Port-controlled Hamiltonian Systems Research Articles

Fixed-time stabilization and [formula omitted] control of time-delay port-controlled Hamiltonian systems

In this paper, we investigate the fixed-time stability (FxTS) and fixed-time H∞ control design of time-delay port-controlled Hamiltonian (PCH) systems. Firstly, we establish an improved FxTS criterion. Secondly, by utilizing this criterion and interconnection and damping assignment passivity-based (IDA-PBC) technique, two new FxTS results are given for PCH systems with the assumption about Hamiltonian functions. Then, a fixed-time H∞ control design procedure is presented by using a new Lyapunov–Krasovskii (L-K) functional. Finally, the forced mathematical pendulum model with a constant time-delay shows the effectiveness of our results.

Practical fixed-time stabilization for discrete-time impulsive switched port-controlled Hamiltonian systems

This paper is concerned with practical fixed-time (FT) stabilization problem of discretetime impulsive switched port-controlled Hamiltonian systems (DISPCH). First, starting with discrete-time port-controlled Hamiltonian systems, a novel controller is presented to achieve practical FT stability of the obtained closed-loop system. Moreover, in order to well handle the abrupt changes at switch moments in practical switched systems, another novel controller is presented in terms of positive-order Lyapunov functions approach and range dwell time method to make discrete-time impulsive switched port-controlled Hamiltonian system practical FT stable. Ultimately, the validity of proposed methods is illustrated by simulations.

Energy-Based Control for Switched Uncertain Port-Controlled Hamiltonian Systems With Its Application to RLC Circuit Systems

Energy-Based Control for Switched Uncertain Port-Controlled Hamiltonian Systems With Its Application to RLC Circuit Systems

FPGA Based Integrated Control of Brushless DC Motor for Renewable Energy Storage System

To reduce air pollution and global warming, renewable energy technologies may generate power. Wind, solar PV, and fuel cell energy are the primary sources. Solar PV system-powered brushless direct current motor (BLDC) drives are used in the automobile industry due to their importance. In this study, Sheppard–Taylor (S-T) converter and Pulse Width Modulated (PWM) Inverter-fed BLDC provide steady voltage across the BLDC motor drive independent of solar PV system power output. When renewable energy is scarce, the proposed battery-supercapacitor hybrid energy storage system (BS-HESS) provides electricity. S-T converters may be used for load matching and power processing to create energy-efficient systems and stabilize PV panel output voltage. The variable step size open circuit voltage-Maximum Power Point Tracking (VSSOCV-MPPT) technique in S-T converter switching pulses extracts maximum power from the solar PV system. This study considers the PVSWPS control function as a Port-Controlled Hamiltonian (PCH) system to continue rural growth and reduce the greatest demand and load. MATLAB/Simulink software simulates the system’s performance, and FPGA controllers validate the controller’s real-time performance.

Finite-time adaptive control for uncertain switched port-controlled Hamiltonian systems

In this paper, the finite-time boundedness (FTB) and H∞ control are discussed for a class of uncertain switched port-controlled Hamiltonian (PCH) systems via adaptive control strategies. In view of the mode-dependent matching principle, the energy-based multiple Lyapunov functions method and the mode-dependent average dwell time (MDADT) approach, sufficient conditions on the FTB are obtained for uncertain switched PCH systems by employing a set of adaptive mode-dependent state feedback controllers. Furthermore, to solve the finite-time H∞ control for the system under consideration, a new set of mode-dependent state feedback controllers are designed to restrain both the structured uncertainties and disturbances, and sufficient conditions on the H∞ control problem are derived for the system under a new MDADT scheme. Finally, the numerical simulations are presented to illustrate the effectiveness of the proposed finite-time adaptive control methods.

Enhanced Synchronization Stability of Grid-Forming Inverters With Passivity-Based Virtual Oscillator Control

In this article, a passivity-based virtual oscillator control strategy with enhanced synchronization stability for grid-forming inverters (GFMs) is proposed. By adopting the port-controlled Hamiltonian system theory for orbital stabilization problems, an energy pumping-and-damping block is proposed to render GFMs globally asymptotically stable with respect to the prespecified solutions of the power-flow equations from any initial condition. This allows for stable integrations of GFMs to any other globally asymptotically stable systems without their explicit knowledge, e.g., helping maintain synchronism with the bulk power system in a wide range of short-circuit-ratio conditions or under large disturbances and keeping synchronism among multiple GFMs in power systems. Both simulations and experiments are presented to demonstrate the proposed control approach.

