Abstract: With the continually increasing operating frequencies, complex high-speed interconnect and package modules require characterization based on measured/simulated data. Several algorithms were recently suggested for macromodeling such types of data to enable unified transient analysis in the presence of external network elements. One of the critical issues involved here is the passivity violations associated with the computed macromodel. To address this issue, a new passivity enforcement algorithm is presented in this paper. The proposed method adopts a global approach for passivity enforcement by ensuring that the passivity correction at a certain region does not introduce new passivity violations at other parts of the frequency spectrum. It also provides an error estimate for the response of the passivity corrected macromodel.

Abstract: This paper proposes a general hierarchical analysis methodology, HiPRIME, to efficiently analyze RLKC power delivery systems. After partitioning the circuits into blocks, we develop and apply the IEKS (Improved Extended Krylov Subspace) method to build the multiport Norton equivalent circuits which transform all the internal sources to Norton current sources at ports. Since there are no active elements inside the Norton circuits, passive or realizable model order reduction techniques such as PRIMA can be applied. The significant speed improvement, 700 times faster than Spice with less than 0.2% error and 7 times faster than a state-of-the-art solver, InductWise, is observed. To further reduce the top-level hierarchy runtime, we develop a second-level model reduction algorithm and prove its passivity.

Abstract: Increasing demands on efficient power management and conversion, together with demands on reduced harmonic generation, higher bandwidths, and reliability, make it necessary to design devices (e.g., controllers, compensators, filters etc.) that ensure a system to meet certain directives. Such devices are most often developed and studied using linear signal-based approaches. However, since virtually all modern systems are highly complex and inherently nonlinear, linear analysis and design techniques might become insufficient as to ensure certain predefined behaviors, robustness and reliability under all operating conditions, especially if the (controlled or compensated) system is subject to large set-point changes, disturbances, or errors that cause the system to deviate from its nominal point of operation. For that reason, the development of dedicated tools that take the systems nonlinearities into account is of utmost importance. This thesis is concerned with the development of new modeling, analysis and control methods for nonlinear electrical networks. A unified power-based framework that provides a systematic dynamical description of a broad class of networks, including switched-mode power converters, is presented. A major advantage of the method is that the underlying physical structure, like the interconnection of the individual elements, nonlinear phenomena and the power flow, are explicitly incorporated in the model. Taking the network power-flow as a starting point, the concept of passivity is considered from a fairly different point of view with respect to the existing energy-based approaches. The resulting passivity properties are of interest in network theory, but also have applications in control as they suggest a so-called Power-Shaping stabilization method which forms an alternative to the existing method of Energy-Shaping. In addition, useful relations with reactive power are established and lead to the notion of reactive Hamiltonians. In the context of the recently proposed Passivity-Based Control (PBC) strategy for switched-mode power converters, the power-based framework reveals and justifies a revised damping injection scenario that significantly improves the robustness of the closed-loop. Some preliminary steps are taken to extend the power basedmodeling and control approach to mechanical and electro-mechanical systems. The developments throughout the thesis heavily rely on the ideas of R.K. Brayton and J.K. Moser stemming from in the early sixties. Where applicable, the newly obtained results are compared with well-known existing energy-based methods, like the Lagrangian and Hamiltonian approach, and several structural relationships between the methods are established.

Abstract: This paper presents a new theory that addresses the issue of passivity in macromodels of electrical interconnects constructed based on the method of characteristics (MoC). The proposed approach develops a new algebraic test to check for passivity in macromodels generated using MoC. The theory behind the developed test is based on deriving the necessary and sufficient conditions for the loss of positive-realness in the admittance matrix of the developed macromodel. An algorithmic procedure is proposed to verify passivity of general macromodels derived from the MoC. The results presented in this paper can be employed to test for positive-realness in dynamical systems described by algebraic delay-differential equations with discrete commensurate delays.

Abstract: Some important features and implications of dissipativity and passivity properties in the discrete-time setting are collected in this paper. These properties are mainly referred to as the stability analysis (feedback stability systems and study of the zero dynamics), the relative degree, the feedback passivity property, and the preservation of passivity under feedback and parallel interconnections. Frequency-domain characteristics are exploited to show some of these properties. The main contribution is the proposal of necessary and sufficient conditions in order to render a multiple-input multiple-output linear discrete-time invariant system passive by means of a static-state feedback and using the properties of the relative degree and zero dynamics of the system. A discrete-time model for the DC-to-DC buck converter is used as an example to illustrate the passivation scheme proposed. In addition, dissipativity frequency-domain properties are related to some feedback stability criteria.

Abstract: A controller able to support bidirectional power flow in a full-bridge rectifier with boost-like topology is obtained. The controller is computed using port Hamiltonian passivity techniques for a suitable generalized state space averaging truncation of the system, which transforms the control objectives, namely constant output voltage dc-bus and unity input power factor, into a regulation problem. Simulation results for the full system show the correctness of the simplifi-cations introduced to obtain the controller.

