Passivity-based Control Method Research Articles

Research on Comprehensive Active Current- Limiting Control Strategy Applied in Two-Port MMC-HVDC Transmission System

Aiming at the defect that the current-limiting strategy based on the modular multilevel converter (MMC)-high-voltage direct current (HVDC) system only focuses on the unilateral ac side or dc side, this article proposes a current-limiting strategy that is suitable for both ac-side ground fault and dc-side short-circuit fault. First, for the ground fault on the ac side, the outer loop controller with power state equation and the inner loop controller with passivity-based control (PBC) strategy are used to control it, and the genetic algorithm, which takes the absolute value of the difference between the reference current and the actual current as the fitness function, is used to fit the optimal injection damping parameters for the PBC method. Then, for the short-circuit fault on the dc side, the capacitor discharge duty ratio is introduced on the basis of the equivalent capacitance without considering the voltage drop, and its segmented control is combined with the current-limiting reactors to achieve current-limiting at different fault points. Finally, a two-port +500-kV HVDC transmission system was built on MATLAB/Simulink software, and the effectiveness of the current-limiting method proposed in this article was verified.

Distributed IDA-PBC for a Class of Nonholonomic Mechanical Systems

Nonholonomic mechanical systems encompass a large class of practically interesting robotic structures, such as wheeled mobile robots, space manipulators, and multi-fingered robot hands. However, few results exist on the cooperative control of such systems in a generic, distributed approach. In this work we extend a recently developed distributed Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) method to such systems. More specifically, relying on port-Hamiltonian system modelling for networks of mechanical systems, we propose a full-state stabilization control law for a class of nonholonomic systems within the framework of distributed IDA-PBC. This enables the cooperative control of heterogeneous, underactuated and nonholonomic systems with a unified control law. This control law primarily relies on the notion of Passive Configuration Decomposition (PCD) and a novel, non-smooth desired potential energy function proposed here. A low-level collision avoidance protocol is also implemented in order to achieve dynamic inter-agent collision avoidance, enhancing the practical relevance of this work. Theoretical results are tested in different simulation scenarios in order to highlight the applicability of the derived method.

Optimal Task-Invariant Energetic Control for a Knee-Ankle Exoskeleton

Task-invariant control methods for powered exoskeletons provide flexibility in assisting humans across multiple activities and environments. Energy shaping control serves this purpose by altering the human body's dynamic characteristics in closed loop. Our previous work on potential energy shaping alters the gravitational vector to reduce the user's perceived gravity, but this method cannot provide velocity-dependent assistance. The interconnection and damping assignment passivity-based control (IDA-PBC) method provides more freedom to shape a dynamical system's energy through the interconnection structure of a port-controlled Hamiltonian system model. This letter derives a novel energetic control strategy based on IDA-PBC for a backdrivable knee-ankle exoskeleton. The control law provides torques that depend on various basis functions related to gravitational and gyroscopic terms. We optimize a set of constant weighting parameters for these basis functions to obtain a control law that produces able-bodied joint torques during walking on multiple ground slopes. We perform experiments with an able-bodied human subject wearing a knee-ankle exoskeleton to demonstrate reduced activation in certain lower-limb muscles.

L2-Gain Adaptive Robust Control for Hybrid Energy Storage System in Electric Vehicles

The underlying voltage/current tracking control is a key issue for a hybrid energy storage system (HESS) in electric vehicles. This article presents an innovative passivity-based L2-gain adaptive robust control (L2-ARC) method for a fully active battery/super-capacitor HESS. First, by exploiting and analyzing the internal structural properties, the port-controlled Hamiltonian model with dissipation for HESS is derived and then, the interconnection and damping assignment-passive based controller (IDA-PBC) is designed to realize the underlying control, where the rule-based energy management strategy is adopted to generate the current references. To overcome the adverse influence of external disturbances and parameter perturbations under complex driving conditions, by combining the L2 gain disturbance attenuation technique with the IDA-PBC method, the L2-ARC method is developed to guarantee fast response, high performance, and robust stability. Moreover, an adaptive mechanism is adopted to estimate the electrical parameters. The performance of L2-ARC is thoroughly investigated and compared through comprehensive case studies with traditional PID, IDA-PBC, and sliding mode controllers. Finally, a control prototype is implemented to validate L2-ARC.

