EACS 2016 paper - A METHOD FOR COMPUTATION OF REALIZABLE OPTIMAL FEEDBACK FOR SEMI-ACTIVE CONTROLLED STRUCTURES (original) (raw)

Semiactive Control Algorithms for Structures with Variable Dampers

Journal of Engineering Mechanics, 1998

Semi-active control systems combine the features of active and passive control to reduce the response of structures to various dynamic loadings. They include: a) active variable stiffness where the stiffness of the structure is adjusted to establish a non-resonant condition between the structure and excitation, and b) active variable damper where the damping coefficient of the device is varied to achieve the most reduction in the response. This study is concerned with examining the effectiveness of variable dampers for seismic applications. Three algorithms for selecting the damping coefficient of variable dampers are presented and compared. They include: a linear quadratic regulator (LQR) algorithm, a generalized LQR algorithm where a penalty is imposed on the acceleration response, and a displacement-acceleration domain algorithm where the damping coefficient is selected by examining the response on the displacement-acceleration plane and assigning different damping coefficients accordingly. Two single-degree-of-freedom structures subjected to 20 ground excitations are analyzed using the three algorithms. The analyses indicate that unlike passive dampers where for flexible structures, an increase in damping coefficient decreases the displacement but increases the acceleration response, variable dampers can be effective in reducing both the displacement and acceleration responses. The study indicates that the generalized LQR algorithm is more efficient than the other two in reducing the displacement and acceleration responses. The algorithms are used to compute the seismic response of two flexible structures-an isolated bridge modeled as a single-degree-of-freedom system and a base-isolated six-story frame modeled as a multi-degree-of-freedom system. The results indicate that variable dampers reduce the displacement and acceleration responses of the two structures to a significant degree.

Semi-active vibration control of structures via variable damping elements

Mechanical Systems and Signal Processing, 1991

A semi-active control strategy is developed to suppress vibration of flexible structures by on-line varying the characteristics of variable dampers. This novel algorithm is designed on the basis of sliding mode control theory. The approach is insensitive to the spillover problem encountered in the fully-active control case. The control law is synthesised and illustrated on a beam structure example. Computer simulations are performed to examine the theoretical predictions. The results of this fundamental study are essential for advancing the technology of designing and controlling complex structural and mechanical systems.

Aspects of Passive Control of Structural Vibrations

Meccanica, 1997

A preliminary attempt to organize innovative strategies such as Base Isolation, Supplemental Energy Dissipation, Tuned Mass Damping and other combined approaches recently proposed by the authors, in a more general theory of Structural Control, is presented. To visualize the relationships between dynamic variables and subsystems, the block-diagram representations are used in order to obtain the regulation properties of the systems. It has been proven that the Base Isolation technique applies an open-loop control law and that Tuned Mass Damping and Supplemental Energy Dissipation realize closed-loop control laws. The block-diagram of the new combined strategy Base Isolation and Tuned Mass Damping is presented. The objectives of the regulating criteria are also discussed in order to shape the dynamic response in the frequency domain. The H 2 and H ∞ methods are considered as optimal control algorithms.

Structural control with dissipative damping devices

2002

Structural vibration mitigation using semiactive control strategies has received special attention recently due to the attractive properties of semiactive devices. The main restriction of a semiactive device is that it can only produce dissipative forces, which may be expressed in mathematical terms as a nonlinear inequality constraint. Standard active control algorithms do not generally account for this kind of constraint. In this paper, the nonlinear dissipativity constraint is integrated into the well-known linear quadratic regulator (LQR) algorithm using linear matrix inequality (LMI) techniques to be utilized in the semiactive control of the structures. First, the linear quadratic regulator problem is recast as an eigenvalue problem (EVP) in terms of LMIs. Then, the dissipativity constraint is appended in weak expected value form to the other constraints in the EVP. The proposed method is demonstrated in semiactive control of a 2DOF structural system. It is found that although the dissipativity constraint is represented in its weak form, the proposed method yielded control forces more dissipative than standard H 2 /LQR methodologies.

