Vibration Suppression Of Flexible Structures Research Articles

Optimum Design of Passive Vibration Suppression Using Piezoelectric Elements and LR Circuit

This paper describes design methods of passive vibration suppression in flexible structures using piezoelectric elements. The piezoelectric device on the structure with an inductance and a resistance connected in series or parallel works like a mechanical dynamic vibration absorber. However, until now the optimum value of the resistance had not been formulated for each series or parallel connection. In this study, new formulations were derived by making use of the two fixed points method, and their effectiveness was investigated by calculation and experiment. Furthermore, formulations to obtain the optimum values for mobility and accelerance were also derived.

Semi‐Active Friction Damping of Large Space Truss Structures

The present approach for vibration suppression of flexible structures is based on friction damping in semi‐active joints. At optimal locations conventional rigid connections of a large truss structure are replaced by semi‐active friction joints. Two different concepts for the control of the normal forces in the friction interfaces are implemented. In the first approach each semi‐active joint has its own local feedback controller, whereas the second concept uses a global, clipped‐optimal controller. Simulation results of a 10‐bay truss structure show the potential of the proposed semi‐active concept.

Robust-Controller design with hard constraint on the control signal - application for active vibration suppression of flexible structure

The paper deals with robust-controller design, as an application for active vibration suppression of flexible structures, in the case of a hard constraint on the control signal. The experimental set-up is a three-story flexible structure with an active mass driver placed on the last story. First, the flexible structure is identified, and the model's parametric uncertainties are deduced. Next, control constraints are presented for the robust-control design problem, taking into account the restriction imposed on the control signal. Finally, the effectiveness of the control system is tested through experiments where the input disturbance is assumed to be a sinusoidal one or a scaled simulation of a historical earthquake (1940 El Centro record).

SIMULTANEOUS OPTIMIZATION OF PIEZOELECTRIC ACTUATOR PLACEMENT AND FEEDBACK FOR VIBRATION SUPPRESSION

This paper formulated a new optimal design methodology for the placement of piezoelectric actuator and the feedback gains in vibration suppression of flexible structure. For the simultaneously optimal design of the location and sizing of collocated piezoelectric actuator/sensor pairs and the feedback gains, the effect of changes in the mass and the stiffness of the structure by addition of actuator/sensor pairs are considered and combined with control performance index to obtain a composite objective function, and the procedure developed in this paper leads to solutions that are independent of initial conditions of the flexible structure.

Simultaneous Optimization of Intelligent Structure and Feedback Gains for Flexible Structure Control

A new optimal design methodology is formulated for the placement of piezoelectric actuator and the feedback gains in vibration suppression of flexible structure. For the simultaneously optimal design of the location and sizing of collocated piezoelectric actuator/sensor pairs and the feedback gains, the effect of changes in the mass and the stiffness of the structure by addition of actuator/sensor pairs is considered and combined with control performance index to obtain a composite objective function, and the procedure developed in this paper leads to solutions that are independent of initial conditions of the flexible structure.}

Robust Pole Assignment for Vibration Control of Flexible Structures

This paper proposes a method of structure/controller design by robust pole assignment for active vibration suppression of flexible structures. The proposed method assigns the closed-loop poles at the specified point in the complex plane and quasi-minimizes the condition number of the closed-loop modal matrix via structure/controller design. Reducing the condition number improves stability robustness and control performance of the designed closed-loop system. This paper also introduces a new index of condition number for the cost function. Use of this index in place of an actual condition number reduces computational effort and improves problem solvability significantly. Feasibility of the proposed method is demonstrated with numerical examples.

A NEW PERSPECTIVE FOR SEMI-AUTOMATED STRUCTURAL VIBRATION CONTROL

The development of an innovative approach for optimum vibration suppression of flexible structures is presented. Utilizing concurrent use of semi-active and active subsections, an intelligent semi-automated alternative is suggested. By altering the adjustable structural properties (in semi-active unit) and control parameters (in active unit), a search is conducted to minimize an objective function subject to constraints, which may reflect performance characteristics. In practice, a user-in-the-loop interprets the resulting performance. A number of options may then be initiated: altering the parameters of the semi-active unit, or re-tuning the control parameters in the active unit, or concurrently adjusting the two. An essential component of this strategy is handling the parametric variations within the system. In order to increase the absorber efficiency against such variations an identification process is utilized in sequence with an optimization for re-tuning the absorber. The feasibility of the re-tuning procedure and performance improvement is demonstrated via simulations for a single-degree-of-freedom (s.d.o.f.) system. It is shown that concurrent adjustment of structural properties and control re-tuning significantly improves the vibration suppression quality.