Passivity-Based Nonlinear Active Suspension Control Utilizing Relative Information

In this paper we present the design of active suspension system by using a kind of passivity-based control method, where the proposed suspension system provides the good ride comfort and the good road holding simultaneously and only uses relative displacement and velocity. We show that the proposed method can be extended to nonlinear case easily. The robustness of proposed method is also analyzed.

Orbital stabilization of nonlinear systems via Mexican sombrero energy shaping and pumping-and-damping injection

In this paper we show that a slight modification to the widely popular interconnection and damping assignment passivity-based control method – originally proposed for stabilization of equilibria of nonlinear systems – allows us to provide a solution to the more challenging orbital stabilization problem. Two different, though related, ways how this procedure can be applied are proposed. First, the assignment of an energy function that has a minimum in a closed curve, i.e., with the shape of a Mexican sombrero. Second, the use of a damping matrix that changes “sign” according to the position of the state trajectory relative to the desired orbit, that is, pumping or dissipating energy. The proposed methodologies are illustrated with the example of the induction motor and prove that it yields the industry standard field oriented control.

Assessment of damping coefficients ranges in design of a free piston Stirling engine: Simulation and experiment

This paper concentrates on investigating the robustness of the free piston Stirling engine (FPSE) considering the uncertainty of the damping coefficients of power and displacer pistons using the vanishing perturbation. First, error state equations of the FPSE possessing nonlinear springs are derived. Next, the passivity-based control method without applying the uncertainty term is employed to achieve the limit cycle for power and displacer pistons motions. Afterwards, the vanishing perturbation is considered to study the robustness of the system against the allowable increase of the power and displacer pistons’ damping coefficients through finding the upper bound. Consequently, the presented paper, first, studied the FPSE behavior without considering the uncertainty term and then, probes the consideration of the uncertainty term. Accordingly, the motions and velocities of pistons as well as the existence of limit cycles in the system response are investigated in detail. Next, the validity of the presented scheme is experimented through a prototype model, namely SUTech-SR-1. Finally, according to the achieved upper bound, the proposed work not only appropriately predicts the FPSE behavior, but also the obtained simulation data are found to be in an acceptable agreement with those of the experiment.

Tracking-error control via the relaxing port-Hamiltonian formulation: Application to level control and batch polymerization reactor

In this paper, a tracking-error-based control design without feedback passivation stage is developed for the stabilization of physical and chemical nonlinear processes. To achieve control objectives, the system dynamics is first formulated under appropriate conditions as a relaxing (pseudo) port-Hamiltonian (PH) representation with some quadratic storage function, in which the positive semi-definite property of damping matrix may not be taken necessarily into account. Then, a reference trajectory expressed by a certain structure passing through a desired set-point (or containing an optimal profile) is suitably chosen. By adding a relevant damping injection, asymptotic and global convergence of error dynamics is guaranteed. Two case studies including the level control of a four-tank process of continuous time type and the optimal tracking of a batch polymerization reactor of discontinuous time type due to the nature of the process operation are used to illustrate the application and the effectiveness of the approach. Besides the control performance comparison with the conventional passivity-based control method and the robustness evaluation against disturbance and/or noise are included.

Passivity Based Control method for the diffusion process

Abstract A passivity based control method is presented for the diffusion process by the use of the concept of available storage and irreversible thermodynamics. A convex extension using the internal energy as generating function will be employed to define a Lyapunov functional for the distributed irreversible port Hamiltonian system (the diffusion process). The latter functional, will be used to suggest a Lyapunov stability condition by applying the so called La Salle’s Invariance principle for infinite dimensional systems on the heat and mass diffusion process.

Passivity-Based Control for Two-Wheeled Robot Stabilization

A passivity-based control system design for two-wheeled robot (TWR) stabilization is presented. A TWR is a statically-unstable non-linear system. A control system is applied to actively stabilize the TWR. Passivity-based control method is applied to design the control system. The design results in a state feedback control law that makes the TWR closed loop system globally asymptotically stable (GAS). The GAS is proven mathematically. The TWR stabilization is demonstrated through computer simulation. The simulation results show that the designed control system is able to stabilize the TWR.

IDA‐PB control with integral action of Y‐connected modular multilevel converter for fractional frequency transmission application

Y-connected modular multilevel converter (Y-MMC) is a new topology of direct AC/AC power conversion, with broad application prospects in fractional-frequency transmission system. This study studies the mathematical model of Y-MMC and builds the port-controlled Hamiltonian model. Since vector control scheme can hardly ensure global stability, the interconnection and damping assignment passivity-based control (IDA-PBC) method is applied for controller design of Y-MMC. Three typical IDA-PBC strategies are then proposed, featuring the asymptotical stability of the desired equilibrium. To eliminate steady-state error, integrators are further added to the IDA-PB controller. Different from the previous research, the proposed method enables the decoupling of different-frequency components and the suppression of frequency leakage. Besides, the reactive power distribution coefficients are introduced to characterise the optimisation allocation of reactive power between arms. Finally, the effectiveness and superiority of the proposed control strategy are verified by both the simulation and experiment results.

