Damping Assignment Passivity-based Control Research Articles

Trajectory Tracking of Flexible-Joint Robots Actuated by PMSM via a Novel Smooth Switching Control Strategy

This paper presents the trajectory tracking control of a flexible-joint manipulator driven by permanent magnet synchronous motor (PMSM). Combining the PMSM electrical equation and mechanical equation of robotic manipulators, a novel smooth switching control scheme is proposed. Firstly, the position loop controller of the system is designed, with an improved hierarchical sliding mode control (IHSMC) algorithm proposed to further the response speed of the system, additionally, a robust interconnection and damping assignment passivity-based controller (IDA-PBC) is designed to improve the steady state performance of the system. Then, the IDA-PBC control strategy is leveraged to design the current loop controller of the system, on which basis a hybrid controller with smooth switching is designed. Furthermore, Gaussian function is applied as the smooth switching function of the hybrid controller to promote the switching performance. As a result, the hybrid controller has both good dynamic and steady performance. The simulation results verify the effectiveness of the algorithms.

A Passivity-Based Control of Euler–Lagrange Model for Suppressing Voltage Low-Frequency Oscillation in High-Speed Railway

The traction network voltage low-frequency oscillation (LFO) in high-speed railways easily leads to the traction blockade of electric multiple units (EMUs), which seriously affects the normal operation of high-speed railways. A passivity-based control (PBC) strategy for single-phase EMUs rectifier is proposed in this paper. First, for the single-phase EMU rectifier, the Euler–Lagrange (EL) mathematical model in dq frame is built, which can realize the decoupling of active power and reactive power. Second, according to the unique characteristics of the rectifier, it is proven that the rectifier is strictly passive, which is the premise of PBC controller design. Third, using the deduced EL mathematical model and the passivity of rectifier, the PBC controller for the single-phase rectifier of EMUs is designed using the damping injecting method. Next, compared with dq current control and interconnection and damping assignment PBC (IDA-PBC), it can be verified that the PBC controller has better dynamic and static characteristics, and can significantly suppress the voltage LFO of traction network. In these strategies listed in this paper, using the PBC, the single-phase rectifier input current has minimal total harmonic distortion, and the dc-link voltage has minimal oscillation. Finally, the dSPACE semiphysical experiment platform of the cascade system of EMUs and traction network is built. Simulation results are validated by the dSPACE semiphysical experiments, which indicate that the PBC has the better inhibitory effect for LFO as compared with that of the IDA-PBC and dq current control in single-phase EMUs rectifier.

Applications of supercapacitor energy storage systems in microgrid with distributed generators via passive fractional-order sliding-mode control

This paper develops a novel passive fractional-order sliding-mode control (PFOSMC) of a supercapacitor energy storage (SCES) system in microgrid with distributed generators. Firstly, a storage function is constructed and thoroughly analysed to investigate the inherent physical characteristics of SCES systems. Then, the beneficial terms are carefully retained for the sake of transient responses improvement, while the other detrimental terms are fully removed to achieve a globally control consistency. In order to further enhance the robustness of the closed-loop system, a fractional-order sliding-mode control (FOSMC) framework is synthesized as an additional input, which employs the fractional-order PDα sliding surface as well as an energy reshaping mechanism to realize a more flexible control performance. Four case studies, including (a) Active power and reactive power supply, (b) System restoration under power grid fault, (c) Power support under stochastic solar energy and wind energy integration, and (d) Robustness with system parameter uncertainties, are carried out to study the control performance of PFOSMC compared to that of PID control, interconnection and damping assignment passivity-based control (IDA-PBC), and FOSMC, Finally, a hardware-in-the-loop (HIL) experiment using dSpace platform is undertaken to validate its implementation feasibility.

