Showing papers by "Petar V. Kokotovic published in 1997"
TL;DR: It is shown that these systems, while not feedback linearizable, can be (globally) transformed by feedback and diffeomorphism into lower-triangular form and this transformation is employed to design a globally stabilizing controller with optimality properties and an input-to-state stability property with respect to matched uncertainties.
165 citations
10 Dec 1997
TL;DR: In this paper, a new saturation control law was proposed for the well known ball-and-beam system, which employs state-dependent saturation levels and guarantees global asymptotic stability.
Abstract: For the well known ball-and-beam system, we design a new saturation control law, which employs state-dependent saturation levels and guarantees global asymptotic stability, not achieved with previous designs.
57 citations
01 Jan 1997
TL;DR: In this paper, a new saturation control law was proposed for the ball-and-beam system, which employs state-dependent saturation levels and guarantees global asymptotic stability, not achieved with previous de- signs.
Abstract: For the well known ball-and-beam system, we de- sign a new saturation control law, which employs state-dependent saturation levels and guarantees global asymptotic stability, not achieved with previous de- signs.
56 citations
TL;DR: An adaptive controller is developed for a class of nonlinear systems for which other approaches may fail to be applicable and an explicit construction of a Lyapunov function for the zero dynamics with respect to a relative degree one output is constructed.
45 citations
10 Dec 1997
TL;DR: In this article, an excitation controller for synchronous machines is presented, where the control law is derived using the control Lyapunov function concept and an equilibrium tracking mechanism, resulting in a dynamic state feedback controller.
Abstract: Presents an excitation controller for synchronous machines. The control law is derived using the control Lyapunov function concept and an equilibrium tracking mechanism, resulting in a dynamic state feedback controller. Both damping improvement and enlargement of the stability region are achieved, and the knowledge of the operating point is not required. Simulation results for a case study are presented showing the significant improvement obtained both in transient stability and dynamic performance.
42 citations
10 Dec 1997
TL;DR: In this article, a system with backlash and flexibility is compensated with an open-loop optimal control law combined with a linear partial-state feedback law, where the compensation of backlash is treated as a rendezvous problem in optimal control, while the linear controller for flexibility is designed using techniques from classical control theory and singular perturbation theory.
Abstract: A system with backlash and flexibility is compensated with an open-loop optimal control law combined with a linear partial-state feedback law. The compensation of backlash is treated as a rendezvous problem in optimal control, while the linear controller for flexibility is designed using techniques from classical control theory and singular perturbation theory. Simulation results show significant improvements in system tracking performance when backlash compensation is active.
30 citations
10 Dec 1997
TL;DR: In this paper, the Bode integral characterization of performance limitations in linear control systems with the limiting cost of a particular linear cheap control is linked to analogous feedback limitations in nonlinear systems, and it is shown how unstable zero dynamics impose unavoidable obstructions to the closed-loop performance.
Abstract: This paper links the Bode integral characterization of performance limitations in linear control systems with the limiting cost of a particular linear cheap control. This link allows us to establish analogous feedback limitations in nonlinear systems. We show how unstable zero dynamics impose unavoidable obstructions to the closed-loop performance.
20 citations
TL;DR: In this article, the adaptive inverse approach employs an adaptive controller structure consisting of an adaptive inverse for cancelling the effect of an unknown nonlinearity and a fixed (or adaptive) linear control law for a known (or unknown) linear dynamics.
Abstract: In this paper we unify our recent results in adaptive control of systems with unknown non-smooth non-linearities such as dead-zone, backlash and hysteresis characteristics at the input or output of a linear dynamics. Our adaptive inverse approach employs an adaptive controller structure consisting of an adaptive inverse for cancelling the effect of an unknown non-linearity and a fixed (or adaptive) linear control law for a known (or unknown) linear dynamics. Despite the bilinear dependence on the unknown parameters, a linearly parametrized error system is constructed which enables us to design robust adaptive laws for updating the controller parameters to ensure closed loop signal boundedness and improve system tracking performance. © 1997 by John Wiley & Sons, Ltd.
18 citations
01 Jul 1997
TL;DR: In this paper, the problem of controlling dynamic systems where the position of the operating point in the state space is unknown is addressed and an adaptive control scheme in which the uncertain parameter is the operating points is proposed.
Abstract: The problem of controlling dynamic systems where the position of the operating point in the state space is unknown is addressed An adaptive control scheme in which the uncertain parameter is the operating point is proposed The usually applied solution to this problem is a particular case, with limited applicability, of the proposed scheme With the proposed scheme the exponential stability of the unknown operating point is obtained under very general conditions Illustrative examples are also presented
15 citations
01 Jan 1997
TL;DR: This construction of Lyapunov functions is a crucial part of the design and is the main topic of this chapter.
Abstract: Several designs in the preceding chapters require the knowledge of Lyapunov functions which need to be constructed during the design. This construction is a crucial part of the design and is the main topic of this chapter
12 citations
01 Jan 1997
TL;DR: It is shown how backstepping and forwarding, the two building blocks of recursive Lyapunov designs, compelement each other by each removing one of the two obstacles to feedback passivation.
