Port-controlled Hamiltonian Research Articles

Finite-time robust control for transformerless H-bridge cascaded STATCOM with star configuration

This article presents a finite-time robust control (FTRC) of a transformerless STATCOM based on a cascaded multilevel H-bridge converter (CMHC) with star configuration. The FTRC is first proposed for the current loop control of a CMHC-based transformerless STATCOM by using the finite time robust control theory. Taking the parameters, perturbations and external disturbances into account and using coordinate transformation method, the nonlinear dynamic model of the CMHC-based transformerless STATCOM is transformed into a standard nonlinear port-controlled dissipative Hamiltonian (PCDH) structure. Based on the PCDH structure, an FTRC is designed for the CMHC-based transformerless STATCOM to improve the transient stability and oscillation damping of power system. Finally, the simulation results demonstrate that the FTRC has better dynamic performance and strong robustness in comparison with the passivity-based control of the CMHC-based transformerless STATCOM.

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.

Output feedback based simultaneous stabilization of two Port-controlled Hamiltonian systems with disturbances

In motor system control design, a single controller is usually employed to simultaneously control two or more motors for saving costs, which also achieves the computational simplification of control. In practical Hamiltonian systems control, more systems also need to be stabilized by a single controller under some working conditions. Thus, this paper studies simultaneous stabilization problem of two nonlinear Port-controlled Hamiltonian (PCH) systems with disturbances by a composite controller. Based on the Hamiltonian structure properties, two PCH systems are combined together to generate an augmented PCH system by utilizing output feedbacks firstly. Then, to estimate disturbances effectively, it is essential to design a nonlinear disturbance observer (NDOB) and the estimate is employed to feedforward compensate the effects of disturbances. Next, combining the output feedback part and the disturbance compensation part together, a simultaneous stabilization controller is developed. Subsequently, it is proved that the closed-loop system under the proposed controller is asymptotically stable. Finally, an example with simulations reveals that the proposed method is effective.

PCDH-based nonlinear H ∞ control of VSC-HVDC with wind power integrated

Based on the port-controlled dissipative Hamiltonian (PCDH) system, a novel nonlinear (NN) control is designed for the wind farm side (WFS) voltage source converter (VSC) of VSC-based high-voltage direct current (VSC-HVDC) transmission system connected large wind farm. Firstly, the uncertain nonlinear dynamical model of WFS VSC in the VSC-HVDC is established by taking external disturbances and parameter variations into account. Then, the dissipative Hamiltonian structure of the WFS VSC system is constructed by means of variable transformation. Thirdly, on the basis of the obtained dissipative Hamiltonian structure, a NN control is put forward. Finally, the simulation results show that the proposed NN control gains the advantage over the interconnection and damping assignment passivity-based (IDA-PB) control.

Stabilization via output feedback for a type of uncertain time-varying port-controlled Hamiltonian system based on linear matrix inequality approach

In this paper, the control of a type of uncertain time-varying port-controlled Hamiltonian (PCH) systems is investigated. As a matter of fact, the control method proposed in this paper is not based on passivity of PCH systems, but a general output equation is introduced inspired by the measured “information” in the systems in traditional control system theory and the problem of output feedback is considered. In this paper, a conception of p-quadratic stability of the type of PCH system is introduced, and the relationship between p-quadratic stability and Lyapunov stability is pointed out. Then, the problem for p-quadratic stabilization of the proposed system via static output feedback is solved in the following two cases, respectively. For the case of unperturbed output equation, a necessary and sufficient condition for the problem is derived in terms of two groups of linear matrix inequalities (LMIs); for the general case that the output equation also has time-varying perturbations, a sufficient condition for p-quadratic stable of closed-loop system is also given in terms of LMIs. It is also shown that conservatism can be greatly reduced when the perturbation variables in the uncertain PCH systems are restricted to vary within certain intervals. Finally, a numerical example is proposed in the end followed by a simulation to verify the effectiveness of the method proposed in this paper.

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.