A global asymptotical stable control scheme for a Hexverter in fractional frequency transmission systems

A fractional frequency transmission system (FFTS) is the most competitive choice for long distance transmission of offshore wind power, while the Hexverter, as a newly proposed direct AC/AC converter, is an attractive choice for its power conversion. This paper proposes a novel control scheme characterizing the global stability and strong robustness of the Hexverter in FFTS applications, which are based on the interconnection and damping assignment passivity-based control (IDA-PBC) methodology. Firstly, the frequency decoupled model of the Hexverter is studied and then a port-controlled Hamiltonian (PCH) model is built. On this basis, the IDA-PB control scheme of the Hexverter is designed. Considering the interference of system parameters and unmodeled dynamics, integrators are added to the IDA-PB controller to eliminate the steady-state error. In addition, the voltage-balancing control is applied in order to balance the capacitor DC voltages to obtain a better performance. Finally, the simulation results and experimental results are presented to verify the effectiveness and superiority of the IDA-PB controller.

Fixed-Time $\mathcal {H}_{\infty }$ Control for Port-Controlled Hamiltonian Systems

In this paper, the locally fixed-time and globally fixed-time $\mathcal {H}_{\infty }$ control problems for the port-controlled Hamiltonian (PCH) systems are investigated via the interconnection and damping assignment passivity-based control (IDA-PBC) technique. Compared with finite-time stabilization, where the convergence time of the closed-loop system's states relies on the initial values, the settling time of fixed-time stabilization can be adjusted to achieve desired equilibrium point regardless of initial conditions. The concepts of fixed-time $\mathcal {H}_{\infty }$ control, fixed-time stability region (or region of attraction), and fixed-time stability boundary are presented in this paper, and the criterions of globally fixed-time attractivity of a prespecified locally fixed-time stability region are obtained. Combining the locally fixed-time stability of an equilibrium point and the globally fixed-time attractivity of a prespecified fixed-time stability region, the globally fixed-time $\mathcal {H}_{\infty }$ control problem of PCH system is effectively solved. Two novel control laws are designed to deal with the globally fixed-time $\mathcal {H}_{\infty }$ control problem, and the conservativeness in estimating the settling time is also briefly discussed. An illustrative example shows that the theoretical results obtained in this paper work very well in the fixed-time $\mathcal {H}_{\infty }$ control design for PCH systems.

Distributed energy resources integration in single-phase microgrids: An application of IDA-PBC and PI-PBC approaches

This paper presents a unified Hamiltonian formulation for controlling distributed energy resources (DERs) in ac single-phase microgrids (SP-MGs) via proportional-integral passivity-based control (PI-PBC), and interconnection and damping assignment passivity-based control (IDA-PBC). The proposed Hamiltonian formulation allows us to consider both pulse-width modulated voltage source converters (PWM-VSC) and pulse-width modulated current source converters (PWM-CSC) under a unified model. Renewable generation and supercapacitor energy storage systems are integrated via PWM-VSC technologies, while superconducting coils are integrated through PWM-CSC technologies. IDA-PBC and PI-PBC theories enable us to design control strategies begin that consider Lyapunov’s stability theory combined with the well-known advantages of proportional and integral control actions. Our simulation’s results corroborate the applicability of the proposed control approaches under stability paradigm. MATLAB/Simulink is employed for computational implementations via begin the SimPowerSystems toolbox.

Interconnection and Damping Assignment Passivity-Based Impedance Control of a Compliant Assistive Robot for Physical Human–Robot Interactions

Interest in series elastic actuators (SEAs) for assistive robots has recently increased due to the unique properties of SEAs compared to those of rigid actuators, such as high force control accuracy, low output impedance, and tolerance to shocks. In this letter, an SEA with a clutch for an assistive robot is designed for accurate torque delivery to provide effective assistance. The mechanical clutch controls the engagement and disengagement of the power transmission during the gait cycle to ensure transparency and user safety. Precise torque control is the main challenge in the control of SEAs. The addition of a clutch in the SEA will result in a new force control challenge with the frequent release and engagement of the clutch aggravating the mechanical vibration and bringing the risk of unsafety to the assistive robot wearer. A new torque control method based on interconnection and damping assignment passivity-based control (IDA-PBC) for SEAs is adopted for the physical human–robot interaction. Experiments are conducted to verify that the IDA-PBC-based SEA torque controller can effectively control actuator timing and allow precise assistive torque control. This letter serves as a stepping stone toward utilizing and designing assistive robots to assist with walking.

