Independent Modal Space Control Method Research Articles

Active vibration optimal control of piezoelectric cantilever beam with uncertainties

Considering the stiffness characteristics of piezoelectric layer, the bending stiffness of piezoelectric cantilever beam is obtained by applying the first-order shear deformation theory. The finite element model of piezoelectric cantilever beam is established by Hamilton variation principle, and the modal superposition method is employed to reduce the order of the finite element model. At the maximum strain point, the sensors/actuators are equipped in pairs. Based on the uncertain dynamic model of piezoelectric cantilever beam, the independent modal space control method based on LQR (linear quadratic regulator) control is employed for the active control of the smart beam structure, and the weighted matrices Q and R are selected according to the energy criterion. The numerical simulations and experiments verify the effectiveness of the proposed finite element model and the active vibration optimal control.

Observer based active vibration control of flexible space structures with prescribed performance

This paper proposes an active vibration control approach to solve the vibration suppression problem of flexible space structures in the presence of external disturbances and parameter uncertainties. Based on the independent modal space control method, each mode can be decoupled and controlled separately. To meet the case that the velocity sensors are not available on the flexible structures, a neural network based state observer is designed for the estimation of the modal velocity. The neural network approximation is introduced into the observer design which can effectively deal with the disturbances and uncertainties in order to obtain more accurate observation results. Further, the controller and the adaptive law are derived by using the backstepping technique and prescribed performance control method with the stability of the whole closed-loop system analyzed via Lyapunov theory. Simulation results illustrate the effectiveness and vibration control performance of the proposed method.

Experimental study and numerical simulation of active vibration control of a highly flexible beam using piezoelectric intelligent material

Active vibration control of a flexible beam with piezoelectric pieces on the surface is investigated experimentally using the independent modal space control method, which is able to control the first three modes of the beam independently. A comparison between the responses of the beam before and after control indicates that the modal damping of the flexible beam is greatly improved and the effects of vibration suppression are very remarkable. The dynamic equation of the beam is deduced by Hamilton's principles, and numerical simulation of the active vibration control of the first three modes of the beam is also conducted in this paper. The simulation results match the experimental results very well. Both the experimental and numerical results indicate that by using piezo-patches as actuators the independent mode control method is a very effective approach to realize vibration suppression, and has promising applications in the aerospace field.

The Spatial Intelligent Structural Active Control Experimental Research

Active control in the application has more and more research, the independent modal space control method is transform the system equation into modal coordinates, then obtain the internal decoupling equations express by modal coordinates, and based on control algorithm calculate the modal control force, which achieve real-time control effect. The control calculation method is simple and efficient to meet the needs of active control. The paper introduce modal control theory and implement methods, design and manufacture the piezoelectric driving lever based on the working principle of the piezoelectric pile, then through the test, give the voltage-driving force relationship, which is linear. An active control experiment on a three-layer intelligence space structure had been done, it can be seen that through the active control, the corresponding modal displacement and acceleration of the structures control are a lot of inhibition; at the same time, through spectral analysis, it can be seen the structured modal damping coefficient corresponding to varying degrees have been improved.

Design of active vibration control for launcher of multiple launch rocket system

This study deals with analysis and design of active vibration control algorithm for the launcher of multiple launch rocket system (MLRS). The new method proposed is that guidance and control package are equipped on launcher, not rocket, to active control motion of launcher for the first time. It has interesting advantages as follows: (1) active vibration control is more competent, more pliable, and more realizable in engineering compared to passive vibration control. (2) The guidance and control package will not be destroyed. In this study, transfer matrix method of multibody system is used to build the controlled dynamic model of MLRS. This method does not need the global dynamic equations of system and has high computational rate. Independent modal space control method and optimal control theorem are applied to design control law with feedforward and feedback control loops. The modal filters are designed as the state estimator to obtain the modal coordinates and their derivatives. Modal disturbance force observer is designed to obtain modal disturbance force. Pulse-width pulse-frequency (PWPF) modulator is used to modulate the continue control force command into discrete control force in order to avoid high non-linear control action of pulse thruster. The control force provided by pulse thruster and parameters of PWPF are obtained. The numerical results indicate that control law determined by optimal theorem integrated with PWPF modulator achieves good performance in active vibration control of launcher. This study improves the performance of MLRS in resisting impact and provides theoretical support for accurate launch.