Constant and switching gains in semi-active damping of vibrating structures

International Journal of Control, 2012

We consider the problem of optimal control of vibrating structures and we analyse the solution provided by collocated semiactive decentralised damping devices. We mainly consider the H 1 criterion and we first study the case of constant dampers, showing that in the case of a single damper the performance is a quasi-convex function of friction so there is a single local minimum which is a global one. The case of multiple dampers does not exhibit this feature and time-expensive computations may be required. Secondly, we consider the case in which dampers may be tuned on line, and in particular the case in which they work in a switching on-off mode. We propose a state-switching feedback control strategy, which outperforms the constant damping approach with the optimal static gain performance as an upper bound. For large distributed flexible structures, state feedback is unrealistic and so we propose a stochastic strategy based on a Markov-jump criterion for which the transition probability are not assigned but designed to optimise average performance, with guaranteed asymptotic stability. Finally, we show that the same result provided for the H 1 case holds for the H 2 and the l 1 criteria.

Design of Supplemental Dampers for Control of Structures

Journal of Structural Engineering, 1996

A suggested method for design of supplemental dampers in multistory structures is presented. Active optimal control theory is adapted to design linear passive viscous or viscoelastic devices dependent on their deformation and velocity (best represented by Kelvin model). The theory using a linear quadratic regulator (LQR) is used to exemplify the procedure. The design is aimed at minimizing a performance cost function, which produces a most suitable minimal configuration of devices while maximizing their effect. The method is fully effective using full-state static feedback. Since the active feedback action require a linear combination of all states and passive devices cannot supply it, the paper introduces a methodology to eliminate the off-diagonal interactions between states using various engineering ways. The paper shows the development for velocity feedback only, for the sake of simplicity. However, the full-state formulation can be manipulated similarly to obtain a combined position-velocity feedback design. The paper shows a numerical implementation of the design methodology for a structural model prepared for further experimental considerations.

Optimal semiactive control of structures with isolated base

International Applied Mechanics, 2006

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

VIBRATION CONTROL OF CIVIL ENGINEERING STRUCTURES VIA LINEAR PROGRAMMING

The paper presents a novel active-control design approach which minimizes the peak response of regulated signals rather than, e.g., r.m.s or energy levels optimized by traditional control techniques. This objective is more relevant for active control of civilengineering structures, as failure occurs after a maximum displacement is exceeded in a structural member, while control constraints typically arise from hard saturation limits on the actuator signal and its rate. The design method is formulated in discrete-time and involves the parametrization of all finite settling-time stabilizing controllers. This leads to a linear programming optimization framework, in which the peak response of the structure is directly minimized, subject to linear constraints on the actuator's peak level signal and its rate. The design method is illustrated via a simulation study based on a simple model corresponding to a benchmark design problem. The simulation results compare favourably to those obtained via LQG active control. Finally, some practical implementation issues related to the method are discussed.

Active Structural Vibration Control: A Review

The Shock and Vibration Digest, 2003

In this paper we review essential aspects involved in the design of an active vibration control system. We present a generic procedure to the design process and give selective examples from the literature on relevant material. Together with examples of their applications, various topics are briefly introduced, such as structure modeling, model reduction, feedback control, feedforward control, controllability and observability, spillover, eigenstructure assignment (pole placement), coordinate coupling control, robust control, optimal control, state observers (estimators), intelligent structure and controller, adaptive control, active control effects on the system, time delay, actuator-structure interaction, and optimal placement of actuators.

Active Vibration Control of Cantilever Beam by using Optimal (LQR) Controller

Stringent behaviour requirements imposed on flexible structures have necessitated the sensing and control of vibrations in these structures in a suitable manner. This issue is particularly important for space and aircraft structures for which the mission requirements are crucial and the divergence from these requirements may be considerably expensive. One of the most likely alternatives to deal with this aspect of vibrations is the use of active vibration control, which makes the structure a Smart structure. In this paper, active vibration control of a cantilever beam using piezoelectric actuators is discussed. In order to design the controller, the mathematical model of the system is required. To form such a model theoretically may be difficult or impossible for complex structures. However, such structures may be easily modeled in an FEM environment like ANSYS © . The mathematical model required is extracted from the results of modal analysis of cantilever beam in ANSYS © . Since the matrices of the full model of any system are very large in general, model reduction is attempted in MATLAB © by discarding those modes, which do not contribute to the response of the system. Then by using this reduced model, design of optimal controller is achieved using Linear Quadratic Regulator (LQR) algorithm with state feedback control law. The responses are obtained in both MATLAB © and ANSYS © based on the obtained optimal control gains and compared. Effect of selection of weighting matrices of performance index of LQR on the performance of optimal controller is also reported. Validity of using reduced model for designing optimal controller is checked by comparing its response with that of full model. If reduced models are used for designing controllers for active vibration control of real life complicated systems, a lot of computational time can be saved.