Fixed-time stabilization control for port-Hamiltonian systems

In this paper, the locally fixed-time and globally fixed-time stabilization problems for the port-Hamiltonian (PH) systems via the interconnection and damping assignment passivity-based control technique are discussed. The definitions of fixed-time stability region (or region of attraction) and fixed-time stability boundary are given in this paper. From this starting point, the sufficient condition of globally fixed-time attractivity of a prespecified locally fixed-time stability region is obtained. Combining the locally fixed-time stability and the globally fixed-time attractivity of a prespecified locally fixed-time stability region, the globally fixed-time stabilization problem for PH system is effectively solved. Furthermore, the globally fixed-time control scheme independent of locally fixed-time stability region has also been derived by constructing a novel Lyapunov function. A illustrative example shows that the results obtained in this paper work very well in fixed-time control design of PH systems.

Aerial physical interaction via IDA-PBC

This paper proposes the use of a novel control method based on interconnection and damping assignment–passivity-based control (IDA-PBC) in order to address the aerial physical interaction (APhI) problem for a quadrotor unmanned aerial vehicle (UAV). The apparent physical properties of the quadrotor are reshaped in order to achieve better APhI performances, while ensuring the stability of the interaction through passivity preservation. The robustness of the IDA-PBC method with respect to sensor noise is also analyzed. The direct measurement of the external wrench, needed to implement the control method, is compared with the use of a nonlinear Lyapunov-based wrench observer and advantages/disadvantages of both methods are discussed. The validity and practicability of the proposed APhI method is evaluated through experiments, where for the first time in the literature, a lightweight all-in-one low-cost force/torque (F/T) sensor is used onboard of a quadrotor. Two main scenarios are shown: a quadrotor responding to external disturbances while hovering (physical human–quadrotor interaction), and the same quadrotor sliding with a rigid tool along an uneven ceiling surface (inspection/painting-like task).

Structure Preserving Observer Design for Port-Hamiltonian Systems

In this paper, a full-order observer design method is proposed for port-Hamiltonian systems. The proposed method is based on the notion of contractive port-Hamiltonian systems. It is the first structure preserving observer design for a broad class of input-state-output port-Hamiltonian systems. The design procedure consists of solving a matching equation, similar to the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) for controller design. The matching equation, as shown in the paper, has some closed-form solutions for general class of mechanical and electromechanical systems. As another feature of the proposed method, it is shown that the existence of solution of the corresponding matching equation for a linear port-Hamiltonian system is equivalent to the detectability property of that system. Upon these facts, the proposed method can be considered as a counterpart of IDA-PBC for observer design. Simulations for some benchmark examples, including ball and beam, magnetic levitation, and permanent magnetic synchronous motor, show the potency and applicability of the method.

A Nonlinear Supplementary Controller for Transient Response Improvement of Distributed Generations in Micro-Grids

This paper proposes a nonlinear supplementary controller for enhancing the transient response of distributed generations (DGs) in micro-grids. The proposed supplementary control system is based on an interconnection and damping assignment passivity-based controller and is designed according to the port-controlled Hamiltonian model of DGs. The controller is applied to the decentralized unified control scheme of DGs that enables seamless transitions between islanded and grid-connected modes. The proposed controller is generic and can be applied to DGs with different types of primary sources. The stability of the proposed supplementary controller is verified analytically, and the performance of the proposed controller is verified in a multi-resource micro-grid via time-domain simulations.

