ROBUST-H∞ CONTROL FOR FLEXIBLE STRUCTURES WITH REDUCED DYNAMICS

Proceedings of the 36th IEEE Conference on Decision and Control, 1997

In this paper an active vibration controller for flexible systems is developed using a sliding manifold approach. The sliding surface consists of a time-invarying part which "eliminates" the selected modes without affecting the other dynamics, and a time-varying part which bounds the control amplitude and its rate in the transient. If the state is not available an observer is needed to implement the control law. In particular, a time varying term is introduced in the observer in order to avoid peaking phenomena.

Smart Materials and Structures, 2013

The interest of this article is to develop a general and systematic robust control methodology for active vibration control of flexible structures. For this purpose, first phase and gain control policies are proposed to impose qualitative frequency-dependent requirements on the controller to consider a complete set of control objectives. Then the proposed control methodology is developed by employing phase and gain control policies in the dynamic output feedback H ∞ control: according to the set of control objectives, phase and gain control policies incorporate necessary weighting functions and determine them in a rational and systematic way; on the other hand, with the appropriate weighting functions efficient H ∞ control algorithms can automatically realize phase and gain control policies and generate a satisfactory H ∞ controller. The proposed control methodology can be used for both SISO and MIMO systems with collocated or non-collocated sensors and actuators. In this article, it is validated on a non-collocated piezoelectric cantilever beam. Both numerical simulations and experimental results demonstrate the effectiveness of the proposed control methodology.

Shock and Vibration, 2007

We propose a two-step strategy for the design of passive controllers for the simultaneous confinement and suppression of vibrations (SCSV) in mechanical structures. Once the sensitive and insensitive elements of these structures are identified, the first design step synthesizes an active control law, which is referred to as the reference control law (RCL), for the SCSV. We show that the problem of SCSV can be formulated as an LQR-optimal control problem through which the maximum amplitudes, associated with the control input and the displacements of the sensitive and insensitive parts, can be regulated. In the second design step, a transformation technique that yields an equivalent passive controller is used. Such a technique uses the square root of sum of squares method to approximate an equivalent passive controller while maximizing the effects of springs and dampers characterizing passive elements that are added to the original structure. The viability of the proposed control design is illustrated using a three-DOF mechanical system subject to an excitation. It is assumed that all of the masses are sensitive to the excitation, and thus the vibratory energy must be confined in the added passive elements (insensitive parts). We show that the vibration amplitudes associated with the sensitive masses are attenuated at fast rate at the expense of slowing down the convergence of the passive elements to their steady states. It is also demonstrated that a combination of the RCL and the equivalent passive control strategy leads to similar structural performance.

Structural Control and Health Monitoring, 2016

In this research effort, a novel approach on the control of structures with magnetorheological (MR) dampers is presented, based on an appropriately adapted closed-loop version of the generic input shaping control theory. The MR damper is a very promising kind of semi-active control system (actuator), mixing the advantages of the active and passive structural control systems, hence their increasing use as attenuators that reject the effects of dynamic loads on civil engineering structures. The main contribution of this article is the application and performance evaluation of the novel 'Linear Matrix Inequality-based' feedback version of the input shaping control theory for the first time in the area of structural control. The need for the use of a feedback version of input shaping control stems from the design trade-off between robustness and speed of response requirements. A simulation of a benchmark three-story building with one MR damper is employed to verify the efficiency of the proposed control approach. The nonlinear behaviour of the MR damper, rigidly connected between the first floor of the structure and the ground, is captured by the well-known Bouc-Wen model. The superiority and effectiveness of the proposed scheme in reducing the responses of the structure were proved using seven quantifiable evaluation criteria and by comparing these results with those achieved by classical and well-established alternative control schemes.