Optimal Research of Actuator Placement for Piezoelectric Smart Structure

The purpose of this paper is to investigate the optimal placement of piezoelectric actuator for active vibration control of smart structure. The structures can be described in the modal space based on the independent modal space control method and dynamic equations derived from finite element model. The modal damping ratios are derived from modal equations and an optimal target is given by maximizing the modal damping ratios. Accumulation method is adopted to the optimization calculation. Simulations are carried out for active vibration control of a conical shell with distributed piezoelectric actuators. Control effects proved the validity of the optimal method above by compared with the non-optimal results. The optimal method in this paper gives a useful guide for quantity optimization of actuators to piezoelectric structures.

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.

Optimal Placement of Piezoelectric Actuators in Adaptive Truss Structures

In the design of actively controlled structures, the determination of the actuator locations is a very important issue. In order to find the optimal placements of piezoelectric acutators in adaptive truss structures, optimal placement strategies developed in conjunction with the independent modal space control method are used in this paper. For this purpose, a finite truss element is developed accounting for the piezoelectric actuators. By using this finite element, eigenvectors consisting not only of nodal displacements but also of electric potentials are computed. The optimization algorithm calculating the optimal actuator placements makes use of the electric potentials to minimize the control effort. The minimization of the spillover energy into uncontrolled modes is an additional objective which can be taken into account by the optimization procedure. The method is illustrated by numerical examples.

Simultaneous Design and Control of Stiffened Laminated Composite Structures

The problem investigated here concerns the simultaneous design and control of structures. The structure considered is a laminated stiffened composite plate for which an optimum control system is designed by the minimization of an appropriate performance index with respect to both the control forces and structural design variables consisting of stiffener areas and the number of plies of a given orientation. To ensure a physically realistic structure appropriate constraints on the stiffener sizes, total weight, and structural frequencies are imposed. Nonlinear mixed‐integer programming is used to force the number of plies to take on integral values. The entire problem is posed as a three‐level optimization problem. Using the well‐known independent modal space control method, effects of plate geometry, initial disturbance conditions, and control effort penalty parameters on the optimal design are considered. The minimization process requires derivatives of eigenvalues and eigenvectors with respect to the des...

Experimental implementation of the modified independent modal space control method

In this study an experimental realization of a Modified Independent Modal Space Control (MIMSC) method to control the vibration of a flexible cantilevered beam is presented. The method relies in its operation on the use of one piezo-electric actuator to control several vibration modes through a uniquely developed “time sharing” strategy. The effectiveness of the MIMSC method, in damping out the beam vibration, is demonstrated clearly by comparing the results with those obtained by other modal control methods. Two methods are considered; namely, the Independent Modal Space Control (IMSC) method and the Pseudo-Inverse (PI) method. The experimental results obtained emphasize the feasibility of the MIMSC method as a viable alternative for controlling large flexible structures with very small number of actuators.

Modified Independent Modal Space Control Method for Active Control of Flexible Systems

A modified independent modal space control (MIMSC) method is developed for designing active vibration control systems for large flexible structures. The method accounts for the interaction between the controlled and residual modes. It also incorporates optimal placement procedures for selecting the optimal locations of the actuators in the structure in order to minimize the structural vibrations as well as the actuation effort. The MIMSC method relies on an important feature which is based on ‘time sharing’ of a small number of actuators, in the modal space, to control effectively a large number of modes. Numerical examples are presented to illustrate the application of the method to generic flexible systems. The obtained results suggest the potential of the devised method in designing efficient active control systems for large flexible structures.

Modal control of traveling waves in flexible structures

This paper is concerned with the control of a traveling wave in a structure by the independent modal-space control method. It is demonstrated that the control forces tend to concentrate in the immediate vicinity of the disturbance, and there are virtually no control forces acting at any point of the structure before the arrival of the disturbance. Two numerical examples are included, one for a string in transverse vibration and one for a beam in bending. Satisfactory control was achieved in spite of the fact that only a finite number of modes was retained for control.

Minimum-fuel control of high-order systems

The minimum-fuel control problem is of special interest in various space systems. To date, solutions of minimum-fuel control problems have been carried out for relatively low-order systems. Space structures, however, are generally characterized by a large number of degrees of freedom, so that minimum-fuel control of such systems requires a new approach. In the independent modal-space control (IMSC) method, the control laws are designed in the modal space for each mode independently. The minimum-fuel problem reduces to that of a set of independent second-order systems, so that minimum-fuel control is possible. This paper shows how the IMSC method can be used to control a space structure with a minimum amount of fuel. A numerical example is presented.

