A decentralized linear quadratic control design method for flexible structures

A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass and stiffness properties

Unsymmetric Lanczos model reduction and linear state function observer for flexible structures

This report summarizes part of the research work accomplished during the second year of a two-year grant. The research, entitled 'Application of Lanczos Vectors to Control Design of Flexible Structures' concerns various ways to use Lanczos vectors and Krylov vectors to obtain reduced-order mathematical models for use in the dynamic response analyses and in control design studies. This report presents a one-sided, unsymmetric block Lanczos algorithm for model reduction of structural dynamics systems with unsymmetric damping matrix, and a control design procedure based on the theory of linear state function observers to design low-order controllers for flexible structures

Eigensystem realization algorithm modal identification experiences with mini-mast

This paper summarizes work performed under a collaborative research effort between the National Aeronautics and Space Administration (NASA) and the German Aerospace Research Establishment (DLR, Deutsche Forschungsanstalt fur Luft- und Raumfahrt). The objective is to develop and demonstrate system identification technology for future large space structures. Recent experiences using the Eigensystem Realization Algorithm (ERA), for modal identification of Mini-Mast, are reported. Mini-Mast is a 20 m long deployable space truss used for structural dynamics and active vibration-control research at the Langley Research Center. A comprehensive analysis of 306 frequency response functions (3 excitation forces and 102 displacement responses) was performed. Emphasis is placed on two topics of current research: (1) gaining an improved understanding of ERA performance characteristics (theory vs. practice); and (2) developing reliable techniques to improve identification results for complex experimental data. Because of nonlinearities and numerous local modes, modal identification of Mini-Mast proved to be surprisingly difficult. Methods were available, ERA, for obtaining detailed, high-confidence results

Wide-Area Control Schemes to Improve Small Signal Stability in Power Systems

One of the main concerns for the secure and reliable operation of power systems is the small signal stability problem. In the complex and highly interconnected structure of future power systems, relying solely on operator responses and conventional controls cannot assure reliability. Therefore, there is a need for advanced Wide-Area Control Schemes (WACS) that can automatically respond to degradation of reliability in the system. The main objective of this dissertation is to address two key challenges regarding the design and implementation of wide-area control schemes for damping inter-area oscillations. First is the high communication cost associated with optimal centralized control approaches. As power networks are large-scale systems, both the synthesis and the implementation of centralized controllers suggested by most of the previous studies are often impossible in practice. Second is the difficulty of obtaining accurate system-wide dynamic models for initiating and updating the control design. In this research, we introduced wide-area damping control strategies that not only ensure the small signal stability with the desired performance but also consider communication and model information limitations in the design. A state feedback formulation is proposed that aims to simultaneously optimize a standard Linear Quadratic Regulator (LQR) cost criterion and induce a pre-defined communication structure. We solved the proposed problem with three different objectives to target a specific wide-area damping control design challenge in each setting. First, the communication structure is enforced as a constraint in the optimization and solved for a large idealized power network with information symmetry. Second, to make the method suitable for systems with arbitrary structures and information patterns, we proposed a group-sparse regularization to be added to the optimization cost function. Applications of the method for inducing the desired communication network and finding effective measurement and control signal combinations were also investigated. Third, we paired the proposed optimal control with a real-time model identification approach, to create a wide-area control framework that is capable of dealing with model information limitations and inaccuracies in online implementation. The performances of the proposed wide-area damping control architectures are validated through nonlinear simulations on different test systems

Control oriented modelling of an integrated attitude and vibration suppression architecture for large space structures

