Independent Modal Space Control Research Articles

Active control of a flexible structure with time delay

Time delay exists inevitably in active control, which may not only degrade the system performance but also render instability to the dynamic system. In this paper, a novel active controller is developed to solve the time delay problem in flexible structures. By using the independent modal space control method, the differential equation of the controlled mode with time delay is obtained from the time-delay system dynamics. Then it is discretized and changed into a first-order difference equation without any explicit time delay by augmenting the state variables. The modal controller is derived based on the augmented system using the discrete variable structure control method. The switching surface is determined by minimizing a discrete quadratic performance index. The modal coordinate is extracted from sensor measurements and the actuator control force is converted from the modal one. Since the time delay is explicitly included throughout the entire controller design without any approximation, the system performance and stability are guaranteed. Numerical simulations show that the proposed controller is feasible and effective in active vibration control of dynamic systems with time delay. If the time delay is not explicitly included in the controller design, instability may occur.

Integrated optimal design of flexible mechanism and vibration control

A method of simultaneous optimal design of flexible mechanisms and control with multiple frequency constraints based on the independent modal space control theory is proposed. Firstly, the performance index for simultaneous mechanism and control design is discussed. Secondly, an integrated optimal design algorithm is developed on the basis of Kuhn–Tucker optimality criteria, in which three damping factors are introduced to guarantee the algorithm that possesses good stability and convergence. Finally, numerical simulations are carried out on a path generating mechanism. Simulation results show that the performance of the control input is improved significantly after integrated optimization.

Active modal control of a flexible rotor

This study explores the applicability of a novel approach by applying a dual-level control for modal vibration suppression of a rotor possessing repeated rigid body modes. Independent modal space control (IMSC) of undamped or proportionally damped systems has been well established. However, the technology was not correctly developed for non-classically damped systems by the pioneer researchers. For non-proportionally damped systems with repeated rigid body modes, the problems of orthogonality and singularity must be treated in a different fashion to facilitate modal vibration control. The present approach applies a first level control to remove any combination of flutter, divergence, rigid body, and/or repeated modes by enabling positive definiteness of the augmented system. A second level control is then applied for the augmented system with complex modes. Ordinary decoupling procedure by using the orthogonality of the left and right eigenvectors can thus be applied for subsequent modal control to suppress excessive vibration of the complex dynamic systems. It is demonstrated that a mode switching approach by directing control to the modes with higher vibration contribution can be beneficial in alleviating the higher mode residual vibration.

Integrated optimization of structure and control for piezoelectric intelligent trusses with uncertain placement of actuators and sensors

The finite element modeling of truss structures with piezoelectric members is presented. Based on the approach of independent modal space control, the controllability and observability indices of the system related to the positions of actuators/sensors are demonstrated. Consequently, the effective damping response time is evaluated. The object of the optimization model is to minimize a specified performance index of the intelligent truss subjected to constraints on the natural frequency and the amplitude of displacement response as well as the applied voltages under a given disturbance. Structural sizing variables, control parameters and actuator/sensor placements are treated as the independent design variables. Coding, the calculation of fitness and the optimization procedure of Genetic Algorithms are discussed so as to solve the integrated optimization with two different types of design variable space: discrete and continuous. Numerical examples are presented to show the effectiveness and usefulness of integrated optimization of structure and control for piezoelectric intelligent trusses.

Optimal modal vibration suppression of a fluid-conveying pipe with a divergent mode

This study deals with the divergence characteristics of pipes conveying fluid and explores the applicability of active modal vibration control for suppressing the associated excessive structural vibration. The Timoshenko beam theory is used to establish the system equation of motion. The analysis is based on the finite element method. Active modal control technique is developed in this work for pipes conveying fluid with a flow speed exceeding the critical one. Optimal independent modal space control (IMSC) is applied for the design. For pipes conveying super-critical flow speed, as considered in this work, the system's eigenvalues have both real and complex roots, which must be dealt with in a different way from what has been established in the literature. A weighting matrix with finite weights is applied for the control of complex modes, whereas a weighting matrix with an infinite weight is used for controlling the divergent mode, with roots being real. From this study, it is demonstrated that the control approach proposed in this work can ensure closed loop stability. The mode switching scheme of directing control to the mode which has higher modal response is found to be beneficial in reducing the overall structural vibration of the fluid-conveying pipe.