Memristor‐based disturbance rejection control for port‐Hamiltonian systems with locally fixed‐time convergence

The memristor is added to the port-Hamiltonian systems to improve the disturbance suppression performance in this paper. The concepts of locally fixed-time stability and locally fixed-time H ∞ $H_{\infty }$ control of port-Hamiltonian systems are presented. From this starting point, two novel memristor-based locally fixed-time controllers are designed to suppress the external disturbance of port-Hamiltonian systems via the interconnection and damping assignment passivity-based control technique. Comparing with the classical interconnection and damping assignment passivity-based control methodology without memristor, there are some advantages. First, the settling-time related to the memristor-based controllers in stabilizing the same port-Hamiltonian systems are shorter. Second, the memristor-based controllers can make the oscillation in the case of the strong periodic disturbance be better suppressed. Theoretical analysis shows that the memristor-based controller possesses good disturbance rejection performance owing to it can make the system states in a neighbourhood accelerate convergence to the desired equilibrium point. Two illustrative examples show that the theoretical results and the controllers designed in this paper work very well.

Efficiency Optimization Strategy of Permanent Magnet Synchronous Motor for Electric Vehicles Based on Energy Balance

This paper presents an efficiency optimization controller for a permanent magnet synchronous motor (PMSM) of an electric vehicle. A new loss model is obtained based on the permanent magnet synchronous motor’s energy balance equation utilizing the theory of the port-controlled Hamiltonian system. Since the energy balance equation is just the power loss of the PMSM, which provides great convenience for us to use the energy method for efficiency optimization. Then, a new loss minimization algorithm (LMA) is designed based on the new loss model by adjusting the ratio of the excitation current in the d–q axis. Moreover, the proposed algorithm is achieved by the principle of the energy shape method of the Hamiltonian system. Simulations are finally presented to verify effectiveness. The main results of these simulations indicate that the dynamic performance of the drive is maintained and the efficiency increase is up to about 7% compared with the id=0 control algorithm, and about 4.5% compared with the conventional LMA at a steady operation of a PMSM.

Finite‐time adaptive control for port‐controlled Hamiltonian systems with parametric perturbations

SummaryIn this article, finite‐time boundedness (FTB) and control are addressed for a class of port‐controlled Hamiltonian (PCH) systems with parametric perturbations. Based on adaptive state feedback control strategies, sufficient conditions are obtained for FTB of the PCH systems with parametric perturbation and external disturbances. Furthermore, another adaptive state feedback controller is applied to compensate the parameter perturbation and attenuate the external disturbances, and finite‐time control conditions are acquired for the PCH systems with parametric perturbation and external disturbances. In addition, the FTB and finite‐time control conditions are also given for uncertain nonlinear systems via the Hamiltonian realization method. Finally, the numerical simulations are presented to verify the feasibility of the proposed results.

Learning Data-Driven PCHD Models for Control Engineering Applications*

The design of control engineering applications usually requires a model that accurately represents the dynamics of the real system. In addition to classical physical modeling, powerful data-driven approaches are increasingly used. However, the resulting models are not necessarily in a form that is advantageous for controller design. In the control engineering domain, it is highly beneficial if the system dynamics is given in PCHD form (Port-Controlled Hamiltonian Systems with Dissipation) because globally stable control laws can be easily realized while physical interpretability is guaranteed. In this work, we exploit the advantages of both strategies and present a new framework to obtain nonlinear high accurate system models in a data-driven way that are directly in PCHD form. We demonstrate the success of our method by model-based application on an academic example, as well as experimentally on a test bed.

Simultaneous exponential stabilization for stochastic port-controlled Hamiltonian systems with actuator saturations, fading channels and delays

This paper is concerned with the simultaneous exponential stabilization problem for a set of stochastic port-controlled Hamiltonian (PCH) systems. Due to the limited bandwidth of the channels, the phenomena of fading channels and transmission delays which are described by a time-varying stochastic model always occur in the communication channels from the controller to the actuator. Meanwhile, actuator saturation constraint is taken into account. On the basis of dissipative Hamiltonian structural and saturating actuator properties, those stochastic PCH systems are combined to generate an augmented system. By utilizing the stochastic analysis theory, sufficient criterions are given for the simultaneous stabilization controller design ensuring that the closed-loop system is simultaneously exponentially mean-square stable (SEMSS). For the case that there exist external disturbances in the systems, some results on stability analysis and controller design are given. The developed controller design scheme is proved by a three-helicopter model simulation example.

