Modal Control Strategy Research Articles

Implementation of Modal Control for Seismically Excited Structures using Magnetorheological Dampers

This paper proposes an implementation of modal control for seismically excited structures using magnetorheological (MR) dampers. Many control algorithms such as clipped-optimal control, decentralized bang-bang control, and the control algorithms based on Lyapunov stability theory have been adopted for semiactive systems including MR dampers. In spite of good features, some algorithms have drawbacks such as poor performance or difficulties in designing the weighting matrix of the controller. However, modal control reshapes the motion of a structure by merely controlling a few selected vibration modes. Hence a modal control scheme is more convenient to design the controller than other control algorithms. Although modal control has been investigated for several decades, its potential for semiactive control, especially for the MR damper, has not been exploited. Thus, in order to study the effectiveness for a MR damper system, a modal control scheme is implemented to seismically excited structures. A Kalman filter is included in a control scheme to estimate modal states from measurements by sensors. Three cases of the structural measurement are considered by a Kalman filter to verify the effect of each measurement; displacement, velocity, and acceleration, respectively. Moreover, a low-pass filter is applied to eliminate the spillover problem. In a numerical example, a six-story building model with the MR dampers on the bottom two floors is used to verify the proposed modal control scheme. The El Centro earthquake is used to excite the system, and the reduction in the drifts, accelerations, and relative displacements throughout the structure is examined. The performance of the proposed modal control scheme is compared with that of other control algorithms previously studied. The numerical results indicate that the motion of the structure is effectively suppressed by merely controlling a few lowest modes, although resulting responses varied greatly depending on the choice of measurements available and weightings.

Probabilistic Approach for Nonlinear Modal Control of MDOF Structures Subjected to Multiple Excitations

Abstract: A nonlinear control strategy with limited control force is applied to the modal control of the multi-degree-of-freedom (MDOF) structure subjected to multiple excitations. For the modal control of the MDOF structure, a new eigenvalue assignment algorithm that modifies the dynamic characteristics of only the specific mode is proposed. For the probabilistic evaluation of the proposed nonlinear modal control, the joint probability density function (PDF) of the equivalent nonlinearly controlled single-degree-of-freedom (SDOF) system is obtained by the solution of the reduced Fokker–Planck equation for the equivalent nonlinear system. To overcome the difficulty in the application of the joint PDF to the MDOF structure controlled by the hybrid mass damper (HMD) system and subjected to multiple excitations, the equivalent damping ratio is proposed. The results of the analysis indicate that the proposed nonlinear modal control strategy is effective for the control of MDOF structures requiring a significantly smaller peak control force than the linear quadratic Gaussian (LQG) controller to produce a similar control performance level.

Effect of debonding in active constrained layer damping patches on hybrid control of smart beams

A new model for a smart beam with a partially debonded active constrained layer damping (ACLD) patch is presented, and the effects of the debonding of the ACLD patch on both passive and hybrid control are investigated. In this model, both shear and compressional vibrations of the viscoelastic material (VEM) layer are considered. The moment inertia and the transverse shear effect are also taken into account based on the Timoshenko’s beam theory. The adhesive layer between the host beam and the piezoelectric sensor patch is modeled as an elastic load transferring media. The debonding of the ACLD patch is approximated by removing the VEM between the constraining layer and the host beam in the debonding region, and the continuity conditions are imposed based on displacement continuity and force balance. A modal velocity observer-based modal control scheme is also given to perform the active modal control of the beam. In order to examine the effects of part debonding of the ACLD patch, the characteristic equation of the beam treated with an ACLD patch is derived. The simulation example results show that an edge debonding of the ACLD patch can significantly affect both passive and hybrid control. It is also found that the additional mode induced by the debonding has unique effects on the modal damping ratios and frequencies of both open-loop and closed-loop system.

Selective Modal Control Theory for Piezolaminated Anisotropic Shells

A general selective modal control design methodology is presented for piezolaminated anisotropic shell systems, which uses selective modal transducers recently developed by the authors for piezo-shells in order to realize any number of possible modal control strategies. A selective modal control design procedure, which dee nes a step-bystep framework through which structural and control subdesign processes are effectively integrated, is specie ed. Several conditions that sufe ciently ensure asymptotic stability are derived and then discussed in the context of deriving selective modal control methods, which are stability-robust to modeling and implementation errors. Several design examples are given. A numerical example is then presented in which a stability-robust optimal selective modal control design is developed for a cantilevered anisotropic cylindrical shell panel. Maintaining a linear feedback law, a selective modal transducer is employed, whose design parameters were chosen so as to optimize the system response to a given initial excitation. Frequency and transient response analyses demonstrate a dramatic enhancement in system performance and are shown to accurately concur with theoretical predictions.