Efficient modal control strategies for active control of vibrations

Some efficient strategies for the active control of vibrations of a beam structure using piezoelectric materials are described. The control algorithms have been implemented for a cantilever beam model developed using finite element formulation. The vibration response of the beam to an impulse excitation has been calculated numerically for the uncontrolled and the controlled cases. The essence of the method proposed is that a feedback force in different modes be applied according to the vibration amplitude in the respective modes i.e., modes having lesser vibration may receive lesser feedback. This weighting may be done on the basis of either displacement or energy present in different modes. This method is compared with existing methods of modal space control, namely the independent modal space control (IMSC), and modified independent modal space control (MIMSC). The method is in fact an extension of the modified independent space control with the addition that it proposes to use the sum of weighted multiple modal forces for control. The proposed method results in a simpler feedback, which is easy to implement on a controller. The procedure is illustrated for vibration control of a cantilever beam. The analytical results show that the maximum feedback control voltage required in the proposed method is further reduced as compared to existing methods of IMSC and MIMSC for similar vibration control. The limitations of the proposed method are discussed.

ACTIVE VIBRATION CONTROL OF AN AIRCRAFT CABIN PANEL USING PIEZOELECTRIC SENSORS AND ACTUATORS

In this paper, the active vibration suppression of an aircraft cabin panel embedded with piezoelectric sensors and actuators under sinusoidal or random excitation is studied experimentally. The Independent Modal Space Control (IMSC) approach is employed in the controller design. The piezoelectric sensors and actuators associated with the IMSC technique have been applied to the active vibration control of the aircraft panel, and shown to be effective in vibration control. A second order controller is selected in the control scheme to suppress the fundamental modal vibration response of the aircraft cabin panel. The mode shapes of the panel are experimentally obtained, and used as the parameters of the objective functions for minimizing the unwanted vibration responses by appropriately selecting the sensor and actuator gains. Based on the experimental results, it is found that the vibration levels of the open and closed loop systems differ by up to 5.0 dB (for sinusoidal excitation) and 7.4 dB (for random excitation), even when the control circuit is interfered by electrical and magnetic noises.

Modified independent modal space control of m.d.o.f. systems

The performance of the independent modal space control (IMSC) algorithm for structural vibration control is examined in this paper. Both the theoretical analysis and numerical simulation show that, for a multi-degree-of-freedom system, the modal control forces may increase the contributions of the vibration of higher modes (uncontrolled modes) to the system response if the IMSC algorithm is used to design a structural control system. Therefore, the responses of the controlled structure may be underestimated if the effects of control forces on the higher modes are not considered in the response analysis. A new control algorithm—modified independent modal space control (MIMSC) algorithm is proposed in this paper for eliminating the effect of modal control force on the uncontrolled modes. Numerical example shows that the structural responses can be effectively reduced when control system design is carried out based on the proposed algorithm. By comparing the simulated results obtained by the IMSC and MIMSC algorithms, it is found that, in order to achieve the same control objective, the proposed algorithm is more effective than IMSC since the modal control forces do not have any effect on the uncontrolled modes. In order to verify the effectiveness of the proposed algorithm, a practical example—active control design of UCLA Math-Science Building is presented and discussed.

Application of discrete-time variable structure control in the vibration reduction of a flexible structure

This paper studies the application of using the discrete-time variable structure control method to reduce the vibration of the flexible structure. The structure is subjected to arbitrary, unmeasurable disturbance forces. The concept of independent modal space control is adopted, and the system is studied by the discrete-time model. Here, discrete sensors and actuators are used. We choose the modal filters as the state estimator to obtain the modal co-ordinates and modal velocities for the modal space control. A discrete-time variable structure controller with a disturbance force observer is adopted due to its distinguished robustness property of insensitiveness to parameter uncertainties and external disturbances. The included disturbance force observer can observe the unknown disturbance modal forces, which are used in the discrete-time variable structure control law to cancel out the excitations. The upperbound limitations of the unknown disturbances in the variable structure control, therefore, are no longer needed. The switching surface, in the discrete-time variable structure control system, is designed in an optimal sense. That is, along the switching surface, the cost function of the states is minimized. The investigation of this research focuses on the optimal switching surface design and the control performances of the discrete-time variable structure controller. The performance of estimating the disturbance modal forces and the robustness property of the control law are also discussed.

Structural Vibration Suppression Using the Piezoelectric Sensors and Actuators

An experimental study for the active vibration control of structures subject to external excitations using piezoelectric sensors and actuators is presented. A simply supported plate and a curved panel are used as the controlled structures in two experiments, respectively. The Independent Modal Space Control (IMSC) approach is employed for the controller design. In order to increase the adaptability, the time-domain modal identification technique is incorporated into the controller to real-time update the system parameters. The adaptive effectiveness of the time-domain modal identification technique is tested by fixing an additional mass on the simply supported plate to change its structural properties. The vibration suppression performances of the controller are 5.7 dB and 10.8 dB for the simply-supported plate with/without the mass subject to a chirp sine excitation, respectively. For the experiment of the curved panel subject to a sinusoidal excitation, the vibration attenuation of the control scheme is 5.0 dB even the control circuit is subject to some noise generated by electrical and magnetic interferences.

