such as the performance function and weight coefficient, at the initial stage of structural design. For the purpose, authors assess the structural properties (equivalent damping factor and equivalent natural circular frequency) of semi-active optimal control system by MR damper to evaluate the structure response. First, the relations between weight coefficient and those system properties are discussed. Secondly, control parameter determination in consideration in the maximum controlling force is proposed. Validity of those design proposals are investigated by real-time hybrid experiments and numerical simulations.

A minimax stochastic optimal semi-active control strategy for uncertain quasi-integrable Hamiltonian systems using magneto-rheological dampers

A minimax stochastic optimal semi-active control strategy for stochastically excited quasi-integrable Hamiltonian systems with parametric uncertainty by using magneto-rheological (MR) dampers is proposed. Firstly, the control problem is formulated as an n-degree-of-freedom (DOF) controlled, uncertain quasi-integrable Hamiltonian system and the control forces produced by MR dampers are split into the passive part and the semi-active part. Then the passive part is incorporated into the uncontrolled system. After that, the stochastic optimal semi-active control problem is solved by applying the minimax stochastic optimal control strategy based on the stochastic averaging method and stochastic differential game. The worst-case disturbances and the optimal controls are obtained by the minimax dynamical programming equation with the constraints of disturbance bounds and MR damper dynamics. Finally, the system response and the control performance are evaluated by using Monte Carlo simulation. An example of a two-DOF system with coupling damping and parametric uncertainty under Gaussian white noise excitations is worked out in detail to illustrate the procedure and effectiveness of the proposed control strategy, which is also compared with the clipped linear-quadratic-Gaussian control strategy to show the advantages.