Passivity-based Control Design Research Articles

IDA-PBC controller design for grid connected Front End Converters under non-ideal grid conditions

A passivity-based non-linear controller design for three-phase front-end converters used to connect renewable energy sources to the grid is proposed in this paper. The control objective is to inject all the generated power to the grid, while adjusting the reactive power exchanged with the power system. Besides, generated currents must have very low distortion, in order to satisfy the standards, even when grid voltages are distorted or unbalanced. The proposed controller is first designed using the Interconnection and Damping Assignment strategy, which allows obtaining controller parameters while ensuring the closed-loop system stability. In order to ensure that the output currents have very low harmonic distortion, the obtained control laws are modified based on the fundamental positive sequence grid voltage, obtained from a positive sequence detector. The proposal allows controlling both injected powers and DC-link voltage, from a unique controller design. Simulation and experimental results are presented to validate the proposed controller.

A constructive procedure for energy shaping of port—Hamiltonian systems

Equilibrium stabilization of nonlinear systems via energy shaping is a well-established, robust, passivity-based controller design technique. Unfortunately, its application is often stymied by the need to solve partial differential equations, which is usually a difficult task. In this paper a new, fully constructive, procedure to shape the energy for a class of port-Hamiltonian systems that obviates the solution of partial differential equations is proposed. Proceeding from the well-known passive, power shaping output we propose a nonlinear static state-feedback that preserves passivity of this output but with a new storage function. A suitable selection of a controller gain makes this function positive definite, hence it is a suitable Lyapunov function for the closed-loop. The resulting controller may be interpreted as a classical PI—connections with other standard passivity-based controllers are also identified.

Adaptive control of fractional-order unified chaotic systems using a passivity-based control approach

Feedback passivity-based controller design for stabilization of fractional-order unified chaotic systems is proposed in this paper. Although feedback passivity-based control is a well-known method for integer-order systems, it has not been investigated for fractional-order systems due to a lack of suited mathematical results. In this paper, a recently established lemma for the Caputo fractional derivative of a quadratic function is utilized to facilitate the design. An adaptive mechanism is also employed such that the controller does not need to known the parameter of the systems. Moreover, based on a fractional-order extension of the Lyapunov direct method, the stability of the zero dynamics of the systems is also provided. Numerical simulations are performed to illustrate the effectiveness of the proposed design. The results show that the controller is able to effectively stabilize the chaotic behavior without the knowledge of the system parameter. In addition, it is also found that the transient dynamics of the controlled system and the control effort are markedly influenced by the fractional order of the system.

Passivity-based robust controller design for a variable speed wind energy conversion system

This paper proposes a design method for a robust controller to improve the stability and system dynamic behavior for variable speed wind energy conversion systems. By analyzing the mathematical model of a wind power conversion system, control strategies for both a generator-side converter and a grid-side converter are given. For the generator-side converter, the well-known maximum power point tracking method is employed, while for the grid-side converter, a robust controller is presented based on passivity theory. The L2 -gain performance is analyzed using linear matrix inequality. Moreover, in order to accelerate the dynamic response and reduce the DC link voltage uctuations, the optimum equilibrium points of the system are designed based on the analysis of the dynamic equations of the DC link voltage. Finally, the proposed method is veried a by hardware-in-the- loop simulation.

Transient Stability and Voltage Regulation in Multimachine Power Systems Vis-à-Vis STATCOM and Battery Energy Storage

This paper examines the application of STATCOM and battery energy storage to enhance the transient stability of large-scale multimachine power systems with synchronous and doubly-fed induction generators (DFIGs). A passivity-based control design method [interconnection and damping assignment passivity-based control (IDA-PBC)] is developed for multimachine power systems and its performance is evaluated on a two-area system consisting of two synchronous generators (SGs) and two DFIG along with STATCOM/battery energy storage system. The main contributions of this paper are threefold: 1) use of a STATCOM and battery energy storage system to enhance transient stability and provide voltage regulation with SG and DFIG; 2) demonstrating the application of nonlinear control theory (specifically the IDA-PBC methodology) for the design of a stabilizing feedback controller in large-scale power systems to improve transient system performance; and 3) developing a methodology that can use the additional degrees of freedom in large-scale power systems in order to further improve system performance, in particular the transient stability margin [measured through critical clearing time (CCT)] and the dynamic transient performance of the system. In order to achieve power angle stability along with the simultaneous regulation of frequency and voltage, the performance of the proposed control scheme after the occurrence of large disturbances is evaluated and compared with a conventional power system stabilizer and a feedback linearizing controller.