Grid-Connected Control Strategy of Five-level Inverter Based on Passive E-L Model

At present, the research on five-level inverters mainly involves the modulation algorithm and topology, and few articles study the five-level inverter from the control strategy. In this paper, the nonlinear passivity-based control (PBC) method is proposed for single-phase uninterruptible power supply inverters. The proposed PBC method is based on an energy shaping and damping injection idea, which is performed to regulate the energy flow of an inverter to a desired level and to assure global asymptotic stability, respectively. Furthermore, this paper presents a control algorithm based on the theory of passivity that gives an inverter in a photovoltaic system additional functions: power factor correction, harmonic currents compensation, and the ability to stabilize the system under varying injection damping. Finally, the effectiveness of the PBC method in terms of both stability and harmonic distortion is verified by the simulation and experiments under resistive and inductive loads.

Interconnection and damping assignment passivity-based control for a compass-like biped robot

A novel procedure for designing an interconnection and damping assignment passivity-based control to perform different walking gaits of a compass-like biped robot is presented. The interconnection and damping assignment passivity-based control method is often used to achieve asymptotic stability of the closed-loop desired equilibrium point in underactuated systems. Nevertheless, in this article, for the first time, this method is used to shape the kinetic energy of the robot and thus perform different gaits by modifying its limit cycle. One degree of underactuation of the compass-like biped robot is considered, and a suitable change of coordinates is made in order to design the proposed control law. The effectiveness of this controller and some advantages with respect to another similar approach are shown through a deep numerical simulation study.

Flexible Structure Control of Unmatched Uncertain Nonlinear Systems via Passivity-based Sliding Mode Technique

This paper considers the problem of passivity-based sliding mode control of uncertain nonlinear systems. For this purpose, two cases are studied. In the first case, it is assumed that only the matched uncertainties exist in the system dynamics. In this case, the passivity-based control approach is used to design an appropriate sliding manifold with a flexible structure such that the asymptotic stability of the reduced-order model (i.e., the motion equations on the proposed sliding manifold) is guaranteed. In the second case, both matched and unmatched uncertainties are considered in the system dynamics and thus the reduced-order model has uncertain terms. In this case, the modified Lyapunov redesign technique is combined with the passivity-based control method for design of robust sliding manifold. The function that is basically used in the classical Lyapunov redesign method is the signum function, which is not differentiable. Since, for evaluating the derivative of the sliding manifold its equation must be differentiable, a new additional continuous control term is suggested. In addition, the robust practical stabilization of the motion equations is guaranteed without considering any limitation on the upper bound of the unmatched uncertainties. Finally, computer simulations are performed for a practical example (flexible spacecraft) and also a numerical example to demonstrate the ability of the proposed controller in robust stabilization of uncertain nonlinear dynamical systems.

Precise Control of Elastic Joint Robot Using an Interconnection and Damping Assignment Passivity-Based Approach

Vibration suppression and precise tracking are the two main challenges in the control of elastic joint robots. In this study, an elastic joint robot with precise position sensors on both the motor and link sides is developed to tackle these challenges. With a two-mass model for elastic joint and a LuGre friction model for joint friction, the elastic joint robot system is modeled and analyzed as an underactuated port-controlled Hamiltonian system with dissipation (PCHD). The proposed elastic joint controller is integrated with friction compensation using the interconnection and damping assignment passivity-based control method, leading to a PCHD closed loop system that can be effectively tuned to suppress vibration associated with elastic joints. In addition, integral control is employed to achieve high tracking precision. Experiments have been conducted and the results have demonstrated high performance of the proposed control method.

Passivity-Based Adaptive Finite-Time Trajectory Tracking Control for Spacecraft Proximity Operations

A passivity-based robust adaptive finite-time trajectory tracking control strategy is developed for a pursuer spacecraft proximity to a cooperative target spacecraft in space. The relative position vector between the pursuer and the target is required to direct toward the docking port of the target while the attitude of the two bodies must be synchronized. With the effective reference trajectory, the finite-time control of relative translational and relative rotational motions is finished simultaneously by using a unified passivity-based adaptive control method. Finite-time stability of the closed-loop system for six degree-of-freedom relative motion is proved in spite of the unknown inertial parameters and external disturbances. Numerical simulations including six-degree-of-freedom rigid-body dynamics are performed to demonstrate the effectiveness of the proposed controller.

