Optimal Semi-active Control Research Articles

Stochastic optimal semi-active control of stay cables by using magneto-rheological damper

Stochastic optimal semi-active control for stay cable multi-mode vibration attenuation by using magneto-rheological (MR) damper is developed. The Bingham model for an MR damper is used. The force produced by an MR damper is split into passive and active parts. The passive part is combined with structural damping forces into effective damping forces. The partially averaged Itô stochastic differential equations for controlled modal energies are derived by applying the stochastic averaging method for quasi-integrable Hamiltonian systems. Then the dynamical programming equation for controlled modal energies with an index involving control force is established by applying the stochastic dynamical programming principle, and a stochastic optimal semi-active control law is obtained by solving the dynamical programming equation. For controlled modal energies with an index not involving control force, bang-bang control law is obtained without solving a dynamical programming equation. A comparison between the two control laws shows that the stochastic optimal semi-active control strategy is superior to the bang-bang control strategy in the sense of higher control effectiveness and efficiency and less chattering.

Optimal Bounded Semi-Active Control of Hysteretic Systems with MR Damper

A bounded stochastic optimal semi-active control strategy for random excited hysteretic systems by using MR damper is proposed and illustrated by an example of a single degree-of-freedom hysteretic system. First, the dynamics of MR damper and the hysteretic force are expressed by using the Bouc-Wen model. Then, the system is converted into an equivalent nonlinear non-hysteretic stochastic system, from which the optimal bounded semi-active control law consisting of optimal unbounded control and bang-bang control is derived by using stochastic averaging method and stochastic dynamical programming principle. Finally, the response of optimally controlled system is predicted from solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Itô equation. Numerical results show that the proposed control strategy has high control effectiveness and efficiency.

Semi-Active Direct Velocity Control Method of Dynamic Response of Spatial Reticulated Structures Based on MR Dampers

In this paper, a semi-active optimal control strategy for spatial reticulated structures (SRS) with MR dampers subjected to dynamic actions was proposed. The motion equation of SRS embedded with MR dampers was set up. The performance function of the optimal control strategy including both the structural responses and the control efforts was constituted for the optimization of feedback gain and MR damper placement in SRS, and an integrated method of genetic-gradient based algorithm was developed to solve this optimization problem. The clipped-optimal semi-active control strategy in the conjunction of velocity output feedback was applied to compute the desired control force from the MR dampers. Finally, a numerical example of SRS dealing with optimal placement of MR dampers and feedback gains of control system demonstrates the validity of the present semi-active optimal control strategy.

Optimal semi-active preview control response of a half car vehicle model with magnetorheological damper

The control of the stationary response of a half car vehicle model moving with a constant velocity over a rough road with magnetorheological (MR) dampers is considered. The MR damper is modelled by the modified Bouc–Wen model. The MR damper parameters adopted in the vehicle model correspond to an actual fabricated damper and are determined so that the MR damper model characteristics match with experimental characteristics. The random road excitation is considered as the output of a first-order linear shaping filter to white noise excitation. The control and response statistics of the nonlinear vehicle model with MR damper are obtained using the equivalent linearization method in an iterative manner and the results are verified by Monte-Carlo simulation. The MR damper performance is sought to be improved by suitable choice of input currents to the levels of performance of an active suspension based on H ∞ control without and with preview by a mean square equivalence of respective control forces. The H ∞ optimal control with preview minimizes a performance index which is a weighted sum of vehicle performance measures such as sprung mass acceleration, pitch acceleration, front and rear suspension strokes, road holding and control forces with the weights obtained by solving a multi-objective optimization problem using a non-dominated sorting genetic algorithm II (NSGA II).

A semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers

A non-clipped semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers is developed based on the stochastic averaging method and stochastic dynamical programming principle. A nonlinear stochastic control structure is first modeled as a semi-actively controlled, stochastically excited and dissipated Hamiltonian system. The control force of an MR damper is separated into passive and semi-active parts. The passive control force components, coupled in structural mode space, are incorporated in the drift coefficients by directly using the stochastic averaging method. Then the stochastic dynamical programming principle is applied to establish a dynamical programming equation, from which the semi-active optimal control law is determined and implementable by MR dampers without clipping in terms of the Bingham model. Under the condition on the control performance function given in section 3, the expressions of nonlinear and linear non-clipped semi-active optimal control force components are obtained as well as the non-clipped semi-active LQG control force, and thus the value function and semi-active nonlinear optimal control force are actually existent according to the developed strategy. An example of the controlled stochastic hysteretic column is given to illustrate the application and effectiveness of the developed semi-active optimal control strategy.

Predictive suboptimal semiactive control of earthquake response

The truly optimal semiactive control establishes the best possible performance of a dynamically excited and a semiactively controlled isolated structure, subjected to the investigated damper constraints. While it is acausal, and cannot be implemented in practice, it provides a performance goal for implementable control schemes. This paper proposes an implementable predictive control to suppress the earthquake response using a nonlinear semiactive damper. The proposed method uses the Kalman Filtering Technique for the prediction of the near-future ground accelerations. The performance of a 2-degree-of-freedom base-isolated structure is investigated for the proposed predictive control and compared with those of the passive damping, passive on–off cases, two causal semiactive controls, the truly optimal control and the uncontrolled case. The results obtained illustrate that the proposed predictive control shows a good agreement with the ideal best passive case and the causal continuous semiactive control while it follows the truly optimal trajectories closely, except for the peak responses. The proposed control is effective in reducing the base drift without increasing the superstructure response. Copyright © 2009 John Wiley & Sons, Ltd.

Trust-region based instantaneous optimal semi-active control of long-span spatially extended structures with MRF-04K damper

In the field of civil engineering, magnetorheological fluid (MRF) damper-based semi-active control systems have received considerable attention for use in protecting structures from natural hazards such as strong earthquakes and high winds. In this paper, the MRF damper-based semi-active control system is applied to a long-span spatially extended structure and its feasibility is discussed. Meanwhile, a trust-region method based instantaneous optimal semi-active control algorithm (TIOC) is proposed to improve the performance of the semi-active control system in a multiple damper situation. The proposed TIOC describes the control process as a bounded constraint optimization problem, in which an optimal semiactive control force vector is solved by the trust-region method in every control step to minimize the structural responses. A numerical example of a railway station roof structure installed with MRF-04K dampers is presented. First, a modified Bouc-Wen model is utilized to describe the behavior of the selected MRF-04K damper. Then, two semi-active control systems, including the well-known clipped-optimal controller and the proposed TIOC controller, are considered. Based on the characteristics of the long-span spatially extended structure, the performance of the control system is evaluated under uniform earthquake excitation and travelling-wave excitation with different apparent velocities. The simulation results indicate that the MR fluid damper-based semi-active control systems have the potential to mitigate the responses of full-scale long-span spatially extended structures under earthquake hazards. The superiority of the proposed TIOC controller is demonstrated by comparing its control effectiveness with the clipped-optimal controller for several different cases.

Friction based semi-active control of cable-stayed bridges

With the rapid increase of bridge spans, research on controlling earthquake-induced vibration of long-span bridges has been a problem of great concern. The concept of varying the normal force in a frictional interface is investigated to enhance the energy dissipation from a vibrating structure and improve the seismic performance of bridge structures. A semi-active optimal control algorithm is formulated to determine the controllable clamping force of a variable friction device; this algorithm uses measurements of the absolute acceleration and device relative displacements for determining the control action to ensure that the algorithm would be implementable on a physical structure. The friction device UHYDE-fbr is designed and manufactured such that the normal force in the friction interface can be influenced with air pressure chamber, hence the normal force and friction damping can be controlled. The friction device is a controllable energy dissipation device that cannot add mechanical energy to the structural system; the proposed control strategy is fail-safe in that bounded-input, bounded-output stability of the controlled structure is guaranteed. The numerical results demonstrated that the performance of the presented control design is nearly the same as that of the active control system; and that the friction device can effectively be used to control seismically excited cable-stayed bridges with multiple-support excitations.

