Vibration Control Problem Research Articles

Power Input to non-deterministic Subsystems via Piezoelectric Patch Actuators: Effect of the patch size and location

Many engineering systems such as aircraft and automotive are considered built-up structures, fabricated from components that are classified as deterministic subsystems (DS) and non-deterministic subsystems (Non-DS). The response of Non-DS is sensitive to uncertainties therefore presents problems in vibration control. Therefore, analytical solution to estimate average power delivered by a piezoelectric (PZT) patch actuator when attached to a Non-DS needs to be established. The response of Non-DS is estimated using statistical modelling technique such as statistical energy analysis (SEA), in which any external input to the subsystem must be represented in terms of power input. In this paper, ensemble average of power given by a PZT patch actuator to a simply-supported plate when subjected to structural uncertainties is studied using Lagrangian method. The effects of size and location of the PZT actuators on the power delivered to the plate are investigated. It is found that changing the patch location on the structure will not affect the average power supplied while changing the patch size will change the power magnitude proportionally but with some variations at higher frequency.

Optimal design of Base Isolation System considering uncertain bounded system parameters

The optimum design of base isolation system considering model parameter uncertainty is usually performed by using the unconditional response of structure obtained by the total probability theory, as the performance index. Though, the probabilistic approach is powerful, it cannot be applied when the maximum possible ranges of variations are known and can be only modelled as uncertain but bounded type. In such cases, the interval analysis method is a viable alternative. The present study focuses on the bounded optimization of base isolation system to mitigate the seismic vibration effect of structures characterized by bounded type system parameters. With this intention in view, the conditional stochastic response quantities are obtained in random vibration framework using the state space formulation. Subsequently, with the aid of matrix perturbation theory using first order Taylor series expansion of dynamic response function and its interval extension, the vibration control problem is transformed to appropriate deterministic optimization problems correspond to a lower bound and upper bound optimum solutions. A lead rubber bearing isolating a multi-storeyed building frame is considered for numerical study to elucidate the proposed bounded optimization procedure and the optimum performance of the isolation system.

Design of causal state observers for regular descriptor systems

In this contribution a new framework for the design of causal state observers for regular descriptor systems is developed. The proposed procedure is derived on the basis of well-known and slightly modified parametric design concepts for state feedback controllers and generalized state observers. The resulting method can be applied under some necessary and sufficient, and thus minimal, existence conditions for causal state observers. The relation between the generalized observer and the observer in state space form is given by a suitable coordinate transformation. In general, neither controllability nor observability or any specific system representation is required. The separation principle holds.The proposed procedure is applied to two examples, namely a differentiating system which can be observed by a causal state observer and a double-beam vibration control problem.

Optimal Vibration Control for Uncertain Nonlinear Sampled-Data Systems With Actuator and Sensor Delays: Application to a Vehicle Suspension

The problem of optimal sampled-data vibration control for nonlinear systems with time delays and uncertainties is considered. With the purpose of simplifying the nonlinear optimal vibration control (NOVC) design, the original time-delay sampled-data system is converted into a discrete-time nondelayed system first, as well as the nonlinear and uncertain terms are treated as external excitations. Therefore, the design procedure for NOVC law is reduced and the successive approximation approach is sequentially developed in it. The obtained NOVC law is derived from a Riccati equation, a Stein equation, and sequences of adjoint vector difference equations. It is combined with a feedforward term, the nonlinearity and uncertainty compensator terms, and some control memory terms, which compensate for the effects produced by the disturbance, the nonlinearity and uncertainties, and the time delays. Moreover, the existence and uniqueness of NOVC law are proved and the stability of the closed-loop system is analyzed. In order to make the controller physically realizable, an observer is constructed and the corresponding dynamical control law is given. Furthermore, by this means, the NOVC law for a sampled-data quarter-car suspension model with actuator and sensor delays is designed. The results of numerical simulations illustrate that the NOVC gives satisfactory conclusions in effectiveness of suspension performance responses and feasibility of the proposed design approach.

Autonomous decentralized intelligent vibration control for large split-blanket solar arrays

Large split-blanket solar arrays are semi-rigid structures. It is difficult for this kind of structure to achieve vibration suppression. In order to solve this problem effectively, firstly, we use the finite element method to construct a dynamic model of a solar array with piezoelectric smart structure, and then we propose a new control method, namely the autonomous decentralized intelligent control to address the vibration control problem. Based on the concept of autonomous decentralized control presented in this paper, the control system can be divided into multiple autonomous subsystems. Each subsystem performs several control functions without external intervention. Numerical simulations are carried out to verify the proposed control strategy. The results indicate that this method is effective. Compared with the traditional positive position feedback control method, the attenuation time of the structural bending vibration can be reduced by half with the proposed method. Furthermore, the control system can perform well even under severe subsystem failure without external intervention.