Limits of vibration suppression in flexible structures

A method is described for the determination of limits of vibration suppression in an elastic structure by means of a given number of control actuators. The method is based on a theorem, described and proved herein, that defines the lower limit of residual deformations for specified disturbances and a given map of placement of actuators which can produce finite control forces. The new method can identify regions of placement which result in acceptable residual deformations, thus making control design easier and reduces the cost of searching for optimal actuator positions. Unlike traditional methods used to solve this class of problems, the new method does not require knowledge about the excitation states of various deformation modes. The method is demonstrated by applying it to a simply supported beam and a plate.

Effect of modal filter errors on vibration control characteristics

When designing a control system for vibration suppression of flexible structures using modal control strategy, one must know the modal displacements and velocities of the controlled modes. If the vibration control forces are designed based on inaccurate modal states, the closed-loop performance of the vibration control system will be degraded depending on the extent of the modal filter errors. In this study, the effect of modal filter errors on the vibration control characteristics of flexible structures is analyzed for IMSC (Independent Modal Space Control). A Lyapunov asymptotic stability condition that depends on the magnitude of the modal filter errors is derived. The extent of the response deviation of the closed-loop system is also derived and evaluated using operator techniques. The extent of the response deviation is found to be proportional to the magnitude of the modal filter errors.

Structure and Controller Design for Vibration Control of Flexible Structures via Robust Pole Assignment.

This paper proposes a method of structure/controller design via robust pole assignment for active vibration suppression of flexible structures. The proposed method assigns the closed-loop poles at the target location and quasi-minimizes the condition number of the closed-loop modal matrix by designing structure and controller parameters. Closed-loop target pole locations can also be redesigned as the design parameters. Reducing the condition number improves stability robustness and control performance of the designed closed-loop system. This paper introduces a new index of condition number as the cost function. Use of this index in place of actual condition number reduces computational effort significantly. Feasibility of the proposed method is illustrated by numerical examples.

Two-stage strategy for simultaneous slewing and vibration suppression of flexible structures

This paper presents an open loop near-minimum-time solution for simultaneous slewing and vibration suppression of flexible structures. The problem is formulated as an open-loop, minimum-system energy and/or control effort optimal control problem in modal space. With parametric control law, a two-level problem-solving strategy is presented. In the first stage, a sequence of rigid mode-based time-optimal control problems is solved and the minimum maneuver time is found by gradually reducing the maneuver time until the solution converges. In the second stage, the optimal parameters of the control law are evaluated using nonlinear programming with prescribed performance index as its objective function. The proposed strategy, through time-optimal control of the rigid mode combined with the parametric quadratic control of the clastic modes, determines the control profiles which give both minimum maneuver time and desired value of performance index. As an example, the optimal control of a slewing flexible beam is presented, and high performance slewing maneuver is achieved.

Displacement Feedback Control of Proof-Mass Actuators for Vibration Suppression.

The use of direct displacement feedback control for vibration suppression of flexible structures by multiple proof-mass actuators is investigated. Closed-loop eigenvalue analysis is carried out considering the influence of actuator dynamics, and closed-loop stability is proved which indicates the stability robustness of the control algorithm. Regarding the performance of the control system, parameters of the actuator are optimized analytically using an eigenvalue criterion for one-degree-of-freedom structure and the optimum parameters are expressed in closed form as a function of feedback gain. In addition, the results of optimum parameters are generalized to adapt to control of multiple-degree-of-freedom structure. A control example of a plane frame structure is given with the actuators used either passively or actively. Simulation results demonstrated the effectiveness of the proposed control procedures.

