Abstract: This paper describes PRIMA, an algorithm for generating provably passive reduced order N-port models for RLC interconnect circuits. It is demonstrated that, in addition to requiring macromodel stability, macromodel passivity is needed to guarantee the overall circuit stability once the active and passive driver/load models are connected. PRIMA extends the block Arnoldi technique to include guaranteed passivity. Moreover, it is empirically observed that the accuracy is superior to existing block Arnoldi methods. While the same passivity extension is not possible for MPVL, we observed comparable accuracy in the frequency domain for all examples considered. Additionally a path tracing algorithm is used to calculate the reduced order macromodel with the utmost efficiency for generalized RLC interconnects.

Abstract: This paper describes PRIMA, an algorithm for generating provably passive reduced order N-port models for RLC interconnect circuits. It is demonstrated that, in addition to requiring macromodel stability, macromodel passivity is needed to guarantee the overall circuit stability once the active and passive driver/load models are connected. PRIMA extends the block Arnoldi technique to include guaranteed passivity. Moreover, it is empirically observed that the accuracy is superior to existing block Arnoldi methods. While the same passivity extension is not possible for MPVL, we observed comparable accuracy in the frequency domain for all examples considered. Additionally a path tracing algorithm is used to calculate the reduced order macromodel with the utmost efficiency for generalized RLC interconnects.

Abstract: Recent work in the area of model-order reduction for RLC interconnect networks has been focused on building reduced-order models that preserve the circuit-theoretic properties of the network, such as stability, passivity, and synthesizability. Passivity is the one circuit-theoretic property that is vital for the successful simulation of a large circuit netlist containing reduced-order models of its interconnect networks. Non-passive reduced-order models may lead to instabilities even if they are themselves stable. In this paper, we address the problem of guaranteeing the accuracy and passivity of reduced-order models of multiport RLC networks at any finite number of expansion points. The novel passivity-preserving model-order reduction scheme is a block version of the rational Arnoldi algorithm. The scheme reduces to that of the PRIMA algorithm when applied to a single expansion point at zero frequency. Although the treatment of this paper is restricted to expansion points that are on the negative real axis, it is shown that the resulting passive reduced-order model is superior in accuracy to the one that would result from expanding the original model around a single point. Nyquist plots are used to illustrate both the passivity and the accuracy of the reduced-order models.

Abstract: Concerns the extension to the general rotating electric machine model of the passivity-based controller method for induction motors. The motor's passivity properties are used at 2 levels. First, we prove that the motor model can be decomposed as the feedback interconnection of two passive subsystems (essentially, the electrical and mechanical dynamics). Then, we design a torque-tracking controller that preserves passivity for the electrical subsystem and leaves the mechanical part as a passive disturbance. This leads to the cascaded controller structure which is typically analyzed involving time-scale separation. Our aim is to characterize a class of machines for which such a passivity-based controller solves the output feedback torque-tracking problem. The class consists of machines whose nonactuated dynamics are damped and whose dynamics can be decoupled. This requires that the air-gap magnetomotive force must be suitably approximated by the first harmonic in its Fourier expansion. These conditions have a clear physical interpretation in terms of the couplings between its dynamics and are satisfied by many machines. The passivity-based controller presented reduces to the well-known indirect vector controller for current-fed induction machines. Our developments constitute an extension to voltage-fed machines of this de facto standard in industrial applications.

Abstract: Work in the area of model-order reduction for RLC interconnect networks has focused on building reduced-order models that preserve the circuit-theoretic properties of the network, such as stability, passivity, and synthesizability (Silveira et al, 1996) Passivity is the one circuit-theoretic property that is vital for the successful simulation of a large circuit netlist containing reduced-order models of its interconnect networks Non-passive reduced-order models may lead to instabilities even if they are themselves stable We address the problem of guaranteeing the accuracy and passivity of reduced-order models of multiport RLC networks at any finite number of expansion points The novel passivity-preserving model-order reduction scheme is a block version of the rational Arnoldi algorithm (Ruhe, 1994) The scheme reduces to that of (Odabasioglu et al, 1997) when applied to a single expansion point at zero frequency Although the treatment of this paper is restricted to expansion points that are on the negative real axis, it is shown that the resulting passive reduced-order model is superior in accuracy to the one that would result from expanding the original model around a single point Nyquist plots are used to illustrate both the passivity and the accuracy of the reduced order models

Abstract: None of the existing network reduction tools preserve passivityfor RLC networks. The loss of passivity can be a serious problembecause simulations of the reduced networks may encounter"time step too small" errors. This paper presents a set oftransformations called "Split Congruence Transformations"(SCT's) which can be used to accurately reduce a RLC networkwhile preserving passivity.