Modal control of seismic structures using augmented state matrix

In conventional methods of modal control, the number of controllable structural modes is usually restrained by the number of sensors that feedback the structural signals. In this paper a modal control scheme where the feedback gain is formulated in an augmented state space is proposed. The advantage of the proposed method is that it increases the number of the controllable modes without adding extra sensors. The method is verified experimentally by an earthquake simulation test with a full-scale building model. The proposed modal control was also compared with the conventional ones in the test. For the building model tested, the performance of the proposed control with only one feedback signal can be as efficient as that of modal control with full state feedback. Copyright © 2001 John Wiley & Sons, Ltd.

Modal Controllers for Active Steering of Railway Vehicles with Solid Axle Wheelsets

This paper presents the development of a modal control strategy for the active steering of solid axle railway vehicles and reveals benefits of actively stabilising the wheelsets of a railway vehicle. A modal decomposition is applied to a 2-axle railway vehicle to de-couple its body lateral and yaw motions and hence to allow more detailed analysis of the vehicle behaviour and more robust design of active controllers. Independent controllers for the two motions are developed based on the two de-coupled modes. Parameter variations such as creep coefficients and wheelset conicity are taken into account in the design process to guarantee a robust design. The study shows that, compared to a passive vehicle, the vehicles with actively steered wheelsets not only perform much better on a curved track, but also improve the ride quality on straight track. Computer simulations are used in the study to verify the development of the controllers and assess the system performance with the control scheme proposed.

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.

Modal control of piezolaminated anisotropic rectangular plates - II Control theory

A general selective modal control design methodology is presented for piezolaminated anisotropic plate systems that utilizes selective modal transducers to realize any number of possible modal control strategies. A selective modal control design procedure is specified that defines a step-by-step framework through which the structural and control subdesign processes are effectively integrated. Several conditions that sufficiently ensure asymptotic stability are derived and then discussed in the context of deriving selective modal control methods that are stability robust to modeling and implementation errors Several selective modal control examples are then given in which selective modal transducers are designed and control laws chosen so as to allow for 1) the contributions of any given mode to the active energy extraction rate to be directly specified and 2) pole locations to be selectively and dynamically varied or 3) both pole locations and selective modal transducer design constants to be optimally determined. A numerical example is presented in which a stability-robust optimal selective modal control method is developed for a cantilevered anisotropic plate. Maintaining a linear feedback law, a single self-sensing selective modal transducer is employed whose design parameters were chosen to optimize the system response to a given initial excitation. Frequency and transient response analyses show a dramatic enhancement in system performance and accurately concur with theoretical predictions. The example serves both to illustrate the design process and to independently validate selective modal transducer and selective modal control theoretical results.

Nonlinear modal control method

This work extends previous work on nonlinear normal modes to include the case of forced response. This allows the nonlinear normal mode method to be applied to the feedback control problem providing a new method of controlling nonlinear multiple-degree-of-freedom systems. The proposed method uses a transformation proposed earlier for homogeneous systems written in state-space form. The coordinate transformation for the forcing vector is defined here in state space and related to the physical coordinate system. The result is a pseudomodal decoupling transformation of a nonlinear inhomogeneous system. Although interesting in its own statement, this transformation also provides a nonlinear modal control scheme. This result is applied to a known coupled two degree-of-freedom oscillator with a cubic stiffness term. The results illustrate the design of a nonlinear modal control law.

Active Control of Sound in Acoustic Waveguides, Part I: Theory

This is the first of two papers in which the performance of active noise control systems in rigid-walled, finite-length, rectangular waveguides is discussed. The theory is developed such that optimal secondary source strengths are found to minimize three performance criteria: pressure at a selected set of points within the waveguide; potential energy in a selected volume of the waveguide; and power in the downstream region of the waveguide. The minimum pressure solution is a double summation over all the modes in the duct. This solution is difficult to interpret unless a finite number of modes are considered, and the pressure is measured to take advantage of the orthogonal properties of the high order modes in the waveguide. When evanescent energy is neglected and the pressure is measured at proper locations, the solution of the pressure minimization problem is similar to the solution of the global problem (i.e., minimization of either potential energy or power). The pressure minimum solution converges to the optimal global solution when the waveguide is infinite or when modal control strategies are implemented.