This thesis is divided into two parts. The main focus of the research, namely active vibration control for large flexible spacecraft, is exposed in Part I and, in parallel, the topic of machine learning techniques for modern space applications is described in Part II. In particular, this thesis aims at proposing an end-to-end general architecture for an integrated attitude-vibration control system, starting from the design of structural models to the synthesis of the control laws. To this purpose, large space structures based on realistic missions are investigated as study cases, in accordance with the tendency of increasing the size of the scientific instruments to improve their sensitivity, being the drawback an increase of its overall flexibility. An active control method is therefore investigated to guarantee satisfactory pointing and maximum deformation by avoiding classical stiffening methods. Therefore, the instrument is designed to be supported by an active deployable frame hosting an optimal minimum set of collocated smart actuators and sensors. Different spatial configurations for the placement of the distributed network of active devices are investigated, both at closed-loop and open-loop levels. Concerning closed-loop techniques, a method to optimally place the poles of the system via a Direct Velocity Feedback (DVF) controller is proposed to identify simultaneously the location and number of active devices for vibration control with an in-cascade optimization technique. Then, two general and computationally efficient open-loop placement techniques, namely Gramian and Modal Strain Energy (MSE)-based methods, are adopted as opposed to heuristic algorithms, which imply high computational costs and are generally not suitable for high-dimensional systems, to propose a placement architecture for generically shaped tridimensional space structures. Then, an integrated robust control architecture for the spacecraft is presented as composed of both an attitude control scheme and a vibration control system. To conclude the study, attitude manoeuvres are performed to excite main flexible modes and prove the efficacy of both attitude and vibration control architectures. Moreover, Part II is dedicated to address the problem of improving autonomy and self-awareness of modern spacecraft, by using machine-learning based techniques to carry out Failure Identification for large space structures and improving the pointing performance of spacecraft (both flexible satellite with sloshing models and small rigid platforms) when performing repetitive Earth Observation manoeuvres

Balanced Dissipative Controllers for Flexible Structures

A balanced approach to shaping the closed-loop properties of the dissipative controllers for flexible structures is presented. In the balanced representation the properties of flexible structures are introduced, and a simple method of designing of the dissipative controllers is obtained. It relates the controller gains with the closed-loop pole locations. The examples illustrate the accuracy of the design method

Optimal Observability-based Modelling, Design and Characterization of Piezoelectric Microactuators.

International audienceThis paper deals with the optimal design of monolithic piezoelectric microactuators with integrated proprioceptive sensors. Dedicated to the microrobotic and micromechatronic fields, these works detail the modelling and the characterization of compliant structures with integrated actuating and sensing elements. The proposed optimal design procedure adresses not only static criteria but also dynamic ones. This leads to microdevices which are more performant with regards to mechanical (displacement, force...) and control (dynamics, stability, precision) characteristics. Efficient design of such devices is achieved using a flexible building block method. A topological optimization method combined with an evolutionary algorithm is used to optimize the design of truss-like planar structure. This method chooses the best location among the different piezoelectric elements. Different mechanical, actuation or sensing elements are accordingly chosen from a data bank. From the control point of view, optimisation criteria are considered to enforce the observability of the vibrational dominant modes of the structure. Therefore, control and observation Gramians are exploited in the optimal design to shape the open loop frequency response of both, actuation and sensing functions of the integrated device. In the last part of the paper, based on these results, the optimal design and manufacturing of an innovative piezoelectric flexible microgripper is proposed. The prototype is manufactured from a monolithic piezoelectric material (PIC 151). Its reduced size (15 mm x 18 mm) fits the requirement of both microrobotics and micromechatronics applications, which is suitable for micromanipulation tasks. The characterization and the performance of this integrated microactuator finally close the paper and the efficiency of the optimal design procedure for micromechatronics applications are shown

Identification of flexible structures for robust control

Documentation is provided of the authors' experience with modeling and identification of an experimental flexible structure for the purpose of control design, with the primary aim being to motivate some important research directions in this area. A multi-input/multi-output (MIMO) model of the structure is generated using the finite element method. This model is inadequate for control design, due to its large variation from the experimental data. Chebyshev polynomials are employed to fit the data with single-input/multi-output (SIMO) transfer function models. Combining these SIMO models leads to a MIMO model with more modes than the original finite element model. To find a physically motivated model, an ad hoc model reduction technique which uses a priori knowledge of the structure is developed. The ad hoc approach is compared with balanced realization model reduction to determine its benefits. Descriptions of the errors between the model and experimental data are formulated for robust control design. Plots of select transfer function models and experimental data are included

Control and structural optimization for maneuvering large spacecraft

Presented here are the results of an advanced control design as well as a discussion of the requirements for automating both the structures and control design efforts for maneuvering a large spacecraft. The advanced control application addresses a general three dimensional slewing problem, and is applied to a large geostationary platform. The platform consists of two flexible antennas attached to the ends of a flexible truss. The control strategy involves an open-loop rigid body control profile which is derived from a nonlinear optimal control problem and provides the main control effort. A perturbation feedback control reduces the response due to the flexibility of the structure. Results are shown which demonstrate the usefulness of the approach. Software issues are considered for developing an integrated structures and control design environment