Abstract: A controller design methodology to regulate the output voltage of a phase-shifted resonant converter is presented. The design objective is to overcome the highly nonlinear characteristics of the phase-shifted resonant converter observed when the load is unknown. The control goal is to maintain the output voltage at desired values in the presence of large load perturbations by varying the phase angle of the full-bridge converter. The controller is derived using passivity theory which ensures that the closed-loop system is exponentially convergent and that only a single output feedback is required. An adaptive version is deduced to estimate the output load resistance for the passivity control. This feature allows the use of an extra output current sensor to be avoided. The structure of the controller derived using passivity theory is very simple. Laboratory experiments performed using a digital signal processor system confirm the robustness of the converter with the passivity-based controller.

Abstract: A control scheme for teleoperation systems with time delay is proposed based on a passivity concept. This control method requires neither the knowledge of the manipulator systems nor the environmental models. Moreover, the approach is applicable for any time delays. This model independence and time delay independence features make the proposed control method well suitable for teleoperation in the physical world. The applications include remote site explorations, telesurgery, space explorations and teleoperation through the Internet. The main contribution of this method is that it is less conservative than the traditional passivity based method. In our method, the passivity controller only operates when the system loses passivity, while in a traditional passivity formulation, the controller works all the time during the operations that may adversely affect the performance of the system

Abstract: Recently proposed stable teleoperation control scheme, based on time domain passivity, is modified to remove several conservatisms. During unconstrained motion and contacting with soft and deformable environments, the two-port time domain passivity approach (Ryu et al., 2004) was excessively dissipating energy even though it was stable without any energy dissipation. The main reason of this conservatism is on the fact that the time domain passivity controller does not include the external energy dissipation elements at the slave manipulator. The measured interaction force between slave and environment allow the time domain passivity observer to include the amount of energy dissipation of the slave manipulator to the monitored energy. With the modified passivity observer, reference energy following idea (Ryu, et al., 2003) is applied to satisfy the passivity condition. The feasibility of the developed methods is proved with experiments. Improved performance is obtained in unconstrained motion and contacting with a soft environment

Abstract: A new algorithm for the enforcement of passivity for large lumped macromodels is presented. An accuracy-controlled adaptive frequency sampling combined with an iterative multishift Arnoldi scheme leads to a fast computation of the imaginary Hamiltonian eigenvalues, which are perturbed until passivity is reached. Up to two orders of magnitude speedup factors are achieved with respect to previous formulations.

Abstract: Reliability and efficiency of tele-micromanipulation systems with haptic feedback over the Internet face to strong problems due to the nonlinear nature of microenvironment and time-varying delays in communication lines. In this paper, a bilateral controller for a micro-teleoperation system is presented using passivity approaches. We showed that the application of wave variable formalism allows the passivity of the system in spite of external perturbations. Mainly, the communication varying delays between the master and the slave and the specific scale factors modeling the interaction between the slave and the environment (structural and surface interactions) are considered. A design framework demonstrates regions where scaling factors keep the passivity of the overall micro-teleoperation system. Finally, the validity of the proposed method is demonstrated by simulations for a pick-and-place micromanipulation task with constant and variable time-delay.

Abstract: The adaptive attitude control of a rigid spacecraft with a cluster of N variable speed control moment gyroscopes is considered from a perspective of passivity. The time-varying, spacecraft inertia matrix is considered to be unknown. The system dynamics are derived using a special form of Euler-Lagrange equations. The spacecraft tracking error dynamics are shown to be passive. When the inertia matrix is assumed to be known, a proportional controller is proposed based on passivity to make the system globally asymptotically stable. The controller is redesigned for the case with an unknown inertia matrix. The control law and parameter adaptation law are designed as an interconnection of two passive systems. Using passivity, the control design is conflgured to globally asymptotically stabilize the closed-loop system and develop an estimate of the unknown spacecraft inertia matrix. A null space solution is used to provide both open/closed-loop power tracking of the spacecraft to complete the integrated power and attitude control problem. Numerical simulations are provided for validation.

Abstract: In this paper, we consider the dynamic visual feedback control with the uncertainty of the camera coordinate frame based on the passivity. Firstly the brief summary of the nominal visual feedback systems with a fixed camera is given with the fundamental representation of a relative rigid body motion. Secondly we construct the visual feedback system with uncertainty which is not be limited to the orientation around the optical axis. Next, we derive the passivity of the dynamic visual feedback system by combining the manipulator dynamics and the visual feedback system. Based on the passivity, stability and L/sub 2/-gain performance analysis are discussed. Finally the validity of the proposed control law can be confirmed by comparing the simulation results.

Abstract: A positive-real like lemma for finite dimensional linear time invariant uncertain systems with state multiplicative noise is derived. The system uncertainties are assumed to be of either polytopic or Markov jump type. Passivity conditions for both cases are derived in terms of linear matrix inequalities. The results are used to the design a direct adaptive controller for a tracking system.