IDA-PBC Algebraico Para Sistemas Polinomiales con Saturación en las Entradas: Un Enfoque Basado en SOS

The necessity to deal with partial differential equations (PDEs) and the dissipation condition are the mainadversities in the application of Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC). Recently,an algebraic solution of IDA-PBC has been explored for a class of affine polynomial systems by using sum of squares(SOS) and semidefinite programming (SDP). In this work, we extend the previous method by incorporating actuatorsaturation (AS) and two minimization objectives in the SDP. Our results are validated on two polynomial systems.

Adaptive IDA-PBC for a Class of UMSs: The IWIP Analysis

In this paper an adaptive control scheme is developed for enhancing the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) technique. The primary objective of the adaptive component is to stabilize a class of Underactuated Mechanical Systems (UMSs) in the presence of uncertainties that are not necessarily matched. This class of UMSs is characterized by the solvability of the IDA-PBC matching condition and an additional adaptive condition. We analyze the asymptotic stability behavior of the Inertia Wheeled Inverted Pendulum (IWIP) under three types of uncertainties: input disturbance, physical damping (friction) and parameter uncertainties in the total energy of the system. Simulations illustrate the effectiveness of the approach.

Port-Controlled Phasor Hamiltonian Modeling and IDA-PBC Control of Solid-State Transformer

This paper presents an application of interconnection and damping assignment passivity-based control (IDA-PBC) principle to the port-controlled phasor Hamiltonian (PCPH) model of solid-state transformer (SST) (comprising of three stages, namely, ac/dc rectifier, dual active bridge converter, and dc/ac inverter). A PCPH model of SST is established for each individual stages using dynamic phasor concept. In comparison with other PBC approaches, IDA-PBC offers an additional degree of freedom to solve the partial differential equations. According to the target of the controller design at each stage, the desired equilibrium point of the system is obtained. The closed-loop system performance achieves regulation of constant output dc-bus voltage and unity input power factor. Large-signal simulation results for the full system validate the simplifications introduced to obtain the controller and verify the proposed controller. Robustness of the controller is demonstrated with 20% load disturbance and 10% input disturbance. For validation of the proposed approach and its effectiveness, hardware-in-loop simulation is carried out using Opal-RT and dSPACE simulators.

Nonlinear control of a subscale submarine in emergency ascent

This paper presents a nonlinear parametric model and proof-of-concept motion control system for a scale model submarine undertaking an emergency ascent. An energy-based model is presented that represents the underactuated submarine in a non-neutrally buoyant state. This model is then used to synthesize a control law using Port-Hamiltonian theory and interconnection and damping assignment passivity-based control. Lyapunov analysis is used to demonstrate stability of the closed-loop system, and a simulation-based study is presented to demonstrate performance of the control law. The results demonstrate that a closed loop non-linear controller is able to improve the quality of emergency rise by automatically compensating for some parasitic effects in the hydrodynamics that can compromise ascent performance.

Control of a self-balancing robot with two degrees of freedom via IDA-PBC

This paper presents an interconnection and damping assignment passivity-based control (IDA-PBC) to drive a self-balancing robot restricted to two degrees of freedom including the dynamics of the actuators. The design of the control law, stability analysis and estimation of the domain of attraction are shown in detail. A convenient change of variables and an appropriate handling of the matching equations have been key to design the control law and to get the asymptotic stability analysis, respectively. Two scalar functions have been used in the design of the controller to underscore how different proposals for the desired potential energy can shape the behavior of the self-balancing robot in closed loop. Experimental results are presented in order to confirm the theoretical proposal and to illustrate the performance of the proposed control law in the regulation task and the practical robustness against external disturbances.