A bounded stochastic optimal semi-active control

A bounded stochastic optimal semi-active control strategy for magneto-rheological/electro-rheological (MR/ER) dampers is developed from the previously proposed strategy by considering the constraint of semi-active control forces. The control force is separated into a semi-active part and passive part incorporated in the uncontrolled system. The control system is converted into an averaged control system for energy processes by using the stochastic averaging method. The bounded and dynamic constraint of semi-active control forces and a performance index are formulated to constitute a bounded stochastic optimal semi-active control problem. Then the dynamical programming equation is established by applying the stochastic dynamical programming principle to the control problem. The bounded optimal semi-active control forces are obtained from solving this equation based on the variation method. A bounded optimal active control law given is implementable by MR/ER dampers. Finally, an example of controlled and stochastically excited nonlinear system is studied to illustrate the efficiency and chattering attenuation of the developed bounded control.

Parametrically excited instability analysis of a semi-actively controlled cable

A semi-active optimal control method for the parametrically excited instability of stay cables is developed based on the LQR control and the Bingham model of MR dampers, and the instability of controlled inclined stay cables under support motions is studied through the cable structure and control factor effects. The partial differential equation of the parametrically excited transverse vibration of a controlled inclined stay cable with sag under support motions is derived by using two transformations of displacements and converted into ordinary differential equations for the cable mode vibration according to the Galerkin method. The optimal control law is obtained by applying the linear quadratic regulation control method to the multi-degree-of-freedom cable system and matched with the MR damper dynamics to determine the semi-active optimal control force. Then the unstable regions of the parametrically excited vibration of the controlled cable are calculated by using the direct numerical approach based on the generalized eigenvalue analysis and revised through numerical simulation to illustrate more effective stability or large-amplitude vibration suppression. The influences of the cable structure parameters and control factors on the parametrically excited instability are analyzed based on large numerical results in terms of unstable regions and minimum parameter-excitation amplitude. The parametrically excited instability of the cable vibration is noticeably affected by decreasing the inclination angle close to the support-motion direction and increasing the time delay in control over a certain value, which effects need to be taken into account for the cable instability control.

Stochastic optimal semi-active control of hysteretic systems by using a magneto-rheologicaldamper

A stochastic optimal semi-active control strategy for stochastically excited hystereticsystems by using a magneto-rheological (MR) damper is proposed. The dynamics ofboth the hysteretic system and the MR damper is characterized by using theBouc–Wen hysteretic model. The control force produced by the damper is split intoa passive part and a semi-active part. The passive part is combined with theuncontrolled system to form a passively controlled system. Then the system isconverted into an equivalent nonlinear non-hysteretic stochastic system, fromwhich a partially averaged Itô stochastic differential equation is derived by usingthe stochastic averaging method of the energy envelope. For the ergodic controlproblem, a dynamical programming equation is established based on the stochasticdynamical programming principle and solved to yield the optimal semi-activecontrol law. The fully averaged Itô equation is obtained by substituting the optimalsemi-active control force into the partially averaged Itô equation and completing theaveraging. Finally, the response of the semi-actively controlled system is obtainedfrom solving the Fokker–Planck–Kolmogorov equation associated with the fullyaveraged Itô equation. The efficacy of the proposed control strategy is illustrated bythe numerical results and comparison with clipped LQG control for an example.

Optimal semiactive control of structures with isolated base

The paper investigates the benefits of implementing the semiactive control systems in relation to passive viscous damping in the context of seismically isolated structures. Frequency response functions are compiled from the computed time history response to pulse-like seismic excitation. A simple semiactive control policy is evaluated in regard to passive linear viscous damping and an optimal non-causal semiactive control strategy. The optimal control strategy minimizes the integral of the squared absolute accelerations subject to the constraint that the nonlinear equations of motion are satisfied. The optimization procedure involves a numerical solution to the Euler-Lagrange equations