Structural Vibration Control Via Electrorheological-Fluid-Based Actuators With Adaptive Viscous And Frictional Damping

It has been recognized that the semi-active control concept is promising for vibration suppression of flexible structures and that the electrorheological (ER) fluid-based device is a good candidate for such applications. In this research, a new control law is developed to maximize the damping effect of ER dampers for structural vibration suppression under actuator constraints and viscous-frictional-combined damping. Numerical simulations and experimental work are carried out to evaluate the semi-active concept. It is illustrated that the performance of the semi-active system is superior to those of the critical damping and maximum damping variety. It is also concluded that the actuator frictional effect is significant, and should be considered in the controller design process.

Nonlinear active vibration damping

A multivariable nonlinear controller is investigated for vibration suppression of flexible structures. The closed-loop gain matrix consists of a varying term added to a constant term. The varying term is proportional to the measured signal, providing rapid cancellation of large deflections and maintaining low noise sensitivity. L/sub 2/-stability is proved, and experimental results show improvement of performance compared to a corresponding linear controller with constant gain.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Dynamics and Control in Space. Vibration Suppression of Flexible Structures by Bang-Bang Control. 2nd Report. Characteristics of Control Methods and Verification by Computer Simulation and Hardware Experiments.

Dynamics and Control in Space. Vibration Suppression of Flexible Structures by Bang-Bang Control. 2nd Report. Characteristics of Control Methods and Verification by Computer Simulation and Hardware Experiments.

Vibration Suppression of Flexible Structures by Bang-Bang Actuators. 1st Report. Evaluation of Basic Characteristics by Numerical Simulation usnig a Flexible Beam.

This study is concerned with basic characteristics and control performance of a bang-bang actuator. The bang-bang actuator studied here is a proof-mass type which is controlled by on-off command. The major advantage is that it can be made to be light in weight and low in energy consumption. Moreover, it does not require a servo-amplifier for each actuator and the number of actuators can be made large, so that it is suitable for distributed control. The analysis model is a flexible beam on which one or more bang-bang actuators is placed. It has been confirmed that the performance is approximately twice as effective as that of a tuned passive damper and nearly equal to that of a proof mass actuator under direct velocity feedback control. Moreover, it has been shown that vibration suppression by bang-bang actuators has definite advantages in energy consumption and robustness over conventional methods.

Experiment of a noncollocated controller for wave cancellation

Wave-absorbing control for vibration suppression of flexible space structures is demonstrated experimentally. The experimental model is a hung flexible beam with a sensor and a noncollocated torque actuator. The wave-absorbing control employs partial differential equations as the mathematical model of structural dynamics, and the controller can be designed without any use of the modal expansion. Thus, the control is free from the crucial truncation effect. The structural vibration is expressed in terms of propagating disturbances in the frequency domain. The control forces are applied to eliminate outgoing waves at the boundaries of the structure. The controller is implemented in the form of a nonrecursive digital filter. Details of the controller implementation are discussed, including the digital filter as a compensator, filter truncation, and the hardware. Experimental results show satisfactory performance of the controller and good agreement with the performance predicted analytically. ARGE space structures (LSS) will be inevitably flexible in their structure, and their structural vibration will be easily excited. Therefore, control techniques of structural vibration are necessary to satisfy performance of LSS. Most of the studies on the control problem of LSS employ the dynamic model with a discretized description for flexible structures that are inherently distributed parameter systems. The discretization is usually employed to adopt the conventional state-space method. Methods free from the discretization are natural and suitable to the control of such distributed parameter systems as the LSS. This paper treats through the experiment the wave-absorbing control for vibration suppression of flexible structures. The wave-absorbing control employs partial differential equations as the mathematical model of structural dynamics to design the controller, and the discretization method is not employed in the analyses. The controller obtained is thus free from the crucial truncation effect. The equations are Laplace transformed with respect to time to describe the structural responses in terms of propagating disturbances in the frequency domain. Boundary conditions of the system are expressed as relations between incoming waves, outgoing waves, and external control forces at the boundaries. External control forces are applied to eliminate outgoing waves at the boundaries. Resulting closed-loop behavior of the system shows drastic improvement for disturbance attenuation in comparison with open-loop behavior. The concept of the traveling wave approach is applied to the control problem of LSS by von Flotow.13 He introduces the viewpoint that the elastic response of LSS may be aptly viewed in terms of the disturbance propagation characteristics of the structure. Active vibration isolation by cancelling traveling waves based on the same concept is studied in Refs. 4-8. The technique aims to isolate one part of a structure from disturbances excited elsewhere in the structure. Actuators are located at midpoints of structural members and cancel passing disturbances so that the disturbances do not disturb downstream portions. A generic description of the traveling wave control for structural networks is given in Ref. 9. Miller et al.