Optimal Vibration Control for Active Suspension Systems with Actuator Delay

This paper deals with the vibration control problem for active suspension systems with actuator delay. Based on the model transformation, the actuator-delayed system is transformed into an equivalent nondelayed one. The delay effect is compensated by a control memory term in the designed controller. The vehicle vibration is reduced by a feedforward compensator. An observer is constructed to make the disturbance state in feedforward control physically realizable. Numerical simulations illustrate the effectiveness and the simplicity of the proposed controller.

A New Method of Calculating the State Feedback Gain Vector of Vibration Control System

Using the random model, the vibration control problem of structures with uncertain parameters is discussed, which is approximated by a deterministic one. The feedback gain matrix is determined based on the deterministic systems, and then it is applied to the actual uncertain systems. A method to calculate the standard deviations for responses of the closed-loop systems with the uncertain parameters is presented by using the random perturbation. This method is applied to a vibration system to illustrate the application. The numerical results show that the present method is effective.

Computationally Efficient Combined Plant Design and Controller Optimization Using a Coupling Measure

This paper presents a novel approach to the optimization of a dynamic systems design and control. Traditionally, these problems have been solved either sequentially or in a combined manner. We propose a novel approach that uses a previously derived coupling measure to quantify the impact of plant design variables on optimal control cost. This proposed approach has two key advantages. First, because the coupling term quantifies the gradient of the control optimization objective with respect to plant design variables, the approach ensures combined plant/control optimality. Second, because the coupling term equals the integral of optimal control co-states multiplied by static gradient terms that can be computed a priori, the proposed approach is computationally attractive. We illustrate this approach using an example cantilever beam structural design and vibration control problem. The results show significant computational cost improvements compared to traditional combined plant/control optimization. This reduction in computational cost becomes more pronounced as the number of plant design variables increases.

MR damper based implementation of nonlinear damping for a pitch plane suspension system

Suppression of vibration transmission from working machineries and other sources is important for the normal operation of a wide range of engineering systems. Traditionally, viscous dampers with approximately linear characteristics are often used to address the issue. However, this solution can have the problem of not being able to reduce the vibration transmission over the whole range of frequencies. In recent studies, the authors have revealed, by both theoretical analysis and experimental test, that nonlinear damping can be applied to resolve the problem. The present study is concerned with the exploitation of this beneficial effect of nonlinear damping to the vibration control of a pitch plane suspension system. A magneto-rheological (MR) damper based implementation of nonlinear damping is applied to provide a novel solution to the pitch plane system vibration control problem. Simulation studies are conducted to demonstrate the effectiveness of the MR damper implementation, and the beneficial effect of nonlinear damping on the pitch plane suspension system vibration control.

Parameter-dependent vibration-attenuation controller design for electro-hydraulic actuated linear structural systems

The problem of robust active vibration control for a class of electro-hydraulic actuated structural systems with time-delay in the control input channel and parameter uncertainties appearing in all the mass, damping and stiffness matrices is investigated in this paper. First, by introducing a linear varying parameter, the nonlinear system is described as a linear parameter varying (LPV) model. Second, based on this LPV model, an LMI-based condition for the system to be asymptotically stabilized is deduced. By solving these LMIs, a parameter-dependent controller is established for the closedloop system to be stable with a prescribed level of disturbance attenuation. The condition is also extended to the uncertain case. Finally, some numerical simulations demonstrate the satisfying performance of the proposed controller.

Optimal Piezoelectric Sensors and Actuators Deployment for Active Vibration Suppression of Satellite Antenna Reflector

To solve the problem of active vibration control for satellite antenna reflector, which is weak damping and closely spaced modes, the optimal actuators/sensors deployment and controller designing need to be considered. Firstly, the optimal criterions of controllability and observability are designed according to the specificity of Gram Matrix eigenvalue in satellite antenna system equations. Secondly, based on the above criterions, piezoelectric materials (as sensors and actuators) and genetic algorithm are utilized to optimize the deployed locations of sensors and actuators. Finally, to suppress the vibration of satellite antenna reflector, a Linear Quadratic Gaussian (LQG) controller is designed under the impulse and white noise excitation respectively. The simulate results show the effectively deployed locations of sensors and actuators, and the correctness of designed LQG controller.