21001 MRダンパーによる非線形特性を考慮した複数連結ビルの地震応答制御(実システムのモデリングと制御(1):建物制振,OS2 実システムのモデリングと制御)

Semi-active control for civil structure has been studied recent years, because it achieves as high performance as active control with less energy consumption. However, nonlinear characteristics such as hysteresis loop of a semi-active control unit make the control system design difficult. While control method taking account of nonlinear characteristics has not been established yet. This research proposes a new design method for semi-active optimal control system. We use a MR damper as an actuator and apply a nonlinear control theory taking account of the nonlinear characteristics. In this method, the optimal, damping coefficient for the MR damper could be explicitly obtained without "clipping". Proposed approach is applied to vibration control of multi buildings connected with the MR damper. Effectiveness of the presented controller and MR damper is examined through simulation and experiment under random and earthquake wave excitations.

Semi-active Control Strategy with Nonlinear Predictive Control and Development of MR Damper with Expanded Variable Damping Region

This paper proposes a new design method of semi-active optimal control system. This method uses the nonlinear predictive control theory proposed by Horiuchi to design a controller and considers nonlinear characteristic of damper or spring that possess variable parameters. This controller predicts the nonlinear response of continuous system one-step ahead by using the state equation. Control inputs are determined by minimization of predictive tracking errors and control inputs. Moreover, this paper proposes a novel MR damper with an expanded variable damping region using both electric and parmanent magnelts. Damping coeffecient of the damper is made increased by adding positive current and decreased by negative current. Proposed approach is applied to vibration control of multi buildings connected with the MR damper. Effectiveness of the presented controller and MR damper is examined through simulation and experiment under random and earthquake wave excitation.

Optimal Semi-active Control and Non-linear Dynamic Response of Variable Stiffness Structures

In this paper we study the semi-active control of structural systems by means of variable stiffness devices, and the resulting non-linear dynamics of the controlled system. In particular, the study is applied to base-excited single-degree-of-freedom systems, controlled by variable ON–OFF elastic devices and subjected to simple motion conditions: free vibrations following initial conditions and stationary response to harmonic input. A performance index, which, in the case of base-excited structures, assumes an original dual formulation following the relative or absolute approaches, has been proposed for instantaneous optimal control. The study includes both the optimal control design and the observation of the resulting non-linear dynamics of the controlled system. The dynamic behavior of the controlled non-linear system is studied with respect to the parameters which characterize the algorithms, the control device, and the input. In this way, also by means of significant (and original) analytical solutions of the equations of motion, the optimal formulation of the algorithms, some particular behaviors of the controlled systems, and the performances of the control approach are shown and explained for the different control strategies.

Optimal Control of Earthquake Response Using Semiactive Isolation

The responses of two, low-rise, 2-degree-of-freedom base isolated structures with different isolation periods to a set of near-field earthquake ground motions are investigated under passive linear and nonlinear viscous damping, two pseudoskyhook semiactive control methods, and optimal semiactive control. The structures are isolated with a low damping elastic isolation system in parallel with a controllable damper. The optimal semiactive control strategy minimizes an integral norm of superstructure absolute accelerations subject to the constraint that the nonlinear equations of motion are satisfied and is determined through a numerical solution to the Euler–Lagrange equations. The optimal closed-loop performance is evaluated for a controllable damper and is compared to passive viscous damping and causal pseudoskyhook control rules. Results obtained from eight different earthquake records illustrate the type of ground motions and structures for which semiactive damping is most promising.

C13 MRダンパの非線形性を考慮した連結構造物のセミアクティブ制御(OS7-2 建築構造物の免震・制振(震)システムII)

This paper proposes a new design method of semi-active optimal control system. This method uses the nonlinear predictive control theory to design a controller and considers nonlinear characteristic of damper that possess variable parameters. This controller predicts the nonlinear response of continuous system one-step ahead by using the state equation. Control inputs are determined by minimization of predictive tracking errors and control inputs. Moreover, this paper proposes a novel MR damper with an expanded variable damping region using both electric and parmanent magnets. Damping coeffecient of the damper is made increased by adding positive current and decreased by negative current. Proposed approach is applied to vibration control of multi buildings connected with the MR damper. Effectiveness of the presented controller and MR damper is examined through simulation and experiment under random and earthquake wave excitation.