Improved passivity‐based control method and its robustness analysis for single‐phase uninterruptible power supply inverters

An improved passivity-based control (IPBC) method is proposed for single-phase uninterruptible power supply inverters. The proposed IPBC method is based on energy shaping and damping injection idea which is performed for regulating the energy flow of inverter to a desired level and assure global asymptotic stability, respectively. It is shown that the control of output voltage can be accomplished indirectly provided that the inductor current tracks its reference. Since the estimated parameters do not match with the actual parameters in practice, a perfect tracking without any output voltage error is not possible. To reduce the influence of parameter mismatch on the output voltage, an outer voltage loop is added into the feedback path of conventional passivity-based control (PBC) method. The robustness of both PBC methods has been investigated and analytical expressions in terms of estimated and actual parameters are derived for the output voltage. The effectiveness of the IPBC method in terms of both robustness and harmonic distortion is verified by the simulations and experiments under resistive and diode rectifier loads. The results demonstrate that the IPBC method not only leads to good quality output voltage with a reasonably low harmonic distortion, but also offers a global asymptotic stable operation with a strong robustness to wide range of parameter mismatch.

Application of Passivity-Based Control and Time-Frequency Representation in a Doubly Fed Induction Generator System

In order to improve the performance of a doubly fed induction generator (DFIG) system, we put forward a high performance nonlinear passivity-based control (PBC) method on DFIG. Firstly, we build a PBC mathematical model for DFIG. We design the passive controller for the inner loop in the control system based on passivity theory. Then we calculate the rotor’s control voltages which are modulated afterwards to pulse to control the rotor side converter. The maximal wind energy capture is effectively realized. The rotor speed and DFIG currents fast track their expected values. The independent regulation of the stator active power and reactive power is achieved. Finally we perform simulations to verify the effectiveness of the proposed method. Furthermore, we employ the Wigner-Ville distribution (WVD) and continuous wavelet transform (CWT) as two time-frequency representation methods to indicate that the proposed method in the paper performs well from the perspective of energy distribution in time and frequency domain.

A novel control method for a VSC-HVDC system in a grid-connected wind farm

The voltage source converter-high voltage direct current (VSC-HVDC) transmission is the ideal integration technology for grid-connected wind farms. A passivity-based control (PBC) method for VSC-HVDC when the wind farm voltage is unbalanced is proposed in this paper. The mathematical model of a VSC with unbalanced voltage is established. The PBC theory including dissipation inequality and system strict passivity is introduced, and then the stability of PBC is proven in light of the Lyapunov stability theory. According to PBC theory, a Euler--Lagrange mathematical model of a VSC is constructed. After that, the strict passivity of the VSC is proven. On the premise of the power factor being 1, the PBC controller for the VSC-HVDC system is designed under d-q coordination. The control law is deduced in detail. In order to accelerate the convergence speed, dampers are added to the PBC controller. The decoupled control of the active power and the reactive power is achieved by this method. The dynamic and steady performances of the VSC-HVDC system in a grid-connected wind farm when the wind farm voltage is unbalanced are significantly improved. Furthermore, the robustness of the system is enhanced. The simulation results verify the feasibility and correctness of the method.

Passivity-based reinforcement learning control of a 2-DOF manipulator arm

Passivity-based control (PBC) is commonly used for the stabilization of port-Hamiltonian (PH) systems. The PH framework is suitable for multi-domain systems, for example mechatronic devices or micro-electro-mechanical systems. Passivity-based control synthesis for PH systems involves solving partial differential equations, which can be cumbersome. Rather than explicitly solving these equations, in our approach the control law is parameterized and the unknown parameter vector is learned using an actor–critic reinforcement learning algorithm. The key advantages of combining learning with PBC are: (i) the complexity of the control design procedure is reduced, (ii) prior knowledge about the system, given in the form of a PH model, speeds up the learning process, (iii) physical meaning can be attributed to the learned control law. In this paper we extended the learning-based PBC method to a regulation problem and present the experimental results for a two-degree-of-freedom manipulator. We show that the learning algorithm is capable of achieving feedback regulation in the presence of model uncertainties.