Nonlinear and adaptive control

The primary thrust of the research was to conduct fundamental research in the theories and methodologies for designing complex high-performance multivariable feedback control systems; and to conduct feasibiltiy studies in application areas of interest to NASA sponsors that point out advantages and shortcomings of available control system design methodologies

Status report #6 on nonlinear and adaptive control

Includes bibliographical references (p. 13-16).Status report; January 31, 1988Supported by NASA. NAG 2-297 MIT OSP. 95178prepared by Michael Athans, Gunter Stein, Lena Valavani

Status report #2 on nonlinear and adaptive control

"December 31, 1985."Bibliography: leaf 10.NASA Grant NSG 2-297 MIT OSP no. 95178Michael Athans, Gunter Stein, Lena Valavani

Status report #4 on nonlinear and adaptive control

Includes bibliographical references.Supported by NASA. NAG 2-297 MIT OSP no.95178prepared by Michael Athans, Gunter Stein, Lena Valavani ; submitted to NASA, Langley Research Center, Ames Research Center

Final report on robust stochastic adaptive control

Includes bibliographical references.Supported by the Office of Naval Research under contract N00014-82-K-0582 NR606-003 MIT OSP no.92775prepared by Lena Valavani, Michael Athans ; submitted to Office of Naval Research, Mathematical Sciences Division

A classification of techniques for the compensation of time delayed processes. Part 2: Structurally optimised controllers

Following on from Part 1, Part 2 of the paper considers the use of structurally optimised controllers to compensate time delayed processes

Prediction for control

5th IFAC Conference on System Structure and Control 1998 (SSC'98), Nantes, France, 8-10 JulyThis paper shows that "optimal" controllers based on "optimal" predictor structures are not "optimal" in their closed loop behaviour and that predictors should be designed taking into account closed-loop considerations. This is first illustrated with a first order plant with delay. The ISE index is computed for two typical optimal controllers (minimum variance controller and generalized predictive controller) when a stochastic disturbance is considered. The results are compared to those obtained by the use of a non optimal PI controller that uses a non optimal Smith predictor and performs better than the optimal controllers for the illustrative example. A general structure for predictors is proposed. In order to illustrate the results, some simulation examples are shown.Ce papier montre que des lois de commandes "optimales" basees sur des structures predictives "optimales" ne sont pas "optimales" dans leur comportement en boucle fermee et que la synthese de predicteurs devrait prendre en compte des considerations de boucle fermee. Cela est d'abord illustre avec un systeme du premier ordre a retard. l'index ISE est calcule pour deux lois de commandes optimales typiques (loi de commande a variance minim ale et loi de commande predictive generalisee), quand une perturbation stochastique est consideree. Les resultats sont compares a. ceux obtenus avec un regulateur PI non optimal base sur un predicteur de Smith non optimal et sont, pour l'exemple illustratif, meilleurs que ceux obtenus avec un regulateur optimal. Vne structure generale de predicteur est proposee. Pour illustrer les resultats, des exemples de simulations sont montres

Diagonalisation of a class of multivariable system via an actuator linearisation technique

Many multivariable (systems with many inputs/outputs) industrial processes can, to a good degree of approximation, be modelled by a transfer function matrix, where all of the interaction occurs in a matrix of constant coefficients. This reflects the fact that the dynamics of the section in which the interaction occurs are very fast compared with the other dynamics in the system. Examples of such systems include steel rolling mills and boiler systems. Such multivariable systems are relatively easy to design controllers for, since the system may be diagonalised by an inverse of the constant gain matrix, followed by suitable single-loop dynamic compensation. However, this approach depends on the linearity of the dynamical elements in the system. Such a condition is voilated by the presence of non-linear actuators, which are a feature of many industrial systems. The presence of such actuators within a multivariable control system as described above can cause very significant interaction problems, with associated degradation in performance, particularly during transients. This paper describes a straightforward technique, which is effective in linearising typical non-linear industrial actuators, allowing diagonalisation to be effectively achieved at all frequencies. The technique relies on a simple describing function analysis and manifests itself as a time-varying linearising precompensator for each non-linear actuator. A simple example is used to demonstrate the effectiveness of the method and it is then shown in application with multivariable boiler and steel mill models

Robust multivariable controller design for flexible spacecraft

Large, flexible spacecraft are typically characterized by a large number of significant elastic modes with very small inherent damping, low, closely spaced natural frequencies, and the lack of accurate knowledge of the structural parameters. Summarized here is some recent research on the design of robust controllers for such spacecraft, which will maintain stability, and possible performance, despite these problems. Two types of controllers are considered, the first being the linear-quadratic-Gaussian-(LQG)-type. The second type utilizes output feedback using collocated sensors and actuators. The problem of designing robust LQG-type controllers using the frequency domain loop transfer recovery (LTR) method is considered, and the method is applied to a large antenna model. Analytical results regarding the regions of stability for LQG-type controllers in the presence of actuator nonlinearities are also presented. The results obtained for the large antenna indicate that the LQG/LTR method is a promising approach for control system design for flexible spacecraft. For the second type of controllers (collocated controllers), it is proved that the stability is maintained in the presence of certain commonly encountered nonlinearities and first-order actuator dynamics. These results indicate that collocated controllers are good candidates for robust control in situations where model errors are large

Robust Control of Nonlinear Multibody Flexible Space Structures

A generic nonlinear math model of a multibody flexible system is developed. Asymptotic stability of such systems using dissipative compensators is established. It is proved that, under certain conditions, this class of systems exhibit global asymptotic stability under dissipative compensation. The dissipative compensators considered are static as well as dynamic dissipative compensators. The stability proofs are based on passivity approaches, Lyapunov methods, as well as a key property of such systems, i.e., skew-symmetricity of certain matrix. The importance of the stability results obtained is that the stability is robust to parametric uncertainties and modeling errors. For static dissipative compensators, it is shown that stability is not only robust to parametric uncertainties and modeling errors but also to certain actuator and sensor nonlinearities. Actuator nonlinearities considered are (0, ∞) sector monotonically non-decreasing type, which include realistic nonlinearities such as the saturation nonlinearity. In the presence of dead-zone and hysteresis type nonlinearities, system trajectories do not approach equilibrium point asymptotically, however, it is shown that there is a compact region of ultimate boundedness and system trajectories do not go unbounded. The sensor nonlinearities considered are (0,$\infty$) sector nonlinearities. A more versatile class of dissipative compensators, called dynamic dissipative compensators, is next considered. A control designer has more design freedom with dynamic dissipative compensators than with the static dissipative type. The increased design degrees of freedom can be used to enhance the performance of the control system. The synthesis techniques for static as well as dynamic dissipative compensators for multibody, nonlinear, flexible systems are currently unknown and it is a topic of future research. The asymptotic stability property of a static dissipative controller for multibody, nonlinear, flexible space structures is demonstrated through a simulation example. The example system used consists of a flexible 10-bay truss structure with a flexible, 2-link manipulator arm attached at one end of the truss. This example system is representative of the class of spacecraft envisioned for the future missions. For dynamic dissipative compensators an application example is shown for a multibody planar system with an articulated member. The controller design is based on locally linearized models in the configuration space of the articulated member. This example also demonstrates the use of dissipative compensators in the integrated design framework