Peiman G. Maghami

Comparison of controller designs for an experimental flexible structure

Control system design and hardware testing are addressed for an experimental structure displaying the characteristics of a typical large flexible spacecraft. The practical aspects associated with designing and implementing various control design methodologies for a real system are described, and the results are given. The design methodologies under investigation include linear-quadratic-Gaussian (LQG) control, static and dynamic dissipative control, and H/sub infinity / optimal control. The merit of each design is based on its capacity for vibration suppression, its stability robustness characteristics with respect to unmodeled dynamics, and its ease of design and implementation. Among the three controllers considered, it is shown, through computer simulation and laboratory experiments, that the dynamic dissipative controller gives the best results.<<ETX>>

Robust eigensystem assignment for state estimators using second-order models

A novel design of a state estimator is presented using second-order dynamic equations of mechanical systems. The eigenvalues and eigenvectors of the state estimator are assigned by solving the second-order eigenvalue problem of the structural system. Three design methods for the state estimator are given in this paper. The first design method uses collocated sensors to measure the desired signals and their derivatives. The second design method uses prefilters to shift signal phases to obtain estimates of the signal derivatives. These two methods are used to build a second-order state estimator model. The third design method is the conventional one that converts a typical second-order dynamic model to a first-order model and then builds a state estimator based on the first-order model. It is shown that all three design methods for state estimation are similar. A numerical example representing a large space structure is given for illustration of the design methods presented in this paper.

Efficient Eigenvalue Assignment for Large Space Structures

A novel and efficient approach for the eigenvalue assignment of large, first-order, time-invariant systems is developed using full-state feedback and output feedback. The full-state feedback approach basically consists of three steps. First, a Schur decomposition is applied to triangularize the state matrix. Second, a series of coordinate rotations (Givens rotations) is used to move the eigenvalue to be reassigned to the end of the diagonal of its Schur form. Third, the eigenvalue is moved to the desired location by a full-state feedback without affecting the remaining eigenvalues. The second and third steps can be repeated until all the assignable eigenvalues are moved to the desired locations. Given the freedom of multiple inputs, the feedback gain matrix is calculated to minimize an objective function composed of a gain matrix norm and/or a robustness index of the closed-loop system. An output feedback approach is also developed using similar procedures as for the full-state feedback wherein the maximum allowable number of eigenvalues may be assigned. Numerical examples are given to demonstrate the feasibility of the proposed approach.

Design of neural networks for fast convergence and accuracy: dynamics and control

A procedure for the design and training of artificial neural networks, used for rapid and efficient controls and dynamics design and analysis for flexible space systems, has been developed. Artificial neural networks are employed, such that once properly trained, they provide a means of evaluating the impact of design changes rapidly. Specifically, two-layer feedforward neural networks are designed to approximate the functional relationship between the component/spacecraft design changes and measures of its performance or nonlinear dynamics of the system/components. A training algorithm, based on statistical sampling theory, is presented, which guarantees that the trained networks provide a designer-specified degree of accuracy in mapping the functional relationship. Within each iteration of this statistical-based algorithm, a sequential design algorithm is used for the design and training of the feedforward network to provide rapid convergence to the network goals. Here, at each sequence a new network is trained to minimize the error of previous network. The proposed method should work for applications wherein an arbitrary large source of training data can be generated. Two numerical examples are performed on a spacecraft application in order to demonstrate the feasibility of the proposed approach.

Integrated Controls-Structures Design Methodology for Flexible Spacecraft

This paper proposes an approach for the design of flexible spacecraft, wherein the structural design and the control system design are performed simultaneously. The integrated design problem is posed as an optimization problem in which both the structural parameters and the control system parameters constitute the design variables, which are used to optimize a common objective function, thereby resulting in an optimal overall design. The approach is demonstrated by application to the integrated design of a geostationary platform, and to a ground-based flexible structure experiment. The numerical results obtained indicate that the integrated design approach generally yields spacecraft designs that are substantially superior compared to the conventional approach, wherein the structural design and control design are performed sequentially.