Passivity-Based Control with Guaranteed Safety via Interconnection and Damping Assignment

In this paper, we study a Passivity-Based Control (PBC) design that solves asymptotic stability with guaranteed safety problem via Interconnection and Damping Assignment (IDA) approach. Akin to the classical IDA-PBC method, the original system is transformed via a state-feedback to a port-Hamiltonian system where the corresponding interconnection and damping matrices and the energy function are shaped according to the given set of unsafe states and to the desired equilibrium point. By embedding it in a hybrid control framework, we show how the global results can also be obtained. We illustrate the efficacy of our proposed method on a nonlinear second-order system.

Passivity-based control of multi-terminal HVDC systems under control saturation constraints

This paper proposes a decentralized, passivity-based control design for power stations in a multi-terminal High Voltage Direct Current transmission system. The control algorithm is shown to asymptotically stabilize the closed-loop system when the voltage set points are appropriately selected. The analysis is carried out taking into account actual power, current and voltage saturations that affect power stations and, consequently, the control action. Numerical results illustrate the performance of the obtained controllers.

Passivity-Based Controller Design of Grid-Connected VSCs for Prevention of Electrical Resonance Instability

The time delay in the current control loop of a grid-connected voltage-source converter (VSC) may cause destabilization of electrical resonances in the grid or in the VSC's input filter. Instability is prevented if the input admittance of the VSC can be made passive. This paper presents an analytical controller design method for obtaining passivity. The method is equally applicable to single- and three-phase systems, i.e., in the latter case, for both stationary- and synchronous-frame control. Simulations and experiments verify the theoretical results.

IDA-PB control design for VSC-HVDC transmission based on PCHD model

SUMMARY An interconnection and damping assignment passivity-based (IDA-PB) control design is proposed to improve the dynamic performance of voltage source converter high-voltage direct current (VSC-HVDC) system. The port-controlled Hamiltonian with dissipation (PCHD) model for voltage source converter (VSC) is developed according to the PCHD equation, and the strict passivity of the PCHD model is proved. On the basis of the PCHD model, a desired energy function is constructed by assigning interconnection and damping matrix and used as Lyapunov function. Then the IDA-PB control is designed according to desired equilibrium point, state variables, and IDA-PB control principle. By using this type of controller, the influence of the equivalent resistance of the VSC direct current side on the VSC-HVDC system is eliminated. The effectiveness of the proposed IDA-PB control is demonstrated through simulation studies on a two-terminal VSC-HVDC system by PSCAD/EMTDC software. The simulation results show that the controller has significant contribution to improve the dynamic behavior of the VSC-HVDC system under a variety of operation conditions. Copyright © 2014 John Wiley & Sons, Ltd.

Passivity-based control of two-dimensional translational oscillator with rotational actuator

An underactuated two-dimensional translational oscillator with rotational actuator (2DTORA) consisting of an actuated rotational proof-mass and two unactuated translational carts is presented. Passivity-based control design is employed for 2DTORA based on its Euler–Lagrange structure and passivity property. Firstly, the dynamics of 2DTORA are derived based on Euler–Lagrange equations. Motivated by constructing a damped close-loop Euler–Lagrange system, the controller dynamics is designed to shape the potential energy and inject the required damping. As a result, the designed controller stabilizes the underactuated 2DTORA with the feedback of the rotational actuator’s position only. Moreover, by modifying controller dynamics with a saturation function, the control input can be constrained to certain bounds. Finally, simulation results demonstrate the feasibility and effectiveness of the proposed controllers.

Passivity-Based Control Scheme for the Modular Multilevel Cascaded Converter (MMCC) as the HVDC-PLUS for Smart Grid Applications

This paper presents the passivity-based controller design methodologies of the 3-phase modular multilevel cascaded converter (MMCC) as HVDC-PLUS for smart grid applications. The mathematical model of the MMCC is derived in the terms of energy dissipation mechanism among the converter cells. The solvability and passivity analysis are presented based on the state-space averaged (SSA) models. The energy shaping (ES) problem is formulated by properly selection of the energy function. And the dissipative characteristics of the MMCC-based HVDC-PLUS is revealed. The interconnection and damping assignment (IDA) technique is proposed to reshape the trajectory of the control objective to guarantee the global convergence and accurate reference tracking. The carrier phase-shifted PWM scheme is adopted to synthesize the control signals for the individual half-bridge converters. The various simulation results under reactive and active power transmission scenarios are presented, which confirms the effectiveness of the proposed passivity-based control methodologies

Passivity-based control for hybrid systems with applications to mechanical systems exhibiting impacts

Motivated by applications of systems interacting with their environments, we study the design of passivity-based controllers for a class of hybrid systems in which the energy dissipation may only happen along either the continuous or the discrete dynamics. A general definition of passivity, encompassing the said special cases, is introduced and, along with detectability and solution conditions, linked to stability and asymptotic stability of compact sets. The proposed results allow us to take advantage of the passivity property of the system at flows or at jumps and are employed to design passivity-based controllers for the class of hybrid systems of interest. Two applications, one pertaining to a point mass physically interacting with a wall and another about controlling a ball bouncing on an actuated surface, illustrate the definitions and results throughout the paper.