Abstract: The problem of feedback stabilization is reformulated as feedback passivation so that the construction of a stabilizing feedback is translated into the construction of a passivating output. This construction is restricted by two geometric requirements of passivity: a relative degree one and a minimum phase property. We show how backstepping and forwarding, the two building blocks of recursive Lyapunov designs, compelement each other by each removing one of the two obstacles to feedback passivation.
01 Jul 1997
TL;DR: In this article, a recursive design procedure which combines steps of backstepping and forwarding is proposed to ensure global stabilizability of interlaced systems, which is defined as a class of systems only characterized by the zero entries of their matrix configuration and a local stabilization condition.
Abstract: Interlaced systems constitute a class of systems only characterized by the zero entries of their matrix configuration and a local stabilizability condition All these systems are globally stabilizable by a recursive design procedure which combines steps of backstepping and forwarding When a nonlinear system misses this structural characterization other types of conditions (sign, growth) are needed to ensure global stabilization
10 Dec 1997
TL;DR: In this article, a dynamic, state feedback control structure is proposed, where the equilibrium in an L/sub g/V control law is the uncertain parameter, which allows the implementation of the controller for systems with unknown equilibrium.
Abstract: A dynamic, state feedback control structure is proposed. The scheme is conceived as an adaptive controller with the equilibrium in an L/sub g/V control law as the uncertain parameter, which allows the implementation of the controller for systems with unknown equilibrium. A new property of L/sub g/V controllers is given, and it is proven that this and other important properties carry on to the proposed scheme. A synchronous machine case study shows that the proposed scheme may give better results than the L/sub g/V controller from which it is derived.
01 Jan 1997
TL;DR: The quantitative concepts of gain and phase stability margins were among the frequency domain tools of the classical Nyquist-Bode designs to guard against dangers of instability.
Abstract: For stabilization of an unstable system, feedback is a necessity. With uncertainties in the operating environment, and in system components, feedback is needed to preserve stability and improve performance. However, feedback can also be dangerous. A tighter feedback loop, instead of achieving better performance, may cause instability. To guard against such dangers, the quantitative concepts of gain and phase stability margins were among the frequency domain tools of the classical Nyquist-Bode designs.
05 Oct 1997
TL;DR: In this article, the authors considered the merits of using dynamic feedback to implement the control law suggested by Sepulchre and Kokotovic (1996), and showed that the dynamic implementation of this control law is able to eliminate rotating stall by stabilizing a small axisymmetric limit cycle around the peak of the compressor characteristic.
Abstract: Several control laws have been formulated by other authors to stabilize the low-order nonlinear state-space model of an axial compression system developed by Moore and Greitzer (1986). Using static nonlinear feedback, these control laws extend the stable operating range of the compressor system. This paper considers the merits of using dynamic feedback to implement the control law suggested by Sepulchre and Kokotovic (1996). Bifurcation and normal form analysis are used to show that the dynamic implementation of this control law is able to eliminate rotating stall by stabilizing a small axisymmetric limit cycle around the peak of the compressor characteristic. The analysis reveals the possibility that controlled dynamics can be used to create new and desirable phenomena.
01 Jan 1997
TL;DR: In this article, the authors describe the use of a parameter estimator (identifier) continuously acquires knowledge about the plant and uses it to tune the controller on-line.
Abstract: Realistic models of physical systems are nonlinear and usually contain parameters (masses, inductances, aerodynamic coefficients, etc.) which are either poorly known or dependent on a slowly changing environment. If the parameters vary in a broad range, it is common to employ adaptation: a parameter estimator—identifier— continuously acquires knowledge about the plant and uses it to tune the controller “on-line”.
01 Jan 1997
TL;DR: The first three sections of this chapter are based on these references from which we extract, and at times reformulate, the most important concepts and system properties to be used in the rest of the book as discussed by the authors.
Abstract: Only a few system theory concepts can match passivity in its physical and intuitive appeal. This explains the longevity of the passivity concept from the time of its first appearance some 60 years ago, to its current use as a tool for nonlinear feedback design. The pioneering results of Lurie and Popov, summarized in the monographs by Aizerman and Gantmacher [3], and Popov [88], were extended by Yakubovich [121], Kalman [51], Zames [123], Willems [120], and Hill and Moylan [37], among others. The first three sections of this chapter are based on these references from which we extract, and at times reformulate, the most important concepts and system properties to be used in the rest of the book.
01 Jan 1997
TL;DR: Adaptive control is one of only a few research areas in which Tom Kailath has not been directly involved but for important special classes of nonlinear systems a discernible progress has recently been made.
Abstract: Adaptive control is one of only a few research areas in which Tom Kailath has not been directly involved. This wouldn’t speak well for adaptive control if it weren’t for Tom’s fascination with estimation. His contributions to nonlinear estimation and filtering are discussed elsewhere in this volume. Although many sharp teeth were broken on that hard nut, for important special classes of nonlinear systems a discernible progress has recently been made.