Abstract: In this paper we survey some recent results on stabilization of nonlinear systems using a passivity approach. In the first part of the paper we treat general systems and develop a unified framework for passivity-based nonlinear control design. In the second part we center our attention on systems described by Euler-Lagrange equations, with particular emphasis on mechanical systems, power converters and AC motors.

Abstract: This paper presents methods which enable the use of passivity-based control design techniques to control non-passive systems. For inherently non-passive finite- dimensional linear time-invaraint systems, passification methods are presented to render such systems passive by suitable compensation. The passified system can then be controlled by a class of passive linear controllers. The idea is to exploit the robust stability properties of passivity-based control laws for uncertain systems. The proposed passification methods are demonstrated by application to the ACC benchmark problem and to pitch-axis control of an F-18 High Alpha Research Vehicle (HARV) model.

Abstract: This paper presents methods which enable the use of passivity-based control design techniques to control nonpassive systems. For inherently nonpassive finite-dimensional linear time-invariant systems, passivation methods are presented to render such systems passive by suitable compensation. The passive system can then be controlled by a class of passive linear controllers. The idea is to exploit the robust stability properties of passivity-based control laws for uncertain systems. The proposed passivation methods are demonstrated by application to the ACC benchmark problem and to pitch-axis control of an F-18 High Alpha Research Vehicle (HARV) model.

Abstract: In this paper we study the viability of extending, to the general rotating electric machine 's model, the passivity-based controller method that we have developed for induction motors. In this approach the passivity (energy dissipation) properties of the motor are taken advantage of at two different levels. First, we prove that the motor model can be decomposed as the feedback interconnection of two passive subsystems, which can essentially be identified with the electrical and mechanical dynamics. Then, we design a torque tracking controller that preserves passivity for the electrical subsystem, and leave the mechanical part as a passive disturbance. In position or speed control applications this procedure naturally leads to the well known cascaded controller structure which is typically analyzed invoking time-scale separation assumptions. A key feature of the new cascaded control paradigm is that the latter arguments are obviated in the stability analysis. Our objective in this paper is to characterize a class of machines for which such a passivity-based controller solves the output feedback torque tracking problem. Roughly speaking, the class consists of machines whose nonactuated dynamics are well damped and whose electrical and mechanical dynamics can be suitably decoupled via a coordinate transformation. The first condition translates into the requirement of approximate knowledge of the rotor resistances to avoid the need of injecting high gain into the loop. The latter condition is known in the electric machines literature as Blondel-Park transformability, and in practical terms it requires that the air-gap magnetomotive force must be suitably approximated by the first harmonic in its Fourier expansion. These conditions, stemming from the construction of the machine, have a clear physical interpretation in terms of the couplings between its electrical, magnetic and mechanical dynamics, and are satisfied by a large number of practical machines. The passivity-based controller presented here reduces to the well known indirect vector controller for current-fed induction machines. Our developments constitute an extension, to voltage-fed machines, of this de facto standard in industrial applications. Furthermore, our analysis provides it with a solid theoretical foundation.

Abstract: An approach to stability analysis for time varying nonlinear systems via passivity analysis is presented in this paper. The necessary and sufficient conditions for continuous dissipation can be obtained. As for linear time invariant systems the obtained result coincides with the Routh criterion.

Abstract: A method is provided for analyzing stability and passivity of physical systems. A physical system having time delays is represented as a linear circuit model. The linear circuit model is transformed into a corresponding transform domain circuit model. Sensitivity analysis is applied to the transform domain circuit model for generating information indicative of the stability or the passivity of the physical system having the time delays. A graphical representation may be created of the information indicative of the stability or passivity of the physical system having the time delays.

Abstract: The phenomenon of passivity was discovered in the 18th century from iron dissolution experiments by Lomonossow, Wenzel, and Keir, and so named "passivity" in 1836 by Schonbein. It described the experimental finding that a thermodynamically expected metal dissolution reaction under certain conditions is kinetically hindered by orders of magnitude.

Abstract: In this paper, the authors design, and also experimentally verify, a passivity-based controller that forces an induction motor which has significant magnetic saturation to track a time-varying optimal flux trajectory. As a result, they are able to provide close tracking of a time-varying speed/position trajectory that requires close to the maximum torque achievable by the motor within its voltage and current limits.