ROBUST VIBRATION CONTROL OF A BEAM USING THE H∞-BASED CONTROLLER WITH MODEL ERROR COMPENSATOR

The vibration control of a flexible beam subjected to arbitrary, unmeasurable disturbance forces is investigated in this paper. The beam is analyzed by using modal expansion theorem. The independent modal space control is adopted for the active vibration control. Discrete sensors and actuators are used here. The modal filters are used as the state estimator to obtain the modal co-ordinates and modal velocities for the state feedback control. Because of the existence of the disturbance forces, the vibration control only with the state feedback control law cannot suppress the vibration well. The method of disturbance forces cancellation is then added in the feedback loop. In order to implement the disturbance forces cancellation, the unknown disturbance forces must be observed. The model error compensator is employed to observe the unknown disturbance modal forces for the direct cancellation. After the implementation of the disturbance modal forces cancellation, there are still some residual disturbance modal forces which excite the beam. The disturbance attenuation problem is of concern in the design of the state feedback control law. For ensuring that influence of the residual disturbance modal forces is reduced to an acceptable level, the robust static H∞ state feedback controller is designed. The vibration control performances of the feedback control with the H∞ controller and the disturbance forces cancellation are discussed.

Flexible Composite Wing with Internal Actuation for Roll Maneuver

Abstract : This paper is concerned with designing an optimum composite flexible wing structure to enhance roll maneuver capability at high dynamic pressures using an embedded actuating system without external control surfaces. A minimum weight design, with constraints on strength for three different flight conditions, on the frequency distribution and lift effectiveness was used for this study. The elastic twist and camber is achieved by providing a system of actuating elements distributed within the internal substructure of the wing to provide control forces. The modal approach is used to develop the dynamic equilibrium equations which culminates in the steady roll maneuver of a wing subjected to aerodynamic loads and the actuating forces. The distribution of actuating forces to achieve the specified steady roll rate and roll angle of the flexible vehicle within a specified time was determined by using Independent Modal-Space Control (IMSC) design approach. Here, a full-scale realistic wing is considered for the assessment of the strain energy and distribution of actuator forces required to produce the antisymmetric twist and camber deformation to achieve the specified roll performance.

A comparison of variable structure control strategy to classical control strategies for active vibration control of distributed structures

Independent Modal Space Control (IMSC) is known as an essential method of active vibration control of distributed elastical structures. However, Meirovitch, who advanced the method at the beginning of the 1980s, and other researchers have only investigated modal control law and control performance due to employing classical linear control strateries (e.g., pole allocation, optimal control, etc.) since the 1980s. In this study, authors theoretically and experimentally investigate the modal control law and control performance as using a nonlinear control strategy called variable structure control (VSC) in IMSC of the distributed structures, and then give a comparison of them to the results from using classical control strategies. Besides strong stablity robustness of VSC, the theoretical analysis also shows that, when the sensor–actuator couples employed are less than the number of the modes one desires to control, use of VSC can efficiently avoid the control spillover that often happens at residual modes. For active vibration control of the elastical structures with the classical control strategies, the control spillover usually is a difficult problem to deal with. [Work supported by Zhejiang STPF, PROC.]

Vibration Control of a Beam Using the Nearly Optimal Control Algorithm with a Disturbance Force Observer

ABSTRACTActive vibration control of a flexible beam subjected to arbitrary, unmeasurable disturbance forces is investigated in this paper. The concept of independent modal space control is adopted. Both the feedforward and feedback control is implemented here to reduce the beam vibration. Because of the existence of the disturbance forces, the feedforward control is applied by employing the idea of force cancellation. A modal space disturbance force observer is then established in this paper to observe the disturbance modal forces for the feedforward control. For obtaining the feedforward and feedback control gains with the optimal sense, the nearly optimal control law is derived, where the modal disturbance forces are regarded as additional states. The vibration control performances and the asymptotic properties of the control law are discussed.

Modal space vibration control of a beam by using the feedforward and feedback control loops

This paper introduces a vibration control method for a flexible beam subjected to arbitrary, unmeasurable disturbance forces. The concept of independent modal space control is adopted. Here, we choose the modal filters as the state estimator to obtain the modal coordinates and modal velocities for the modal space control. Because of the existence of the disturbance forces, applying only the state feedback to suppress the vibration usually cannot achieve the desired control performance. The modal space feedforward control is then introduced to cancel out the disturbance forces. In this paper, the feedforward and feedback control method is implemented to reduce the beam vibration. The disturbance force observer is established to observe the disturbance modal forces for the feedforward control. The control gains are derived from the extended optimal control algorithm, where the disturbance modal forces are treated as exogenous state variables. By combining the feedback, feedforward control laws and the disturbance force observer together, the vibration control performances are discussed.