Passivity-Based Tracking Control Design for Underactuated Mechanical Systems

Passivity-based tracking control of the underactuated linear mechanical systems is investigated in this paper. As our main contribution, the matching condition is decreased into two equations and an adjustable gain (damping gain) is introduced into the controller by setting the desired closed-loop system properly. Stability of the closed-loop system is proved based on passivity of the system. Furthermore, as examples, tracking control of 2-DOF Acrobot and 2-DOF Pendubot are studied. The systems are linearized at their equilibriums and the passivity-based controller design method is applied to the linearized systems. Matching conditions are solved and the design procedures of associate controllers for the two robots are provided. The simulation results show that the designed controllers can realize asymptotical tracking for the given desired trajectories.

Delay-Dependent Passivity and Passification for Uncertain Singularly Perturbed Markovian Jump Systems with Time-Varying Delay

This paper is concerned with passivity analysis and passivity-based controller design for uncertain singularly perturbed Markovian jump systems with time-varying delay in an interval. Firstly, a delay-dependent condition for the considered system to be mean-square exponentially stable and robustly passive is derived in terms of linear matrix inequality. Then, the passification problem is investigated. Based on the obtained passivity condition, the existence of the desired state feedback controller is established. Numerical examples are presented to show the effectiveness of the proposed method.

Passivity-based control of the new hyperchaotic system

This paper considers the problem of passivity-based controller design for a new hyperchaotic system. By transforming this hyperchaotic system into an equivalent passive system, it is proved that the equivalent system can be asymptotically tracking the desired trajectories. The feasibility and effectiveness of the proposed scheme is demonstrated.

Passivity Based Controller Design Based on EL and PCHD Model

In this paper, the method of passivity based controller design, is introduced according to passivity, EL (Euler-Lagrange) and PCHD(Port Controlled Hamiltonian with Dissipation) model of nonlinear system. In order to improve the property of system, energy shaping and damping injection are adopted in passivity based controller design. Passivity based controller is used in PWM rectifier, the properties of PWM rectifier is improved. The paper points out deficiencies of passivity based controller design based on EL and PCHD model, and further research.

Power-Based Controller for a Bidirectional AC-DC Power Converter

AbstractThrough the last three decades, Passivity-Based Control (PBC) has been positioned as an important framework for the control of nonlinear systems, and PBC design has been widely used for controlling switched-mode power converters. In this paper, a power-based controller is derived for the indirect stabilization of the average constant voltage in the dc-side and unity power-factor in the ac-side for the boost full bridge converter. These control objectives are achieved for both the rectifier and the regenerative operating mode, since the AC-DC power converter is operating in bidirectional power flow. Moreover, the approach used here is based on the Brayton-Moser framework which naturally renders the conditions of stability and tuning of control parameters. Simulated result confirm the validity of theoretical design.

Passivity-based control for Hopfield neural networks using convex representation

This paper considers the problem of passivity-based controller design for Hopfield neural networks. By making use of a convex representation of nonlinearities, a feedback control scheme based on passivity and Lyapunov theory is presented. A criterion for existence of the controller is given in terms of linear matrix inequality (LMI), which can be easily solved by a convex optimization problem. An example and its numerical simulation are given to show the effectiveness of the proposed method.

Geometric Aspects of IDA-PBC

The purpose of this work is to introduce a geometric definition of problems arising in passivity-based control design. We present a coordinate-free version of the well-known matching equations resulting from the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) design and show that feedback equivalence between control-affine systems can be used to define a family of matching problems for which an explicit solution is known. We illustrate our findings on a non-isothermal CSTR model.

Asymptotic stabilization via control by interconnection of port-Hamiltonian systems

We study the asymptotic properties of control by interconnection, a passivity-based controller design methodology for stabilization of port-Hamiltonian systems. It is well-known that the method, in its basic form, imposes some unnatural controller initialization to yield asymptotic stability of the desired equilibrium. We propose two different ways to overcome this restriction, one based on adaptation ideas, and the other one adding an extra damping injection to the controller. The analysis and design principles are illustrated through an academic example.