Stochastic Optimal Semi-Active Control of Nonlinear Systems by Using MR Dampers

A stochastic optimal semi-active control strategy for strongly nonlinear oscillator subjected to external and/or parametric excitations of Gaussian white noises using magneto-rheological (MR) damper is proposed. The dynamic behavior of an MR damper is characterized by using the Bouc-Wen hysteretic model. The control force produced by the MR damper is split into a passive part and a semi-active part. The passive part is incorporated with the uncontrolled system to form a passive control system. Then the system is converted into an equivalent nonlinear non-hysteretic stochastic control system, from which an Itô stochastic differential equation for total energy is derived by using the stochastic averaging method of energy envelope. For the ergodic control problem, a dynamical programming equation for the controlled total energy process is established based on the stochastic dynamical programming principle. The optimal control law is obtained by minimizing the dynamical programming equation and can be implemented by the MR damper without clipping. Then the fully averaged Itô equation for the controlled total energy process is obtained by replacing the control force with the optimal control force and completing the averaging. Finally, the response of semi-actively controlled system is obtained from solving the final dynamical programming equation and the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Itô equation. The efficacy of the proposed stochastic optimal semi-active control strategy is illustrated by using the numerical results for two examples.

A General Method for Semi-Active Feedback Control of Variable Friction Dampers

Although there are many well-established control methods for vibration mitigation of seismic structures with active devices, their direct application for structures with semi-active control devices are limited. This limitation is primarily contributed by the fact that a semi-active device can only provide a resistant (passive) force to the controlled structure. In this paper, a general method for semi-active feedback control of seismic structures with variable friction dampers (VFD) is proposed. In order to overcome the force limitation of friction dampers, the method forms a semi-active feedback gain by multiplying an active gain with Heaviside functions. Based on this method, two newly developed control laws, i.e., semi-active modal control and semi-active optimal control were numerically investigated. A multiple DOF structural system with various sensor deployments, for either full-state or direct-output feedbacks was considered in the numerical study. The performances of both semi-active control laws for seismic vibration mitigation were compared with those of passive and active controls. The numerical results showed that both semi-active controls resulted in better acceleration reductions than the passive case and were able to closely imitate the performance of their active control counterparts.

Semi-active optimal control of linearized systems with multi-degree of freedom and application

A semi-active optimal control method for non-linear multi-degree-of-freedom systems and its application to a building structure for random response reduction are presented in this paper. A structural system with semi-active control devices under random loading is modelled as a controlled, randomly excited and dissipated Hamiltonian system of multi-degree of freedom. The control force produced by a semi-active control device is split into semi-active part and passive part incorporated in the uncontrolled system. Applying the statistical linearization method to the non-linear multi-degree-of-freedom system with passive control force components yields quasi-linear equations of motion, which can tend to corresponding linear ones with system response reduction. By applying the dynamical programming principle to the controlled linearized system, a dynamical programming equation is established and in particular, for a non-filtering white noise excitation, is solved as an optimal regulation problem to determine the quasi-linear quadratic optimal control law and furthermore semi-active optimal control law according to the variational principle. Then the semi-active optimal control of a tall building structure with magnetorheological-tuned liquid column damper (MR-TLCD) under random wind excitation is performed by using the proposed method. The non-linear model of the structural system with semi-active MR-TLCD is formulated in structural mode space and uncoupled between structural and MR fluid accelerations. The quasi-linear equations for system states are derived from the model and the dynamical programming equation for the system is obtained. In the case that the random wind excitation with the Davenport power spectrum cannot be modelled as a linear filtering white noise, the dynamical programming equation is solved as an optimal regulation problem to obtain the semi-active optimal control force, on which the clipping treatment may be performed to ensure the control force implementable actually. Eventually, the response statistics of the semi-actively controlled structure under random wind excitation are evaluated by using the statistical linearization method, and are compared with those of the passively controlled structure to determine the control efficacy. Numerical results illustrate the high control effectiveness of the proposed semi-active optimal control method for building structures with MR-TLCDs.