Variable structure control of vibration of the simply-supported plates

Robust active vibration control technology is still on its way to develop, though there has been a great number of studies on active vibration control (AVC) topic published since 1980s. The key is to find a good control strategy fitting AVC use and with strong control robustness, in addition to other qualities. As a newer member of robust control strategies, variable structure control (VSC) has attracted control researchers to study its application potentiality at different engineering areas for recent years. Few of them, however, have already paid attention to use in AVC area. In this paper, VSC design methodology used for AVC of a simply-support rectangular plate is investigated. The control design process at the modal state-space is deduced and the matching conditions introduced. Numerically simulated results by using VSC under scheme of the independent modal space control are obtained and compared to those obtained by using least quadratic control and the poles allocation method. It shows that VSC has advantages over the traditional control strategies at control robustness and can control more vibratory modes. [Work supported by the Zhejiang Science and Technology plan fund, PRC.]

Active modal control of timoshenko pipes conveying fluid

This paper deals with vibration control of Timoshenko pipes conveying fluid. Excessive vibration in this flow induced vibration problem is suppressed via an active feedback control scheme. The strategy of the active vibration suppression technique will be presented and system dynamics formulated. Optimal independent modal space control technique is applied for best obtainable system performance. The computation consideration, implementation of control strategy, and the effectiveness of the control scheme are addressed. A finite element method is used for both the vibration and control analyses of the problem considered. Classical analysis by solving the partial differential equation is only applicable to systems with simple boundary conditions, such as simply supported pipes. When a more complex situation occurs, a closed form expression becomes very difficult, if not impossible, to obtain. The use of a finite element approach alleviates such deficiencies and is readily applicable to pipes with intermediate supports, nonuniform cross sections, and flexible supports. The problem of a large model size for the control system due to the use of the finite element approach is avoided by using the control technique presented. It is demonstrated in this work that a critical damping design can be achieved for the targeted mode controlled disregarding how large the model size is.

Maximal Modal Force Rule for Optimal Placement of Point Piezoelectric Actuators for Plates

Optimal placement of actuators on intelligent structures is an important part of intelligent structure designs. The optimal collocation of actuators includes placement collocation and number collocation. It decides stability, controllability and control efficiency of structural control systems. With the development of control technology, the optimal collocation of actuators in structures is more and more important. Although optimal collocation of actuators can be determined by experience in some cases, experience is useless for complicated structures. So optimal collocation of actuators must be realized by optimal theory. Based on modal control theory, the Maximal Modal Force Rule is put forward for intelligent flexible plates bonded point piezoelectric actuators on their surface in this paper. The rule points out that point piezoelectric actuators should be bonded on the places of maximal modal strains of every order mode to produce maximal modal control forces. The formulae for independent modal space control and coupling modal space control are derived. The results of computer emulating of a plate show that the rule is right and effective.

Modal Filters and Neural Networks for Adaptive Vibration Control

An adaptive control algorithm is investigated for the vibration suppression of a space truss structure using modal filters for independent modal space control and a neural network for online system identification. The modal filters are computed off-line using measured frequency response functions and estimated pole values for the modes of interest. They are used to conduct transformation of response measurements from physical coordinates to modal coordinates. The time histories in the modal coordinates are then processed in real time by the neural network to extract estimates of modal parameters, namely, natural frequency, damping ratio, and modal gain. To examine the performance of the adaptive control approach, a controller was designed using the modal filters and implemented on a laboratory space truss using a single reaction-mass actuator and 32 accelerometers. The performance of the modal filter-based controller is compared to that of a local rate feedback controller using the same actuator. The applicability of the neural network to adaptive control was demonstrated by real-time estimation of the modal parameters of the truss with and without control. Because the modal filter control gain can be adjusted to maintain a desired closed-loop damping ratio, which is tracked by the neural network, adaptive control of individual modes in a time-varying system is possible. Eventually, this type of adaptive controller will help develop a control system that can maintain desired closed- loop performance characteristics under significant modal parameter variations.

Non-spillover control design of tall buildings in modal space

In this paper, a new algorithm for active control design of structures is proposed and investigated. The algorithm preserves the decoupling property of the modal vibration equation and eliminates the spillover problem, which is the main shortcoming in the independent modal space control(IMSC) algorithm. With linear quadratic regulator(LQR) control law, the analytical solution of algebraic Riccati equation and the optimal actuator control force are obtained, and the control design procedure is significantly simplified. A numerical example for the control design of a tall building subjected to wind loads demonstrates the effectiveness of the proposed algorithm in reducing the acceleration and displacement responses of tall buildings under wind actions.