Finite-time stability and stabilization of nonlinear singular time-delay systems via Hamiltonian method

This paper investigates the finite-time stability (FTS) and finite-time stabilization for a class of nonlinear singular time-delay Hamiltonian systems, and proposes a number of new results on these issues. Firstly, an equivalent form is obtained for the nonlinear singular time-delay Hamiltonian systems by the singular matrix decomposition method, based on which some delay-independent and delay-dependent conditions on the FTS are derived for the systems by constructing a kind of novel Lyapunov function. Secondly, we use the equivalent form as well as the energy shaping plus damping injection technique to investigate the finite-time stabilization problem for a class of nonlinear singular port-controlled Hamiltonian (PCH) systems with time delay, and present a specific control design procedure for the systems. Finally, we give several illustrative examples to show the effectiveness of the results obtained in this paper.

Robust $${{\cal H}_\infty}$$ Control for Switched Nonlinear Port-controlled Hamiltonian Systems

In the paper, the robust $${{\cal H}_\infty}$$ control for switched nonlinear port-controlled Hamiltonian (SNPCH) systems with external disturbances is investigated via the multiple Lyapunov functions method. Under two cases that the SNPCH system is subject to actuator saturation (AS) and the SNPCH system is without AS, a design approach for the switching robust $${{\cal H}_\infty}$$ feedback controller is developed to attenuate the external disturbances. The sufficient conditions are established for $${{\cal H}_\infty}$$ control of the corresponding closed-loop systems based on Hamilton-Jacobi inequality techniques. Furthermore, via the Hamiltonian realization method, the obtained results are applied to solve the $${{\cal H}_\infty}$$ control for switched nonlinear affine systems with external disturbances. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed $${{\cal H}_\infty}$$ control methods.

Stability analysis and control design based on average dwell time approaches for switched nonlinear port-controlled Hamiltonian systems

This paper addresses the problems of the stability, stabilization and H∞ control for switched port-controlled Hamiltonian (SPCH) systems. For unforced SPCH systems, via energy-based multiple Lyapunov functions methods, sufficient conditions of both exponential stability and asymptotical stability are obtained under arbitrary switching signals with an average dwell time scheme. Then, based on the state feedback, a switching controller is designed to stabilize SPCH systems, and a switching H∞ controller is presented to attenuate the external disturbances for SPCH systems, while SPCH systems are subject to actuator saturation, the stabilization and H∞ control are investigated and the truncation-inequality method is employed to deal with the saturation. Finally, two numerical simulation examples are provided to verify the effectiveness of the proposed methods.

A hybrid coordination controller for speed and heading control of underactuated unmanned surface vehicles system

The speed and heading control problem of an underactuated unmanned surface vehicle (USV) has been studied in this paper. The thrust system consists of two propellers which are driven by two electric-powered motors. A hybrid coordination control strategy based on signal and energy method is proposed. The energy controller uses the Port-Controlled Hamiltonian (PCH) control approach, and the signal controller uses the Lyapunov's direct method and backstepping approach. The design of coordination control strategy is used to adjust the strength of the signal controller and energy controller. Simulation results confirm the validity and stability of control algorithm, and the results show that the proposed algorithm can quickly track signals with energy optimization.

Circulating current reduction of a grid-connected parallel interleaved converter using energy shaping control

This paper proposes a method to control low frequency circulating currents generated in parallel interleaved converters. In this configuration, inverters are parallelized using magnetically linked inductors. Generally, to improve the harmonic content of the output voltage, carrier interleaving is used. This results in a higher circulating current (differential mode current) to flow through the two Voltage Source Converters (VSCs). High frequency components of circulating currents are efficiently reduced by the mutual inductance of the Coupled Inductors (CI). However, CI cannot efficiently filter the low frequency components. When the uncontrolled circulating currents become too high; they lead to CI saturation, higher switching losses, and degrade the overall performances of the converter. Therefore, this paper presents a global control strategy for a grid-connected parallel interleaved converter based on the concept of Port Controlled Hamiltonian (PCH). With this controller, active and reactive powers delivered to the grid are efficiently controlled. In addition, the controller considerably reduces the value of the low frequency circulating current. Converter performances are evaluated by simulation and compared with the classical PI control and the Linear Quadratic (LQ) control. An experimental setup was developed to verify the feasibility of the proposed system. Results obtained from experiments show a good agreement with the simulation, confirming the performances of the proposed method.