Protocol design for group output consensus of disturbed port-controlled Hamiltonian multi-agent systems

This paper considers the group output consensus problem for a class of disturbed port-controlled Hamiltonian multi-agent systems via a composite control method. The composite distributed control protocol is proposed by combining the damping injection and energy shaping method, the finite-time disturbance observer (FTDO) technique and distributed protocol, which makes the closed-loop Hamiltonian multi-agent systems asymptotically stable and the group outputs reach consensus. It is shown that many kinds of disturbances can be estimated accurately via the FTDO. The advantage is that this control scheme exhibits not only better robustness against disturbances, but also the nominal system recovery performance. Two illustrative examples reveal that the designed control protocol is effective.

Finite-time stabilization and H∞ control of Port-controlled Hamiltonian systems with disturbances and saturation.

The finite-time stabilization and finite-time H∞ control problems of Port-controlled Hamiltonian (PCH) systems with disturbances and input saturation (IS) are studied in this paper. First, by designing an appropriate output feedback, a strictly dissipative PCH system is obtained and finite-time stabilization result for nominal system is given. Second, with the help of the Hamilton function method and truncation inequality technique, a novel output feedback controller is developed to make the PCH system finite-time stable when IS occurs. Further, a finite-time H∞ controller is designed to attenuate disturbances for PCH systems with IS, and sufficient conditions are presented. Finally, a numerical example and a circuit example are given to reveal the feasibility of the obtained theoretical results.

Control of port-Hamiltonian systems with minimal energy supply

We investigate optimal control of linear port-Hamiltonian systems with control constraints, in which one aims to perform a state transition with minimal energy supply. Decomposing the state space into dissipative and non-dissipative (i.e. conservative) subspaces, we show that the set of reachable states is bounded w.r.t. the dissipative subspace. We prove that the optimal control problem exhibits the turnpike property with respect to the non-dissipative subspace, i.e., for varying initial conditions and time horizons optimal state trajectories evolve close to the conservative subspace most of the time. We analyze the corresponding steady-state optimization problem and prove that all optimal steady states lie in the non-dissipative subspace. We conclude this paper by illustrating these results by a numerical example from mechanics.

PASSIVITY-BASED CONTROL SYSTEM FOR STAND-ALONE HYBRID ELECTROGENERATING COMPLEX

The desire for energy independence presupposes the use of various types of elements for energy generation from renewable sources, for the stand-alone operation of which energy storage devices are required. Apower generation complex created in this way must perform a number of tasks that are formed by the energy management system. The control system performs these tasks and ensures proper static and dynamic characteristics of this complex with many inputs and outputs. The results of recent world researches, as well as the authors experience of this work, show that,for creating such control systems, it is advisable to use Passive-Based Control (PBC), presenting the control object as a Port-Controlled Hamiltonian (PCH) system. Thanks to the developed method of additional interconnections and damping injection (Interconnection & Damping Assignment -IDA) passive control provides ample opportunities to adjust the control effects, while ensuring the asymptotic stability of the system as a whole. This is particularly useful in the complex system considered in this paper that includes both a hybrid power plant for electricity generation from the sun and windanda hybrid energystorage unit consisting of the battery and supercapacitor module. This article shows the procedure of PBCsystem synthesis, according to which three structures of control influence formers (CIF) were designed and investigated. These structures have different combinations of additional interconnections and damping, which allows forming the desired energy flows inside the closed-loop systemand therefore provide desired control results.Among them, there are tasks of maintaining voltages on the DC bus and the supercapacitor module at referencelevels, and the smoothness of the battery current transients.A comparative simulation studies were performed on a computer model of the power generation complex with synthesized control systems, whichwas created in the MATLAB/Simulink environment. It showed the efficiency of their work and the advantages of different CIF structures.