Research on Active Vibration Control of Simply supported Beam Base on Piezoelectric Actuator

The active vibration control is becoming an effective mean to solve the vibration control problems of the aerospace and other fields. This paper builds up the active vibration control system of simply-supported beam based on piezoelectric actuator. The mathematical model of simply supported is derived and the displacement response curve of the beam is obtained by simulation analysis through MATLAB software. The vibration tests of simply supported beam under an initial disturbance and continuous incentives were carried out, according to the experimental results it can be concluded that the proposed control method has a suitable and efficient performance for vibrations control.

Output Regulation in Discrete‐Time Switched Bimodal Systems Based on Youla Parameterized Stabilizing Controllers

Motivated by a class of contact vibration control problems in mechanical systems, this paper considers a regulation problem for discrete‐time switched bimodal linear systems where it is desired to achieve output regulation against partially known deterministic and unknown random exogenous signals. First, a set of observer‐based Youla parameterized stabilizing controllers is constructed, based on which the regulation conditions for the switched system against the deterministic signals along with an H2 performance constraint against the unknown random signals are derived. Then a corresponding regulator synthesis algorithm is developed based on solving properly formulated linear matrix inequalities. The proposed regulator is successfully evaluated on an experimental setup involving a switched bimodal mechanical system subject to contact vibrations, hence, demonstrating the effectiveness of the proposed regulation approach.

Polyvinylidene fluoride film sensors in collocated feedback structural control: application for suppressing impact-induced disturbances

Polyvinylidene fluoride (PVDF) films are light, flexible, and have high piezoelectricity. Because of these advantages, they have been widely used as sensors in applications such as underwater investigation, nondestructive damage detection, robotics, and active vibration suppression. PVDF sensors are especially preferred over conventional strain gauges in active vibration control because the PVDF sensors are easy to cut into different sizes or shapes as piezoelectric actuators and they can then be placed as collocated pairs. In this work, to focus on demonstrating the dynamic sensing performance of the PVDF film sensor, we revisit the active vibration control problem of a cantilever beam using a collocated lead zirconate titanate (PZT) actuator/PVDF film sensor pair. Before applying active vibration control, the measurement characteristics of the PVDF film sensor are studied by simultaneous comparison with a strain gauge. The loading effect of the piezoelectric actuator on the cantilever beam is also investigated in this paper. Finally, four simple, robust active vibration controllers are employed with the collocated PZT/PVDF pair to suppress vibration of the cantilever beam subjected to impact loadings. The four controllers are the velocity feedback controller, the integral resonant controller (IRC), the resonant controller, and the positive position feedback (PPF) controller. Suppression of impact disturbances is especially suitable for the purpose of demonstrating the dynamic sensing performance of the PVDF sensor. The experimental results also provide suggestions for choosing between the previously mentioned controllers, which have been proven to be effective in suppressing impact-induced vibrations.

The Standard Deviations for Repeated Eigenvalues of Vibration Control for Structures with Uncertainties

The vibration control problem of repeated eigenvalue systems with random parameters is discussed, which is approximated by a deterministic one. A method for calculating the standard deviations of repeated eigenvalues of the control systems with random parameters is presented by using the random perturbation. It will not require the distribution function of the random parameters of the systems other than their means and variances. The numerical results show that the present method is effective.

Design of robust-stable and quadratic finite-horizon optimal active vibration controllers with low trajectory sensitivity for the uncertain flexible rotor systems via the orthogonal-functions approach and the hybrid Taguchi-genetic algorithm

By studying the robust stabilizability condition, the orthogonal-functions approach (OFA), and the hybrid Taguchi-genetic algorithm (HTGA), an integrative method is presented in this paper to design the robust-stable and quadratic finite-horizon optimal active vibration controller with low trajectory sensitivity such that (i) the flexible rotor system with elemental parametric uncertainties can be robustly stabilized, and (ii) a quadratic finite-horizon integral performance index, including a quadratic trajectory sensitivity term for the nominal flexible rotor system, can be minimized. In this paper, the robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived in this paper for solving the nominal flexible rotor system feedback dynamic equations. By using the OFA and the LMI-based robust stabilizability condition, the robust-stable and quadratic finite-horizon optimal active vibration control problem for the uncertain flexible rotor system is transformed into a static constrained-optimization problem represented by the algebraic equations with constraint of LMI-based robust stabilizability condition. Then, for the static constrained-optimization problem, the HTGA is employed to find the robust-stable and quadratic finite-horizon optimal active vibration controllers of the uncertain flexible rotor system. An example is given to demonstrate the applicability of the proposed integrative approach.