Decoupling Vibration Control of a Flexible Rotor System with Symmetric Mass and Stiffness Properties

The paper investigates the control problem for a flexible rotor system with symmetric mass and stiffness properties and proposes an internal and external decoupling control scheme to simplify the controller design for such a system, where the existence of gyroscopic effects during rotation is neglected. The whole flexible rotor system can eventually be separated into four flexible subsystems without knowledge of the system parameters, and the control algorithm for each subsystem can be designed and implemented independently. Simulation results demonstrate the effectiveness of using the proposed scheme in conjunction with the optimal modal space control scheme.

Nonlinear oscillations of a controlled periodic system

The motion of a spinning symmetric satellite in an elliptic orbit is examined. The linearized equations of motion for the system have periodic coefficients, and a modal control scheme for such systems is used to stabilize the linearized equations. The nonlinear behavior of both the controlled and uncontrolled system is examined using Poincare maps. The behavior of the nonlinear controlled system is shown to depend on the controller gain with stable periodic solutions appearing at higher gains.

Implementation of actuators for the independent modal space control scheme

The Independent Modal Space Control (IMSC) method avoids control spillover generated by conventional control schemes such as Coupled Model Control (CMC) by decoupling the large flexible space structure into independent subsystems of second order and controlling each mode independently. The IMSC implementation requires that the number of actuators be equal to that of modeled modes, which is in general very huge. Consequently the number of required actuators is unrealizable. In this paper, two methods are proposed for the implementation of IMSC with a reduced number of actuators. In the first method, the first m modes are optimized, leaving the last ( n − m) modes unchanged. In the second method, generalized inverse matrices are employed to design the feedback controller so that the control scheme is suboptimal with respect to IMSC. The performance of the proposed methods is tested by performing computer simulation on a simply supported beam. Simulation results will be presented and discussed.

Pole assignment in rotating disk vibration control using complex modal state feedback

Modal state feedback controls of rotating disk vibrations in real and complex fields are formulated and compared. Pole assignment in real modal space necessitates the simultaneous assignment of eigenvalues and eigenvectors to uniquely determine the feedback gain matrix. Pole assignment in complex modal space, however, uniquely determines the feedback gain matrix, because preservation of the isotropic nature in the uncontrolled and controlled modal systems only allows the assignment of the isotropic eigenstructure. The proposed complex modal control scheme reduces the order of the system to be dealt with. It also minimises the required control energy and the transient magnitudes of the state.

Travelling Wave Control of Rotating Discs and Analysis of its Spillover Effect

A modal control scheme for rotating disc systems is developed based upon the finite-dimensional sub-system model including a few lower backward travelling waves important to the disc response. For the single discrete sensor and actuator system, a polynomial equation, which determines the closed-loop system poles, is derived and the spillover effect is analysed, providing a sufficient condition for stability. Finally, simulation studies are performed to show the effectiveness of the travelling wave control scheme proposed.

Adaptive modal control of structural dynamic systems using recursivelattice filters

This paper describes the way in which a parameter identification scheme can be interfaced with a modal control scheme in order to achieve adaptive control of structural dynamic systems. The identification scheme is based on recursive least square lattice filters and the control scheme is a modal pole placement technique for vibration suppression. To achieve stable adaptive control and meet performance requirements, the identification and control schemes must be properly interfaced. This has been done by analyzing the control law to determine the range of parameter errors that will result in stability and acceptable performance. This information is used to determine the requirements for accuracy of an on-line parameter identification scheme. The general philosophy considers the testing of the suitability of the identified parameters for control system design. The tests consist of checking the fit error, convergence of the parameters, and the signal-to-noise level in the measurement data. After all the tests are passed, the new parameters are used to modify the control system feedback gains and the control forces are applied. This paper presents a detailed description of the test procedures and their application to the simulations of closed-loop adaptive control for the 12-ft, free-free beam apparatus at NASA Langley Research Center.

Minimal Time Control of Spatial Xenon Oscillations in Nuclear Power Reactors

The theoretical minimal time modal control strategy to suppress xenon oscillations in nuclear reactors was found to be of the Bang-Bang type. Such control policy implies instantaneous variation of ...