Abstract: This paper addresses passivity-based control of elastic systems. For inherently passive nonlinear and linear elastic systems such as flexible structures with collocated and compatible actuators and sensors, robust linear and nonlinear control laws are presented. For linear elastic systems that are inherently nonpassive, a method is presented to render them passive by compensation. The resulting system can then be controlled by a class of passive linear controllers. The method is applied to two elastic systems and is found to give robust stability and performance.

Abstract: The paper deals with the stability of nonlinear time varying systems. The new concept of T-passivity is introduced and based on it several stability results for nonlinear systems are obtained.

Abstract: This paper shows a first approximation of the use of bond graphs to determine flatness and passivity properties of physical systems. In the case of the flatness property, the topology of the bond graph was used directly in order to obtain paths in the bond graph which generated the equations of the linearized outputs. In the case of the passivity property, we tried to use the topology of the graph directly but, not being successful, the scattering matrix of the system was used as an intermediate step.

Abstract: Presents an overview of certain passivity-based control laws for a class of nonlinear multibody flexible space structures. The control laws presented achieve globally asymptotically stable large-angle closed-loop manoeuvres. The control laws use inherent passivity of such systems and are robust to unmodeled dynamics, parametric uncertainties, and, in some cases, certain actuator/sensor nonlinearities. Some results on trajectory tracking of rigid and flexible multibody space systems are also given.

Abstract: The passivity equation is the main necessary condition of passivity and dissipativity of nonlinear control system. The paper presents necessary and sufficient conditions of its solvability with respect to some nonnegative storage function. These results can be a basis for further investigations on passivity of control systems. Furthermore, they have applications in adaptive control.

Abstract: Two passivity-based controllers and an input-output linearization controller for current-fed saturated induction motors are presented. Advantages and disadvantages of the controllers are discussed. Finally, experimental results obtained with one of the passivity-based controllers are presented.

Abstract: In this paper, we present a brief review of the various definitions on passivity of nonlinear systems and positive real transfer functions. The relationships between the definitions are clarified and illustrated with examples. Furthermore we review the stability of the feedback interconnection of passive systems to relax the assumptions on the plant to be controlled. In particular we present a version of the passivity theorem that requires weaker conditions on the interconnected systems.

Abstract: This paper describes PRIMA, an algorithm for generating provably passive reduced order N-port models for RLC interconnect circuits. It is demonstrated that, in addition to requiring macromodel stability, macromodel passivity is needed to guarantee the overall circuit stabiliQ once the active and passive drivernoad models are connected. PRIMA extends the block Amoldi technique to include guaranteed passivity Moreovel; it is empirically observed that the accuracy is superior to existing block Arnoldi methods. While the same passivity extension is not possible for MPVL, we observed comparable accuracy in the frequency domain for all examples considered, Additionally, a path tracing algorithm is used to calculate the reduced order macromodel with the utmost efficienc>i for generalized RLC interconnects.

Abstract: It is shown that an integral with negative feedback from its output terminal through a strictly passive system is still strictly passive. By using successive negative feedback around integrals, the conditions of strict passivity and a unified approach for constructing strictly passive systems are obtained for time-varying nonlinear systems of different orders. A new concept of "dissipation factor" is defined in this paper. The stability of a class of time-varying nonlinear systems is examined by using this passivity analysis.

Abstract: This paper deals with the nonlinear adaptive control of static condensers (STATCON), which belong to the class of FACTS (Flexible AC Transmission Systems) used for the control of electrical networks The here-proposed methodology is based on the passivity property of Lagrangian systems, due to the so-called skew-symmetry property of such systems [2] In a first part of the paper, we show that the averaged dynamics of static condensers may be described by using Euler-Lagrange formalism and, therefore, may be controlled by using passivity Then, a passivity-based dynamic feedback is proposed on the basis of the averaged dynamics, by using a partial inversion approach In a second part, we propose an adaptive version of this controller, in order to take some parameter uncertainties into account Finally, some simulation results are presented in order to demonstrate the effectiveness of this approach, when the control is applied to the switched model of the STATCON

Abstract: Passivity of systems comprising a continuous time plant and discrete time controller is considered. This topic is motivated by stability considerations arising in the control of robots and force-reflecting human interfaces (“haptic interfaces”). Necessary conditions for passivity are found via a small gain condition, and sufficient conditions are found via an application of Parseval's theorem and a sequence of frequency domain manipulations. An example—implementation of a “virtual wall” via a one degree-of-freedom haptic interface—is given and discussed in some detail. © 1997 John Wiley & Sons, Inc.