Showing papers by "Petar V. Kokotovic published in 1989"

Adaptive regulation of nonlinear systems with unmodeled dynamics

Abstract: A feedback linearization design is presented which includes unknown parameters and unmodeled dynamics. An adaptive update law which counteracts the effects of unknown parameters is shown to be robust to the unmodeled dynamics. The proposed design methodology is based on a conceptually simple stability analysis. Conditions are given for global stability of an adaptive control law designed for the reduced-order model of a class of nonlinear plants. In the presence of unmodeled dynamics, the regulation property is preserved in a stability region. The size of the region is estimated using bounds that not only prove robustness, but also allow a comparison between adaptive and nonadaptive nonlinear controls. >

Global stabilization of partially linear composite systems

Abstract: It is shown that a cascade system consisting of a linearly controllable system and a nonlinearly asymptotically stable system is globally stabilizable by smooth dynamic state feedback if the linear subsystem is right-invertible and weakly minimum phase and the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output. Both of these conditions are coordinate-free, and there is freedom of choice for the linear output variable. This result generalizes several earlier sufficient conditions for stabilizability. The weak minimum-phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem. >

Integral manifold as a tool for reduced-order modeling of nonlinear systems: A synchronous machine case study

Abstract: A discussion is presented of the use of integral manifolds as a tool for reduced-order modeling in nonlinear systems. It specifically addresses its application to synchronous machine modeling. Not only does the integral manifold approach contribute to the understanding of the origin and validity of reduced-order models, but it also produces a systematic reduction procedure. While illustrated on a synchronous machine case study, the method has broad applications in a wide class of nonlinear dynamic systems. >

Nonlinear control via approximate input-output linearization: the ball and beam example

Abstract: The authors present an approach for the approximate input-output linearization of nonlinear systems, particularly those for which relative degree is not well defined. They show that there is a great deal of freedom in the selection of an approximation and that, by designing a tracking controller based on the approximating system, tracking of reasonable trajectories can be achieved with small error. The approximating system is itself a nonlinear system, with the difference that it is input-output linearizable by state feedback. The authors demonstrate some properties of the accuracy of the approximation and, in the context of the ball and beam example, show it to be far superior to the Jacobian approximation. The results are focused on finding regular SISO systems which are close to systems which are not regular and controlling these approximate regular systems. >

Parameter Convergence Conditions Independent of Plant Order

Abstract: A pseudogradient adaptive approach for slow adaptation is developed combining sensitivity results from the 1960's and recent developments in averaging and integral manifold methods. In this approach, the parametrization and number of parameters are not related to the plant order. Sufficient conditions for parameter convergence are developed using a-priori knowledge of a feedback system consisting of the plant and a nominal controller.

Self tuning of conflicting oscillatory modes: a case study

Abstract: An analysis of a single-parameter self-tuning scheme for a high-order system is presented and applied to a typical power-system stabilizer, as a representative of systems in which stabilization of some modes decreases the damping of other modes. Integral manifolds and averaging are used to find conditions for convergence to a compromise setting of the conflicting modes. >

Global and local stability properties of a non-SPR output error estimator

Abstract: Conditions for local instability are compared with conditions for global asymptotic stability of an output error adaptive estimation algorithm for continuous-time systems. A boundedness conjecture is made that all signals within this adaptive system including the output error and parameter estimates remain globally bounded for all time despite any locally unstable behaviour. A global stability criterion applied to a transfer function, which is not strictly positive real, states that for a large enough adaptation gain the system will be asymptotically stable. However, a local result states that for a small enough adaptation gain the same system is unstable. The results suggested by the computer simulations are verified by an exact analysis of a linearized periodic version of the adaptive system.