Passivity-based control and stability analysis for hydro-turbine governing systems

• Nonlinear dynamic model of hydro-turbine governing systems with surge tank is shown. • A controller of a hydro-turbine governing system with surge tank based on pH systems is proposed. • The proposed controller is based on interconnection and damping assignment passivity-based control. • A comparison of the proposed controller with two standard controllers is presented. Low-frequency oscillations can occur in hydropower systems under in the new context of power system and the classical controller for hydro-turbine governing systems need to be enhanced with the purpose of improving its stability. We propose a controller based on passivity theory with the aim of damping oscillations in a power system. Passivity-based control arises as a natural choice for hydro-turbine governing system since its open-loop dynamic has a port-Hamiltonian structure, which allows designing a controller that preserves the passive structure in closed-loop via interconnection and damping reassignment. The proposed controller considers the complete non-linear model of the system and guarantees global asymptotic stability in the sense of Lyapunov. Time-domain simulations demonstrate the robustness and proper performance of the proposed methodology under different operative conditions when is compared with the classical controllers.

Interconnection and Damping Assignment Passivity–Based Control of an Underactuated 2–DOF Gyroscope

Abstract In this paper we present interconnection and damping assignment passivity-based control (IDA-PBC) applied to a 2 degrees of freedom (DOFs) underactuated gyroscope. First, the equations of motion of the complete system (3-DOF) are presented in both Lagrangian and Hamiltonian formalisms. Moreover, the conditions to reduce the system from a 3-DOF to a 2- DOF gyroscope, by using Routh’s equations of motion, are shown. Next, the solutions of the partial differential equations involved in getting the proper controller are presented using a reduction method to handle them as ordinary differential equations. Besides, since the gyroscope has no potential energy, it presents the inconvenience that neither the desired potential energy function nor the desired Hamiltonian function has an isolated minimum, both being only positive semidefinite functions; however, by focusing on an open-loop nonholonomic constraint, it is possible to get the Hamiltonian of the closed-loop system as a positive definite function. Then, the Lyapunov direct method is used, in order to assure stability. Finally, by invoking LaSalle’s theorem, we arrive at the asymptotic stability of the desired equilibrium point. Experiments with an underactuated gyroscopic mechanical system show the effectiveness of the proposed scheme.

A Robust IDA-PBC Approach for Handling Uncertainties in Underactuated Mechanical Systems

Interconnection and damping assignment passivity-based control (IDA-PBC) is a method that has been developed to (asymptotically) stabilize nonlinear systems formulated in the port-controlled Hamiltonian (PCH) structure. This method has gained increasing popularity and has been successfully applied to a wide range of dynamical systems. However, little is known about the robustness of this method in response to the effects of uncertainty which could result from disturbances, noises, and modeling errors. This paper explores the possibility of extending some energy shaping methods, taking into account the robustness aspects, with the aim of maintaining (asymptotic) stability of the system in the presence of perturbations which inevitably exist in any realistic applications. We propose constructive results on robust IDA-PBC controllers for underactuated mechanical systems that are quite commonly found in practice and have the most challenging control problems within this context. The proposed results extend some existing methods and provide a new framework that allows the implementation of integral and input-to-state stability controllers to underactuated mechanical systems. The results are applied to two physical systems: an inertia wheel pendulum and a rotary inverted pendulum that represent separable and nonseparable PCH systems, respectively.

Indirect IDA-PBC for active and reactive power support in distribution networks using SMES systems with PWM-CSC

Abstract In this paper an indirect interconnection and damping assignment passivity-based control (IDA-PBC) applied to the three-phase superconducting magnetic energy storage systems (SMES) is proposed to support active and reactive power in distribution systems. The SMES is connected to the distribution network using a pulse-width-modulated current source converter (PWM-CSC), due to its intrinsic current features that are more natural for controlling the current of a superconducting coil. A Hamiltonian function is selected as an hyperboloid representation taking into account the open loop dynamics of the system. The indirect control strategy is used to decouple the dynamical behavior between ac and dc side of the system, which allows to control active and reactive power independently in the ac side, while the dc side of the converter is employed as a supervisor controller for active power interchange. Simulation results demonstrate the efficiency and robustness of the proposed control methodology applied on a low-voltage distribution network under different operative conditions where the tracking errors were less than 6.2%.