Structural control technology: system identification and control of flexible structures

Many future space missions involving flexible structures for large optics may require active vibration control to satisfy mission objectives. Thus, it is important for active control of flexible structures to be practically demonstrated in ground based experiments. These experiments can validate (or invalidate) existing theories and technology and provide directions for future research. This paper discusses three experiments conducted by Harris which successfully demonstrate control of flexible structures. The paper concludes with some remarks on the lessons learned from conducting these experiments.

This paper presents a survey of ground experiments primarily conducted in the United States and U.S. facilities dedicated to the study of active control of flexible structures. The facilities are briefly described in terms of capability, configuration, size, and instruments. Topics on the experiments include vibration suppression, slewing control, and system identification. The experiments are listed in tables containing the experiment's name, the responsible organization, a brief description of the test article configuration, and the actuator/sensor devices used in the experiment. Selected experiments will be further discussed to help illustrate the control problems. Some of the test facilities dedicated to ground testing of large space structures are discussed in more detail, to give the reader a better appreciation of ground-testin g work. Several research issues are mentioned, including real-time computer systems, test article suspension, and new actuator/sensor technology development.

Active vibration control of large flexible space structure is a challenging topic in the system dynamics and control of spacecraft. This paper proposes a novel approach for vibration control on a large hoop truss structure, typically used as mesh satellite antenna. First, to suppress the first-order bending modal response of the hoop truss structure with an initial disturbance, a piezoelectric bending actuator with excellent bending actuation performance was carefully designed as a key component of an active vibration control system. Then, the actuating characteristics of the actuator and the dynamic equations of the active structure were analyzed and formulated based on a finite element method. In order to improve the vibration-attenuating effect of the control system, a Mamdani-type fuzzy logic algorithm was employed in a closed-loop control system. Finally, simulations and experiments were implemented to validate the effectiveness of the proposed active control approach and structure. The experimental results showed that the decay time of first-order bending modal response (around 0.34 Hz) of control system reduces by 75% compared with that of the uncontrolled system. The results demonstrate that the proposed active vibration control system has good application potential in controlling the bending modes of a large flexible spacecraft.

Active robust vibration control of flexible structures

Many new promising model order reduction (MOR) methods and algorithms were developed during the last decade. Industry and academic research institutions intend to test, validate, compare, and use these new promising MOR techniques with their own models. Therefore, an MOR toolbox bridging the gap between theoretical, algorithmic, and numerical developments to an end-user-oriented program, usable by non-experts, was developed called ‘Model Order Reduction of Elastic Multibody Systems’ (Morembs). A C++ implementation as well as a Matlab implementation including an intuitive graphical user interface is available. Import from various FE programs is possible, and the reduced elastic bodies can be exported to a variety of programs to simulate the compact models. In the course of the various projects, many improvements on the algorithmic side were added. As we learned over the years, there is not one ‘optimal’ MOR method. ‘Optimal’ MOR depends on circumstances, like boundary conditions, excitation spectra, further model usage. The toolbox is now used, e.g., in solid mechanics, biomechanics, vehicle dynamics, control of flexible structures, or crash simulations. In all these use cases, the toolbox allows the user to facilitate their well-known modeling and simulation environment. Only the critical MOR process during preprocessing is performed with Morembs, which helps to compare the various MOR techniques to find the most suited one.

A new method is devised for the active control of flexible structures using output rate weighted linear optimal control. The method has an advantage over the traditional linear optimal control method in that it assigns weightage to the time rate-of-output, which may not be available for direct measurement in several important applications, such as gust and maneuver load alleviation in airplanes and ridequality augmentation in a variety of passenger vehicles. In applications to a single degree-offreedom system and a cantilevered beam, the rate-weighted optimal controller demonstrates a much better performance in terms of the smoothness of transient response, peak rate of transient response and settling time when compared to the traditional linear quadratic regulator. Introduction Generally, there are three different approaches applied to controlling flexible structures: (a) passive addition of structural damping and stiffness (b) generating specificaNy shaped input&* ,and (c) designing an optimal feedback controlle?S4. The first option is usually cumbersome and adds mass to the structure, while the second option, requiring generation of inputs that are insensitive to modeling errors and which do not excite unwanted dynamics, is di&tilt to achieve in practice. This leaves the third option of an active feedback controller as the most practical choice for controlling structural dynamics. The optimal linear *Assistant Professor, Department of Aerospace Engineering. Senior Member, AIAA. Copyright

: The goals of these research projects were to examine the nonlinear dynamics and control of flexible structures, some of which might be used for space applications. This project was a collaborative one involving structural, electrical and mechanical engineers. A major part of the research was on trusses/frames structures. Five different truss structures from three to ten meters in size were constructed, two with active controls. However, nonlinear dynamics of continuous beam type structures were also investigated. One of the principal themes was to explore what types of nonlinearities would result in chaotic and unpredictable vibrations. Loose joints in truss structures, friction, buckling and geometric nonlinearities were all found to lead to chaotic motions under certain periodic forcing conditions. Actuators and sensors for space truss active vibration suppression was investigated. New methods were developed for structural control using techniques for simulated annealing for actuator placement, nonlinear random vibrations of pin-jointed trusses, vibration analysis and new models to analyze chaotic dynamics in nonlinear structures with large deformations and friction forces. Finally, a major numerical effort resulted in new codes to predict large motions of structures under active control using parallel processing algorithms.