Abstract: Abstract This paper proposes a simple computer-aided feedback design strategy for polynomial control systems. The design strategy is based on passivity and semidefinite programming, two well-established concepts from control theory and optimization. The combination of these two concepts leads to a physically motivated feedback design strategy which can be efficiently and reliably solved on a computer. In particular, this paper addresses the problem of designing globally stabilizing feedbacks via state feedback passivation and via dynamic output feedback passivation using semidefinite programming and the sum of squares decomposition.

Abstract: In this paper, a bilateral controller for a microteleoperation system is presented using passivity approaches. We showed that the application of wave variable formalism allows the passivity of the system in spite of the communication delays between the master and the slave, the varying scaling factors and uncertainties of the microenvironment. Conditions on passivity/transparency are given for the micro teleoperation system. Finally, numerical simulation results are presented showing the stability-transparency performances of the resulting system with constant and variable time-delay

Abstract: In this paper, we investigate the control and the estimation of dynamic visual feedback systems with a fixed camera. Firstly the fundamental representation of the visual feedback system with four coordinate frames is established by using the homogeneous representation and adjoint transformation. Secondly we consider the observer which is reproduced from the fundamental representation of relative rigid body motion just as Luenberger observer for linear systems. Then, the relationship between the estimation error in the 3D workspace and in the image plane is established. Next, we derive the passivity of the dynamic visual feedback system by combining the passivity of both the visual feedback system and the manipulator dynamics. The stability via Lyapunov method for the full 3D dynamic visual feedback system is discussed based on the passivity. The L2-gain performance analysis for the disturbance attenuation problem is considered via the dissipative systems theory. Finally simulation results are shown to verify the stability and L2-gain performance of the dynamic visual feedback system.

Abstract: This paper deals with the robust passivity synthesis problem for a class of uncertain linear systems with time-varying delay in state and control input. The parameter uncertainties are norm-bounded and allowed to appear in all matrices of the model. The problem aims at designing an observer-based dynamic output-feedback controller that robustly stabilizes the uncertain systems and achieves the strict passivity of closed-loop systems for all admissible uncertainties. By converting the problem at hand into a class of strictly passive control problem for a parameterized system, the explicit solution is established and expressed in terms of a linear matrix inequality. A numerical example is provided to demonstrate the validity of the proposed approach.

Abstract: This paper presents a passivity-based controller design capable of achieving autonomous obstacle avoidance for robot manipulators subject to joint position and joint rate constraints. The control objectives are achieved by exploiting the passivity properties of the system and utilizing barrier function ideas to reshape the control Lyapunov function. The final control Lyapunov function is reminiscent of those used in the artificial potential field method.

Abstract: We develop a realizable circuit reduction to generate the interconnect macro-model for parasitic estimation in wideband applications. The inductance is represented by VPEC (vector potential equivalent circuit) model, which not only enables the passive sparsification but also gives correct low-frequency response, whereas the recent Y-/spl Delta/ circuit reduction intrinsically has inaccurate ac value and low-frequency response due to nodal-susceptance formulation. Applying hierarchical circuit-reduction enhanced by multi-point expansions, we can obtain an accurate high-order impedance function to capture the high-frequency response. The impedance function is further enforced passivity by convex programming, and realized by a Foster's synthesis. Experiments show that our method is as accurate as PRIMA in high frequency range, but leads to a realized circuit model with up to 10/spl times/ times less complexity and up to 8/spl times/ smaller simulation time. In addition, under the same reduction ratio, its error margin is less than that for the time-constant based reduction in both time-domain and frequency-domain simulations.

Abstract: In this chapter, which is a distilled version of [271], we present a novel way to approach the interconnection of a continuous and a discrete time physical system firstly presented in [270, 268, 257]. This is done in a way which preserves passivity of the coupled system independently of the sampling time T. This strategy can be used both in the field of telemanipulation, for the implementation of a passive master-slave system on a digital transmission line with varying time delays and possible loss of packets (e.g. the Internet), and in the field of haptics, where the virtual environment should ‘feel’ like a physical equivalent system.

Abstract: The robotic control problem is considered from the passivity– based control point of view and a modified version of the computed torque method for rigid robots is briefly reviewed. A control strategy suitable for flexible–link robots manipulating large payloads is also presented, which effectively exploits the passivity property satisfied by a suitably defined set of inputs and outputs for the system in conjunction with an approximate model of the dynamics. Both of the above control schemes are experimentally implemented on a flexible– link, multi-joint arm in order to investigate their characteristics and provide useful insight into the control problem for flexible robots.

Abstract: A passivity-based controller taking account of efficiency optimization for induction motor is proposed. Based on the passivity theory of dynamic system,in which the energy exchange plays a central role,the speed control system of induction motor is designed. The rotor speed and flux converge to the given value asymptotically with the energy function as Lyapunov function. From the energy-balance equation of passive system,the optimal rotor flux is obtained to minimize the energy loss.Simulative results show a perfect performance of drive system,and the power loss is reduced re-markably under light load. This project is supported by Sci. and Tech. Fund of Beijing Jiaotong University(2004RC013).