Structural identifiability of linear Port Hamiltonian systems

This paper, puts in discussion the structural identifiability of LTI Port-Controlled Hamiltonian (PCH) systems, in order to develop a specific identification and control theory. This is due to their remarkable properties of power conservation and stability under power preserving interconnection. The main part of the paper, presents a power based identifiability approach, with specific propositions and definitions. It is based on the power knowledge associated with the system ports, interconnected by a Dirac structure, for selected input signals. In a preliminary section, corresponding transfer functions, system outputs, Markov parameters, observability conditions, port-observability or infinite Grammians are defined for each port. Beside this, a port-identifiability concept is introduced for the identifiability analysis of one port. It is proved that between the input and system ports, a specific model can be determined for identification analysis, preserving in the same time the PCH structure. As examples to demonstrate the theory, a controlled LC circuit and a DC motor are selected for the lossless and lossy cases, respectively.

Observer Design for a Class of Nonlinear Hamiltonian Systems

In this paper, the observer design problem for Port-Controlled Hamiltonian systems is approached. It is considered a particular class of these systems and a full-order order observer is proposed which belongs to the Structure Preserving approach since it is a copy of the original system with an output corrective term. Concerning the class of systems, it corresponds to nonlinear systems that exhibit nonlinearities given by the products between components of the state vector. The fact that this kind of behavior corresponds to a special property of the interconnection matrix is exploited to obtain a representation for the estimation error dynamics that is suitable to formally state the convergence properties of the observer. The usefulness of the contribution is illustrated by solving the speed observation problem for a Permanent Magnet Synchronous Motor.

Interconnection structure preservation design for a type of port‐controlled hamiltonian systems—A parametric approach

It is a very important issue to minimise the change of the interconnect structure matrix when stabilising a port-controlled Hamiltonian (PCH) system. Toward this problem, a parametric design method is proposed in this paper for a type of PCH systems. First, concepts of H-damping-assignable and H-damping-assigning controller are introduced, and the stability of the closed-loop system resulting from this type of controller is discussed. Secondly, a necessary and sufficient condition for the system to be H-damping-assignable is given, and, when this condition is met, a parametric general expression of all the H-damping-assigning controllers is obtained. Thirdly, the free parameters are optimised to minimize the change of the interconnect structure matrix and also the norm of the control gain matrix. The parameter optimisation is formulated as a standard quadratic programming problem, to which analytical solutions are obtained. Finally, comparative simulations are carried out for a numerical example to verify the effect and the superiority of the proposed method.

IMPROVED STRUCTURE OF PASSIVITY-BASED CONTROL OF BATTERY-SUPERCAPACITOR HUBRID ENERGY STORAGE SYSTEM

Energy storage systems are a topical modern area of research due to the rapid development of renewable energy and electric vehicle construction. Due to the current lack of a source or accumulator of electricity with high specific energy and power, it is being replaced by hybrid electricity storage systems, which consist of separate, complementary sources. Among them, the combination of electrochemical battery – supercapacitor bank is the most common. The paper considers its active configuration, in which both sources are connected to the output network through bidirectional pulse DC-DC converters. The studied hybrid battery-supercapacitor system is a nonlinear dynamic system with multiple inputs, multiple outputs, and two control channels, the operation of which is described by five differential equations. To solve the problem of synthesis of a stable and efficient control system for such an object, the energy approach, namely energy-shaping control has been used. To do this, the studied system is mathematically described as Port-Controlled Hamiltonian system, and two descriptions are compared with different options for choosing the basic vector of the system state. The structural synthesis of the passive control system was performed by the Interconnection and Damping Assignment method. Based on the energy management strategy developed for the system under study, all possible options for introducing interconnections and damping into the passive control system were explored using a computer program developed in the MathCad environment. The effectiveness of the obtained structures of control influence formers on the investigated dynamic system was studied by computer simulation in the Matlab/Simulink environment. According to the results of the research, the variant of control influence former with the best combination of introduced interconnections and damping is formed according to the principle of superposition. To stabilize the voltage values of the output network and the supercapacitor unit set by the control strategy, a proportional-integrated voltage regulator is additionally used, and a sliding regulator between two passive control structures is exploited to limit the allowable battery current. The results of the computer simulation showed the full implementation of the tasks ofthe energy management strategy, including a smooth increase and limitation of the battery current.

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.