Integrated Controls-Structures Design: A Practical Design Tool For Modern Spacecraft

An integrated controls-structures design approach is developed for a class of flexible spacecraft. The integrated design problem is posed in the form of simultaneous optimization of both the structural and the control design variables. The approach is demonstrated by application to integrated design of a geostationary platform and to a ground-based flexible structure experiment. The numerical results obtained indicate that the integrated design approach can yield spacecraft designs that have substantially superior performance over the conventional design approach wherein the structural design and control design are performed sequentially.

Eigensystem assignment with output feedback

A new approach for the eigenvalue assignment of linear, first-order, time-invariant systems using output feedback is developed. The approach can assign the maximum allowable number of closed-loop eigenvalues through output feedback provided that the system is fully controllable and observable, and both the input influence and output influence matrices are full rank. First, a collection of bases for the space of attainable closed-loop eigenvectors is generated using the Singular Value Decomposition or QR Decomposition techniques. Then, an algorithm based on subspace intersections is developed and used to compute the corresponding coefficients of the bases, and the required output feedback gain matrix. Moreover, the additional freedom provided by the multi-inputs and multi-outputs beyond the eigenvalue assignment is characterized for possible exploitation. A numerical example is given to demonstrate the viability of the proposed approach.

Design of Neural Networks for Fast Convergence and Accuracy

A novel procedure for the design and training of artificial neural networks, used for rapid and efficient controls and dynamics design and analysis for flexible space systems, has been developed. Artificial neural networks are employed to provide a means of evaluating the impact of design changes rapidly. Specifically, two-layer feedforward neural networks are designed to approximate the functional relationship between the component spacecraft design changes and measures of its performance. A training algorithm, based on statistical sampling theory, is presented, which guarantees that the trained networks provide a designer-specified degree of accuracy in mapping the functional relationship. Within each iteration of this statistical-based algorithm, a sequential design algorithm is used for the design and training of the feedforward network to provide rapid convergence to the network goals. Here, at each sequence a new network is trained to minimize the error of previous network. The design algorithm attempts to avoid the local minima phenomenon that hampers the traditional network training. A numerical example is performed on a spacecraft application in order to demonstrate the feasibility of the proposed approach.

Design of Constant Gain Dissipative Controllers for Eigensystem Assignment in Passive LTI Systems

Partial eigensystem assignment with output feedback can lead to an unstable closed-loop system. However, output feedback with passive linear time-invariant systems, such as flexible space structures, is guaranteed to be stable if the controller is dissipative. This paper presents a novel approach for synthesis of dissipative output feedback gain matrices for assigning a selected number of closed-loop poles. Dissipativity of a gain matrix is known to be equivalent to positive semidefiniteness of the symmetric part of the matrix. A sequential procedure is presented to assign one self-conjugate pair of closed-loop eigenvalues at each step using dissipative output feedback gain matrices, while ensuring that the eigenvalues assigned in the previous steps are not disturbed. The problem of assigning one closed-loop pair is reduced to a constrained solution of a system of quadratic equations, and necessary and sufficient conditions for the existence of a solution are presented. A minimax approach is presented for determining parameters which satisfy these conditions. This method can assign as many closed-loop system poles as the number of control inputs. A numerical example of damping enhancement for a flexible structure is presented to demonstrate the approach.

Neural networks for rapid design and analysis

Artificial neural networks have been employed for rapid and efficient dynamics and control analysis of flexible systems. Specifically, feedforward neural networks are designed to approximate nonlinear dynamic components over prescribed input ranges, and are used in simulations as a means to speed up the overall time response analysis process. To capture the recursive nature of dynamic components with artificial neural networks, recurrent networks, which use state feedback with the appropriate number of time delays, as inputs to the networks, are employed. Once properly trained, neural networks can give very good approximations to nonlinear dynamic components, and by their judicious use in simulations, allow the analyst the potential to speed up the analysis process considerably. To illustrate this potential speed up, an existing simulation model of a spacecraft reaction wheel system is executed, first conventionally, and then with an artificial neural network in place.