Sliding mode control of a large flexible space structure

A formulation of simultaneous optimization a passively damped structure and active controller has been attempted. In this study, viscoelastic materials (VEMs) have been utilized as one of device to enhance damping passively. The formulation needs to adopt the modeling method that is capable of designing not only the viscous passive damping but also the active controller adequately. For such requirement, the time domain approach that results the accurate model on the time domain is employed for the modeling of the viscoelastic structures. In order to create the reduced order model (ROM) for system design, the complex modal analysis has been developed, and the ROM is obtained with using both truncation and the balanced realization method. The accuracy of the ROM has been investigated based on a cantilevered partially viscoelastic beam example. The numerical results indicate that the time domain approach is more appropriate than the modal strain energy (MSE) method for creation of the ROM. Moreover, the strategy to derive the ROM is included into the formulation of simultaneous optimization of a viscoelastic structure and active controller. The formulation is applied to the design of a sandwich beam like space structure. The optimization results indicate that the optimization of viscous passive damping is useful for the total system cost reduction.

: Volume 2 presents theoretical advances and demonstrations in vibration control against broadband disturbances and in large-angle linear tracking control for flexible optical support structures. Stability results for discrete-time vibration control are also given. The importance of active transducer selection for broadband disturbance accommodation is emphasized. An algorithm for systematically selecting actuators with high influence on the regulated variables is described, together with its theoretical foundation. The algorithm is demonstrated on the ACOSS Model No. 2 structure, obtaining minimal selections with substantially fewer actuators than controlled modes. Disturbance-rejection control designs based on these selections exhibit stability in the presence of residual modes over a frequency range well beyond that of the design model. Sampled-data control for flexible structures is examined using second-order difference equations. A sufficient condition for geometric stability with velocity output feedback requiring non-colocation of actuators and sensors is obtained. Non-colocation reduces to colocation as the sampling period converges to zero. Optimal large-angle slew for linear tracking and terminal convergence is considered. Explicit solutions as a function of matrices satisfying linear algebraic equations are obtained. Demonstrations on a rotating rigid hub with four flexible appendages exhibit the computational efficiency of the solution techniques.

Active control of structures has been under intensive development for the last ten years. Reference 2 reviews much of the identification and control technology for structural control developed during this time. The technology was initially focused on space structure and weapon applications; however, recently the technology is also being directed toward applications in manufacturing and transportation. Much of this technology focused on multiple-input/multiple-output (MIMO) identification and control methodology because many of the applications require a coordinated control involving multiple disturbances and control objectives where multiple actuators and sensors are necessary for high performance. There have been many optimal robust control methods developed for the design of MIMO robust control laws; however, there appears to be a significant gap between the theoretical development and experimental evaluation of control and identification methods to address structural control applications. Many methods have been developed for MIMO identification and control of structures, such as the Eigensystem Realization Algorithm (ERA), Q-Markov Covariance Equivalent Realization (Q-Markov COVER) for identification; and, Linear Quadratic Gaussian (LQG), Frequency Weighted LQG and H-/ii-synthesis methods for control. Upon implementation, many of the identification and control methods have shown limitations such as the excitation of unmodelled dynamics and sensitivity to system parameter variations. As a result, research on methods which address these problems have been conducted.

In this paper we propose an active vibration control method for multiple high-rise buildings arranged in parallel. According to the proposed method, some flexible buildings connected by control devices called "active control bridges", are controlled through active interactions among them. This method has the merit of achieving sufficient control force under low frequency. Using this method, it is possible to control vibrations of super-tall buildings against strong winds and large earthquakes. In this study, three model buildings are connected with two actuators. The objective of this research is to control the first bending and torsional modes of each building using this method. The control effect is evaluated by exciting the base of the structures by time response and measuring the frequency response of the structures. Both simulation and experimental results show that fairly good control performance has been achieved by this method.

In this work, control system design and implementation for active vibration control (AVC) of flexible structures with piezoelectric actuators is studied. The goal is to reduce the effect of harmonic disturbances with known time-varying frequencies acting on a system. As a test bed, a thin flexible aluminum cantilevered beam with two symmetrically bonded piezoelectric actuators is used. The harmonic excitation is generated by two DC motors each of them with an unbalanced mass. A discrete-time model is obtained through black-box system identification methods. The control algorithm design is based on a plant description with a disturbance model as a linear parameter varying (LPV) system in linear fractional transformation (LFT) form. This results in a gain-scheduled controller where the harmonic disturbance frequencies are the scheduling variables. The experimental real-time results show the effectiveness of the controller and its capability to suppress time-varying harmonic disturbances, whose frequencies are measured directly from the DC motors. The design method leads to a controller that stabilizes the closed-loop system even for arbitrarily fast changes in the disturbance frequencies. In the real-time experiment, the controller suppresses a disturbance consisting of two independent harmonics with frequencies that vary over a range of 15 Hz.

** Wakes of aircraft external stores can generate high acoustic loads on downstream structures that lead to fatigue and failure of structural components. Structural vibration control systems have been employed to dampen structural loads but can become ineffective at high dynamic pressures. A recent wind tunnel study conducted at low subsonic speeds demonstrated that active flow control can enhance the effectiveness of a structural vibration control system on a fin submerged in the wake of an external store. This study continues this research and development effort through a transonic wind tunnel demonstration of an integrated aerodynamic wake and structural vibration control system. Results confirm that suppression strategies demonstrated at low subsonic speeds are applicable at transonic speeds and indicate that the integrated wake and structural vibration control system with limited control authority can provide suppression comparable to a highly capable vibration control system alone with only a fraction of the input power requirements.

An Overview of Modeling and Control of Large Flexible Space Structures