Wave-absorbing control for flexible structures with noncollocated sensors and actuators

A control method for vibration suppression of flexible structures with noncollocated sensors and actuators is introduced. A simple expression of response of flexible structural networks is also shown. The control method is an extension of wave-absorbin g control based on the concept of disturbance propagation. Disturbance propagation in a flexible structure modeled as a distributed parameter system is treated in the frequency domain, and the usual modal expansions are not employed for modeling the system. Response of structural networks is obtained from exact solutions of Laplace-transformed equations of motion. Boundary conditions are expressed in terms of reflection/transmission of traveling waves, and controllers with noncollocated sensors and actuators are designed to suppress outgoing waves at boundaries of the structure. Responses of the controlled systems to external disturbances are analyzed through numerical examples. I. Introduction S UPPRESSION of traveling disturbances of flexible space structures becomes one of significant topics in the control problem of large space structures (LSS) in accordance with increase of size and flexibility of LSS. Disturbances applied on an LSS propagate over the structure through structural members, reflect at ends or junctions of the structure, and finally form standing waves. Control of traveling waves is required to cancel the generated disturbances in the neighborhood of each excited point before they propagate over the structure. The conventional modal approach to the vibration control is also applicable to control of traveling waves. Modal control of traveling waves, however, needs a large number of modes to describe traveling waves in a sufficient degree of accuracy and results in a controller that requires much computation. Bennighof and Meirovitch1 apply independent modal-space control (IMSC) and direct feedback control to active suppression of traveling waves in structures. Their approach requires a number of actuators as well as controlled modes, and it is demonstrated that direct feedback control is more suitable than IMSC truncated to low order for the problem in which a large number of higher modes have to be controlled. Wave-absorbing control, which results from a description of the structural response in terms of propagating elastic disturbances, is the alternative to the modal control method, and its theoretical features are more suitable for control of traveling waves than the modal approach. System model of the structures is treated as distributed parameter system in frequency domain, and the modal methods are not employed in the present analysis. The model responses are described in terms of propagating disturbances. The concept of the wave-absorbing control is applied to the control of LSS by von Flotow2'3 and von Flotow and Schafer.4 They introduce the viewpoint that the elastic response of large spacecraft structures may be aptly viewed in terms of the disturbance propagation characteristics of the structure2 and

Vibration Suppression Using a Proofmass Actuator Operating in Stroke/Force Saturation

We consider proofmass actuators for vibration suppression in flexible structures. Proofmass actuators appear to have a significant force-to-weight ratio over other types of actuators; hence, there has been considerable interest in them recently. These actuators, however, have a maximum force capability imposed in part by the stroke length of the proofmass. This nonlinearity is difficult to handle because this constraint cannot be violated (unlike saturation of electronic devices). Furthermore, this constraint is peculiar to this type of actuator. In this paper we consider the control loop structure of a feedback control system which contains a proofmass actuator for vibration suppression. This loop structure is decomposed into inner control loops directly related to the actuator and outer loops which add damping to the structure. The inner loops determine the frequency response of the actuator. Evidently, when the frequency response of the actuator is matched to the stroke/force saturation curve, the actuator is most effective in the vibration suppression loops. Since the stroke/force saturation curve is characterized by the stroke length, mass of the proofmass, and the maximum current delivered by motor electronics, this actuator can be easily sized for a particular application. We also discuss the interaction between the inner loops around the actuator and the structure (with the vibration loops open). To illustrate our results, we consider linear DC motors as proofmass actuators for the COFS-I Mast. To discuss the interaction the actuator and the structure, we develop a simple result based on classical control theory. This result is of independent interest since it leads to a simple procedure for designing low order compensators for single-input-single-output systems with poles near the imaginary axis.

A sequential linear optimization approach for controller design

A linear optimization approach with a simple, real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first-order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam, finite element model for the optimal sizing and placement of active/passive structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to the initial conditions of the linear optimization approach is also demonstrated.