A Novel Speed Control Method Based on Port-Controlled Hamiltonian and Disturbance Observer for PMSM Drives

This paper is mainly focusing on the problem of speed tracking control for permanent magnet synchronous motor (PMSM) drive system subject to matched and mismatched disturbance. This is achieved by a novel Port-Controlled Hamiltonian control method with nonlinear disturbance observer. Different from the traditional speed-current cascade control for PMSM, the speed-current single loop controller is designed. Firstly, the Port-Controlled Hamiltonian model of PMSM is established, then the Hamiltonian speed controller is designed by using interconnection assignment and damping assignment method. However, the standard Hamiltonian controller cannot achieve the satisfying behavior in the presence of the parameter variations and external disturbance, thus a nonlinear disturbance observer is designed to estimate the lump disturbance of the system, which is used to the feed-forward compensation control. Finally, simulation and experiment on the speed control system of PMSM are implemented. The results show that the proposed method has fast speed control performance and strong robustness for the different disturbance.

An Accurate Forced Oscillation Location and Participation Assessment Method for DFIG Wind Turbine

With the integration of wind energy, the widely used doubly fed induction generator wind turbines (DFIG-WT) could induce Power System forced oscillations (FOs), which threaten the safety of power grid. In this paper, an accurate FOs location method is proposed to pinpoint sources of FOs to the specific components inside a DFIG-WT and a participation assessment method is proposed to evaluate the role of DFIG-WTs in the FOs event. Firstly, the energy structure of the DFIG-WT is constructed and the correspondence between the physical components and energy structure of the DFIG-WT is established. Thus, the sources of FOs can be located by the energy flow among the converter, wind turbine and induction generator. Furthermore, the port-controlled Hamiltonian (PCH) method is used to analyze the influence of external disturbances to the potential energy of DFIG-WT, based on which the participation factor of the DFIG-WT in FOs event can be defined. The simulation results demonstrate that the proposed method is able to locate the oscillation sources accurately and reveal the participation of the DFIG-WT in FOs events effectively.

Interconnection and Damping Assignment Passivity for the Control of PV/Battery Hybrid Power Source in Islanded Microgrid

This work proposes an Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) to enhance power quality of an islanded Micro-grid (MG) including a photovoltaic main source (PV) and a Li-ion battery based Energy Storage System (ESS). In this MG, the PV generator-unit is controlled to provide its maximum power and the ESS-unit is controlled to ensure the desired voltage waveform at the Point of Common Coupling (PCC) and to support the PV source in order to satisfy the local loads. The IDA-PBC approach is chosen for its proprieties which allow the synthesis of asymptotically stable controllers for passive systems by the mean of the power system energy. In fact, the damping and interconnection coupling matrices of the IDA-PBC controller allows additional degree of freedoms in comparison to classical passivity controllers that enhance the convergence rapidity and the robustness under uncertainties. The mathematical model of the PV source and the Li-ion battery based ESS are presented. The power interface circuits are firstly represented through Park-coordinates then expressed in a Port-Controlled Hamiltonian (PCH) form. The obtained models are used to the design of the proposed IDA-PBC controller where the stability conditions are checked. The proposed control validity and performance are verified through comparison simulation tests with a conventional Proportional-Integral (PI) based control strategy. The obtained results show that the proposed control algorithm allows reducing the current and voltage overshoots under transient’s conditions in comparison to the PI controller. Furthermore, the proposed control achieves better voltage waveform at the PCC in steady state.

Energy-based Hamiltonian approach in H∞ controller design for n-degree of freedom mechanical systems

This paper studies the energy-based approach for controller design of -degree of freedom mechanical systems. In this approach, the Hamiltonian function, which is the sum of kinetic and potential energies of the system, is considered as the Lyapunov function for stability analysis. The stability analysis is done based on the port-controlled Hamiltonian (PCH) model. In this regard, two theorems are given and proved that the proposed controllers lead to disturbance attenuation for both absolutely known system model and unknown ones with parametric uncertainties. In the case of parametric uncertainties, the energy-based controller has an adaptive approach. Performance of proposed controllers is illustrated through simulations taken on a 2-link robot manipulator system, which validate the theoretical achievements of this paper.