Closed-form equations for coupling linear structures using stiffness and damping elements

SUMMARY Larger and more flexible structures are being constructed. As a result, there is an increasing need for more effective, efficient, and innovative displacement control strategies. One such method is the idea of connecting adjacent structures. This control method has the merit of generating sufficient control forces under low frequencies, a property that is necessary for minimizing the displacement response of high-rise structures. In the present work, closed-form equations are derived for solving the vibration control problem of connecting two adjacent structures. In this design method, the maximum absolute displacement transmissibility of each structure is reduced. The closed-form solution is derived for a passive control method, where the structures are coupled via stiffness and damping elements connected in parallel. The presence of the stiffness element allows for the simultaneous tuning of both structures. The method is demonstrated for passive control of adjacent connected buildings subject to the El Centro ground motion. It is shown that the passive connection method is effective in reducing the response of both structures compared with the uncontrolled (unconnected) case. Copyright © 2011 John Wiley & Sons, Ltd.

Design of robust-stable and quadratic finite-horizon optimal active vibration controllers with low trajectory sensitivity for uncertain flexible mechanical systems using an integrative computational method

By integrating the robust stabilizability condition, the orthogonal-functions approach (OFA), and the hybrid Taguchi-genetic algorithm (HTGA), an integrative method is presented in this paper to design the robust-stable and quadratic finite-horizon optimal active vibration controller with low trajectory sensitivity such that (i) the flexible mechanical system with elemental parametric uncertainties can be robustly stabilized, and (ii) a quadratic finite-horizon integral performance index including a quadratic trajectory sensitivity term for the nominal flexible mechanical system can be minimized. In this paper, the robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal flexible mechanical feedback dynamic equations. By using the OFA and the LMI-based robust stabilizability condition, the robust-stable and quadratic finite-horizon optimal active vibration control problem for the uncertain flexible mechanical dynamic systems is transformed into a static constrained-optimization problem represented by the algebraic equations with constraint of LMI-based robust stabilizability condition; thus greatly simplifying the robust-stable and quadratic finite-horizon optimal active vibration control design problem. Then, for the static constrained-optimization problem, the HTGA is employed to find the robust-optimal active vibration controllers of the uncertain flexible mechanical systems. A design example is given to demonstrate the applicability of the proposed integrative approach.

FPGA-based implementation of high-speed active noise and vibration controllers

This manuscript describes the implementation of a general purpose multi-tonal disturbance compensator for active noise and vibration control problems on a high-speed computational architecture, based on a field programmable gate array (FPGA). The attenuation of the multi-tonal disturbance is addressed here using active control techniques for narrowband noise attenuation, namely designing an adaptive feedforward controller based on multiple notch filters. Simulation tests are reported to illustrate the potential benefits and achievable performance of the proposed architecture.

Placement optimization of actuator and sensor and decentralized adaptive fuzzy vibration control for large space intelligent truss structure

Large space truss structure is widely used in spacecrafts. The vibration of this kind of structure will cause some serious problems. For instance, it will disturb the work of the payloads which are supported on the truss, even worse, it will deactivate the spacecrafts. Therefore, it is highly in need of executing vibration control for large space truss structure. Large space intelligent truss system (LSITS) is not a normal truss structure but a complex truss system consisting of common rods and active rods, and there are at least one actuator and one sensor in each active rod. One of the key points in the vibration control for LSITS is the location assignment of actuators and sensors. The positions of actuators and sensors will directly determine the properties of the control system, such as stability, controllability, observability, etc. In this paper, placement optimization of actuators and sensors (POAS) and decentralized adaptive fuzzy control methods are presented to solve the vibration control problem. The electro-mechanical coupled equations of the active rod are established, and the optimization criterion which does not depend upon control methods is proposed. The optimal positions of actuators and sensors in LSITS are obtained by using genetic algorithm (GA). Furthermore, the decentralized adaptive fuzzy vibration controller is designed to control LSITS. The LSITS dynamic equations with considering those remaining modes are derived. The adaptive fuzzy control scheme is improved via sliding control method. One T-typed truss structure is taken as an example and a demonstration experiment is carried out. The experimental results show that the GA is reliable and valid for placement optimization of actuators and sensors, and the adaptive fuzzy controller can effectively suppress the vibration of LSITS without control spillovers and observation spillovers.