1989

This paper examines the control of flexible structures for those systems with actuators that are modeled by second order dynamics. Two modeling approaches are investigated. First a stability and performance analysis is performed using a low order finite dimensional model of the structure. Secondly, a continuum model of the flexible structure to be controlled, coupled with lumped parameter second order dynamic models of the actuators performing the control is used. This model is appropriate in the modeling of the control of a flexible panel by proof-mass actuators as well as other beam, plate and shell like structural members. The model is verified with experimental measurements.

Along the line of past publications of the authors on the topic of active vibration control of flexible structures, the present paper proposes an improvement of the robust control strategy leading to strongly stabilizing bandpass controllers. The improvement consists in the extension of the approach to the case of active control systems with more sensors than actuators, which is very frequent in practical applications. In fact, quite often the application requirements do not allow the control engineer to install actuator/sensor couples in any desired location but only a sensor. In such cases, sensors can be usefully placed in the locations where the primary force fields act on the structure, so as to provide the controller with a direct information on the disturbance effects in terms of structural vibrations. This leads to a control problem with a rectangular plant, which complicates the design, especially if the same characteristics of strongly stabilizing bandpass controllers are desired. The design problem is here solved by resorting to an LMI (Linear Matrix Inequality) technique, which allows also to select the performance weights based on different design requirements. Experimental results are presented for a vibration reduction problem of a stiffened aeronautical panel controlled by piezoelectric actuators.

Smart Materials and Structures, 2002

This study deals with the development and application of an active control law for the vibration suppression of beam-like flexible structures experiencing transient disturbances. Collocated pairs of sensors/actuators provide active control of the structure. A design methodology for the closed-loop control algorithm based on fuzzy logic is proposed. First, the behavior of the open-loop system is observed. Then, the number and locations of collocated actuator/sensor pairs are selected. The proposed control law, which is based on the principles of passivity, commands the actuator to emulate the behavior of a dynamic vibration absorber. The absorber is tuned to a targeted frequency, whereas the damping coefficient of the dashpot is varied in a closed loop using a fuzzy logic based algorithm. This approach not only ensures inherent stability associated with passive absorbers, but also circumvents the phenomenon of modal spillover. The developed controller is applied to the AFWAL/FIB 10 bar truss. Simulated results using MATLAB © show that the closed-loop system exhibits fairly quick settling times and desirable performance, as well as robustness characteristics. To demonstrate the robustness of the control system to changes in the temporal dynamics of the flexible structure, the transient response to a considerably perturbed plant is simulated. The modal frequencies of the 10 bar truss were raised as well as lowered substantially, thereby significantly perturbing the natural frequencies of vibration. For these cases, too, the developed control law provides adequate settling times and rates of vibrational energy dissipation.

Journal of Structural Control, 2001

This paper is an extended abstract of the thesis of J. 3. Briffaut. It treats the active control of flexible structures. In the first part the design of open-loop control laws for beams is considered. In the second the implementation of Komornik's full state feedback law. In the third and fourth numerical results for the control of frames made of beams under bending and tract ion-compression.

Advances in Acoustics and Vibration, 2012

Along the line of past publications of the authors on the topic of active vibration control of flexible structures, the present paper proposes an improvement of the robust control strategy leading to strongly stabilizing bandpass controllers. The improvement consists in the extension of the approach to the case of active control systems with more sensors than actuators, which is very frequent in practical applications. In fact, quite often the application requirements do not allow the control engineer to install actuator/sensor couples in any desired location but only a sensor. In such cases, sensors can be usefully placed in the locations where the primary force fields act on the structure, so as to provide the controller with a direct information on the disturbance effects in terms of structural vibrations. This leads to a control problem with a rectangular plant, which complicates the design, especially if the same characteristics of strongly stabilizing bandpass controllers are desired. The design problem is here solved by resorting to an LMI (Linear Matrix Inequality) technique, which allows also to select the performance weights based on different design requirements. Experimental results are presented for a vibration reduction problem of a stiffened aeronautical panel controlled by piezoelectric actuators.