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.

A novel superconducting magnetic energy storage system design based on a three-level T-type converter and its energy-shaping control strategy

Superconducting magnetic energy storage (SMES) has been widely used to stabilize the power fluctuations of wind farms to achieve efficient grid connections. However, conventional converters can rarely satisfy the high power quality requirements of a power grid. Compared to other convertors, a three-level T-type converter (3LT2C) can improve the output performance and operating efficiency of a system and reduce the voltage stress and conduction loss of power switches. Therefore, the 3LT2C has broad application prospects for electric power storage. A precise control strategy is also necessary for the practical application of an SMES system, which has significant nonlinear dynamic characteristics. Energy-shaping (ES) control is a nonlinear control method that is based on the theoretical design of interconnection and damping assignment (IDA), which considers both the nonlinear nature of a system and the energy perspective. This study proposes an ES control strategy for an SMES system based on a 3LT2C. Mathematical models and port-controlled Hamiltonian (PCH) models of the SMES are established. The ES control strategy of the SMES system is designed based on a feedback interconnection structure through analysis of the novel SMES topology. Finally, the effectiveness of the control strategy and the proposed topology are verified through simulations.

Interconnection and damping assignment automatic voltage regulator for synchronous generators

In this paper a new nonlinear regulation for synchronous generator excitation control is presented. This method comprises the nonlinear Interconnection and Damping Assignment (IDA) method together with the generator voltage feedback giving a nonlinear Automatic Voltage Regulator (AVR). First, the IDA excitation control is introduced in the third order salient pole synchronous generator mathematical model represented as a Port Controlled Hamiltonian (PCH) system. Thereafter, a generator voltage feedback signal is added. It is proven that adding the feedback to IDA control preserves a PCH structure of a system and the system is therefore passive. In the paper it is also proven that the gained system is stable and that the reference operating point corresponds to the minimal energy point of the system. Finally, the gained IDA AVR is tested with seventh order synchronous generator model and compared to classical generator excitation controllers. The simulations show the efficient tracking of generator voltage reference value, as well as the maintenance of stability in case of grid-side short-circuit occurrence. The main advantages of the proposed controller are efficiently generator voltage tracking and attenuation of electromechanical oscillations in case of a large disturbance, such as grid-side short-circuit.

Hybrid Tracking Control of 2-DOF SCARA Robot via Port-Controlled Hamiltonian and Backstepping

In this paper, we propose a hybrid coordinated control method based on port-controlled Hamiltonian and backstepping to improve the position tracking performance for two degree of freedom SCARA robot. The port-controlled Hamiltonian (PCH) control is designated to ensure the stability of the system, and the backstepping control targets to improve the response speed of the system. Exponential function is used as a coordination function to achieve the coordinated control strategy to adapt to the position tracking control of 2-DOF SCARA robot. This hybrid coordination control system not only realizes a quick tracking control, but also improves the steady-state performance of the output signal. The simulation results show that when the external interference exists in the mechanical system of a 2-DOF SCARA robot, the hybrid tracking control system takes on the advantages of both methods, which shows good dynamic performance, good steady-state performance, and strong resistance to external interference.

Port-Controlled Hamiltonian and Sliding Mode Control of Gantry Robot Based on Induction Motor Drives

A port-controlled Hamiltonian (PCH) control approach is presented to solve the position tracking problem of gantry robot based on induction motor (IM) drives. First, a robot model is established. Second, a PCH controller is designed to realize accurate position tracking of a gantry robot. For IM drives, it is convenient to choose a direct torque control strategy based on the sliding mode control, which overcomes the higher ripples of torque and flux. Third, a voltage reconstruction technique is introduced to calculate the stator voltage of the IM, which replaces the stator voltage measurement of the IM. Finally, the load torque observer is developed to estimate an unknown load torque. The asymptotic stability of the robot system is proved by the Lyapunov stability theory. Simulation results indicate that the system has excellent position tracking performances and load disturbance attenuation ability.