Control of non-self-adjoint distributed-parameter systems

Systems involving viscous damping forces, circulatory forces, and aerodynamic forces are non-self-adjoint. A method capable of controlling non-self-adjoint distributed systems is the independent modal-space control method, whereby the problem of controlling a distributed-parameter system is reduced to that of controlling an infinite set of independent, complex, second-order ordinary differential equations. In the case of optimal control, one must solve independent, complex, scalar Riccati equations. The transient solution of the Riccati equations can be found with relative ease and the steady-state solution can be found in closed form. A numerical example demonstrates the effectiveness of the method.

Modal decoupling conditions for distributed control of flexible structures

Introduction T problem of the control of distributed parameter systems can be roughly divided into two approaches: 1) discretize the system in space and then use finite dimensional control theory; and 2) deal with the distributed model directly without discretizing. Recently, Meirovitch and Baruh proposed a scheme for the optimal control of a certain class of conservative distributed parameter systems without resorting to discretization. In particular, they treated the control of self-adjoint conservative systems having known eigensolutions. It is the intent of this Note to point out that their results are applicable to a more general class of problems that includes nonconservative forces and to note that the necessary conditions are available for the existence of decoupling control laws. Decoupling control laws are defined to be those control laws dependent only on the modal state vector of the decoupled equation. This yields an infinite set of independent equations including the feedback control. The use of decoupled controls allows the distributed parameter control problem to be solved by the independent modal-space control method. This method allows each mode to be designed independently of other modes. As a result, the standard control problems involving optimal control and the regulator problem can be solved without difficulty. This method of control is not discussed in detail here, but is mentioned to supply motivation and application for the results that follow.

A comparison of control techniques for large flexible systems

Two broad approaches to the active control of large flexible systems are compared, namely, coupled control and independent modal-space control. The basic difference between the two approaches lies in the manner in which the feedback controls are designed. The two methods are compared qualitatively from design and computational viewpoints, and quantitatively through the work done, performance index, and spillover effects. The comparison shows the independent modal-space control method to possess many advantages over coupled control, as it permits easier design and implementation and requires less computational effort and control energy for implementation.

Robustness of the independent modal-space control method

The effect of parameter uncertainties on the control system performance of distributed-p arameter systems is examined. Because in general, the parameters contained in the equations of motion of the actual distributed system are, not known accurately, control forces designed on the basis of a postulated model will not control the actual distributed system effectively. In this paper it is shown by means of a stability theorem that, when the independent modal-space control (IMSC) method is used in conjunction with modal filters, any errors in the system parameters cannot lead to instability of the closed-loop system, so that the control system is very robust. A perturbation analysis is proposed for the computation of the closed-loop poles of large-order systems in the presence of parameter changes. I. Introduction T HE motion of a distributed-parameter system is governed generally by a set of simultaneous partial differential equations of motion. 1 The parameters contained in the equations of motion are, in general, continuous functions of the spatial variables. For flexible structures, these parameters represent mass, stiffness, and damping distributions. To control the distributed system, one must construct a mathematical model of the distributed system. The control forces then are designed on the basis of the mathematical model. A common approach to modeling is to convert the partial differential equations of the distributed system into an infinite set of ordinary differential equations.1'3 Then, a limited number of modes (generally the lowest) are retained for control. In designing the control system, one assumes that the eigensolution associated with the controlled modes is known with sufficient accuracy, which, in turn, assumes that the system parameters are known accurately. Errors in the eigensolution produce errors in the design and implementation of the controls. Hence, the question arises whether the control system designed on the basis of system parameters that are in error can control the actual system effectively; i.e., whether the control system is robust. The answer clearly depends on the degree of inaccuracy in the estimated state of the distributed system. For cases when this error is not very large, one intuitively expects very small deviations from the control system performance. In general, one should make some allowance in the control system design for parameter uncertainties. For cases when the parameters contained in the equations of motion, such as the mass and stiffness distributions, are known to within a multiplicative constant, only the system eigenvalues change and the eigenfunctions retain the same shape.4 A sensitivity study, based on a perturbation analysis treating the parameter errors as perturbations reveals that if the independent modal-space control (IMSC) method is used in conjunction with modal filters, the control system is relatively insensitive to parameter errors.4 When the spatial distributions of the system parameters are not known, however, both the estimated eigenvalues and eigenfunctions tend to differ from their actual values, so that the sensitivity analysis of Ref. 4 is not applicable.