Stochastic and adaptive systems : interim report

Includes bibliographical references.Research supported by Air Force Office of Scientific Research (AFSC), Research Grant AFOSR 77-3281. Covers time period, March 1, 1977 to February 28, 1978.by Michael Athans and Sanjoy K. Mitter

A final report of research on stochastic and adaptive systems under grant AFOSR 77-3281B for the period February 1, 1978 to January 31, 1979

Final report"March 1979."Bibliography: p. 17-19.Grant AFOSR-77-3281Bby Michael Athans and Sanjoy K. Mitter

Precise control of flexible manipulators

The design and experimental testing of end point position controllers for a very flexible one link lightweight manipulator are summarized. The latest upgraded version of the experimental set up, and the basic differences between conventional joint angle feedback and end point position feedback are described. A general procedure for application of modern control methods to the problem is outlined. The relationship between weighting parameters and the bandwidth and control stiffness of the resulting end point position closed loop system is shown. It is found that joint rate angle feedback in addition to the primary end point position sensor is essential for adequate disturbance rejection capability of the closed loop system. The use of a low order multivariable compensator design computer code; called Sandy is documented. A solution to the problem of control mode switching between position sensor sets is outlined. The proof of concept for endpoint position feedback for a one link flexible manipulator was demonstrated. The bandwidth obtained with the experimental end point position controller is about twice as fast as the beam's first natural cantilevered frequency, and comes within a factor of four of the absolute physical speed limit imposed by the wave propagation time of the beam

Environmental test chamber for the support of learning and teaching in intelligent control

The paper describes the utility of a low cost, 1 m2 by 2 m forced ventilation, micro-climate test chamber, for the support of research and teaching in mechatronics. Initially developed for the evaluation of a new ventilation rate controller, the fully instrumented chamber now provides numerous learning opportunities and individual projects for both undergraduate and postgraduate research students

A semidefinite relaxation procedure for fault-tolerant observer design

A fault-tolerant observer design methodology is proposed. The aim is to guarantee a minimum level of closed-loop performance under all possible sensor fault combinations while optimizing performance under the nominal, fault-free condition. A novel approach is proposed to tackle the combinatorial nature of the problem, which is computationally intractable even for a moderate number of sensors, by recasting the problem as a robust performance problem, where the uncertainty set is composed of all combinations of a set of binary variables. A procedure based on an elimination lemma and an extension of a semidefinite relaxation procedure for binary variables is then used to derive sufficient conditions (necessary and sufficient in the case of one binary variable) for the solution of the problem which significantly reduces the number of matrix inequalities needed to solve the problem. The procedure is illustrated by considering a fault-tolerant observer switching scheme in which the observer outputs track the actual sensor fault condition. A numerical example from an electric power application is presented to illustrate the effectiveness of the design

Research on optimal control, stabilization and computational algorithms for aerospace applications

The research carried out in the areas of optimal control and estimation theory and its applications under this grant is reviewed. A listing of the 257 publications that document the research results is presented

Proportional-integral-plus control applications of state-dependent parameter models

This paper considers proportional-integral-plus (PIP) control of non-linear systems defined by state-dependent parameter models, with particular emphasis on three practical demonstrators: a microclimate test chamber, a 1/5th-scale laboratory representation of an intelligent excavator, and a full-scale (commercial) vibrolance system used for ground improvement on a construction site. In each case, the system is represented using a quasi-linear state-dependent parameter (SDP) model structure, in which the parameters are functionally dependent on other variables in the system. The approach yields novel SDP-PIP control algorithms with improved performance and robustness in comparison with conventional linear PIP control. In particular, the new approach better handles the large disturbances and other non-linearities typical in the application areas considered

A homotopy algorithm for digital optimal projection control GASD-HADOC

The linear-quadratic-gaussian (LQG) compensator was developed to facilitate the design of control laws for multi-input, multi-output (MIMO) systems. The compensator is computed by solving two algebraic equations for which standard closed-loop solutions exist. Unfortunately, the minimal dimension of an LQG compensator is almost always equal to the dimension of the plant and can thus often violate practical implementation constraints on controller order. This deficiency is especially highlighted when considering control-design for high-order systems such as flexible space structures. This deficiency motivated the development of techniques that enable the design of optimal controllers whose dimension is less than that of the design plant. A homotopy approach based on the optimal projection equations that characterize the necessary conditions for optimal reduced-order control. Homotopy algorithms have global convergence properties and hence do not require that the initializing reduced-order controller be close to the optimal reduced-order controller to guarantee convergence. However, the homotopy algorithm previously developed for solving the optimal projection equations has sublinear convergence properties and the convergence slows at higher authority levels and may fail. A new homotopy algorithm for synthesizing optimal reduced-order controllers for discrete-time systems is described. Unlike the previous homotopy approach, the new algorithm is a gradient-based, parameter optimization formulation and was implemented in MATLAB. The results reported may offer the foundation for a reliable approach to optimal, reduced-order controller design

Control optimization, stabilization and computer algorithms for aircraft applications

Description based on: 22nd, Mar./Sept.1977 Edited by: Michael Athans, Alan S. Willsky, 1979/80-NASA Grant NGL 22-009-124. M.I.T. Project OSP 76265. Issued by: M.I.T. Electronic Systems Laboratory, -1978; M.I.T. Laboratory for Information and Decision Systems, 197