Passivity-based Control Method Research Articles

Port-Hamiltonian modeling and jumping trajectory tracking control for a bio-inspired quadruped robot

Applying jumping locomotion into autonomous mobile robot is an effective way for improving abilities to overcome barriers and pass through complex terrains. In this paper, based on the designed structural framework for bio-inspired quadruped jumping robot, dynamic model is established by utilizing port-Hamiltonian with dissipation (pHd) method, and a passivity-based control strategy for the robot joints trajectory tracking is presented. First, morphology and biomimetics knowledges of frogs (a kind of animals with excellent jumping skill) motivate us to complete a bio-inspired jumping robot framework based on frog’s motion mechanism and body structure with torsional springs as energy storage device. Then, combining system passivity and dissipation, port-Hamiltonian method is utilized to build a dynamic model for expressing the relationship of energy and force in the designed robot. Jumping process analysis of different stages is also designed for ensuring the robot to complete taking-off and landing stages successfully. Next, with the definition of extending feasible robotic joint trajectory by La Salle invariant set principle, interconnection and damping assignment passivity-based control (IDA-PBC) method is exerted to obtain a trajectory controller for realizing smoothly and stably trajectory tracking in joint space. At last, simulation results show the reasonableness of the designed framework. By comparing our method with state-feedback and sliding mode control, effectiveness of the dynamic model and trajectory controller is also verified.

Mode decomposed passivity-based speed control of DC drive with bidirectional Zeta-SEPIC DC-DC converter for light electric vehicles

Currently, light electric vehicles are rapidly developing in various kinds. To power these vehicles with batteries, the simplest electric drive system is a DC motor controlled by a DC-DC converter. This work utilizes a bidirectional Zeta-SEPIC DC-DC converter with an integrated DC motor. This implementation enables control of motor speed and torque in traction and regenerative braking modes. Additionally, it allows for the use of a lower voltage battery compared to the motor's rated voltage, reducing battery weight and increasing safety. In this work, a decomposition approach is applied. Two separate port-controlled Hamiltonian subsystems are obtained to adjust the motor angular velocity in the traction (Zeta) and braking (SEPIC) modes of the DC-DC converter. The Passivity-Based Control (PBC) method is used to synthesize the drive control subsystems in these modes. This method is based on the energy laws of processes in systems and provides asymptotic stability of nonlinear systems, in this case, two fourth-order subsystems for speed control. Two third-order current control subsystems synthesized by the PBC were used to limit the motor current at a given level. The synthesis resulted in sets of possible structures of control influence formers (CIFs) for all PBC subsystems using Zeta and SEPIC DC-DC converters. The study analyzed the operation of the obtained structures of the CIFs, selected the most effective ones, and determined the laws of adaptation of their parameters to the value of the motor angular velocity through computer simulation in Matlab/Simulink. The results of the simulation showed that the drive operated well in both static and dynamic modes.

Research on strategy of load-side resonant soft-switching inverter based on interconnection and damping assignment-passivity based control

Soft-switching technologies can effectively solve the problem of switching losses caused by increasing switching frequency of grid-connected inverters. As a branch of soft-switching technologies, load-side resonant soft-switching is a hotspot for applications of high-frequency inverters, because it has the advantage of achieving soft-switching without using additional components. However, the traditional PI control strategy based on the linear model is prone to destabilization and non-robust dynamic performance when large signal perturbation occurs. In this paper, a novel Passivity-Based Control (PBC) method is proposed to improve the dynamic performance of load-side resonant soft-switching grid-connected inverter. Besides, the model based on the Port Controlled Hamiltonian (PCH) model of the soft switching inverter is carried out, and the passivity-based controller is designed based on the established model using the way of interconnection and damping assignmentpassivity based control (IDA-PBC). Both stable performance and dynamic performance of the load-side resonant soft-switching inverter can be improved over the whole operating range. Finally, a 750 W load-side resonant soft-switching inverter simulation model is built and the output performance is compared with the traditional PI control strategy under stable and dynamic conditions. The simulation results show that the proposed control strategy reduces the harmonic distortion rate and improves the quality of the output waveforms.

Robust passivity-based nonlinear controller design for bilateral teleoperation system under variable time delay and variable load disturbance

Abstract This research focuses on implementing a robust passivity-based nonlinear control method for bilateral/teleoperation systems. The key challenge is addressing communication pathways between the master and slave, control delays, and load disturbances, which can lead to instability and reduced transparency. To tackle these issues, the proposed controller incorporates a second-order super-twisting sliding-mode observer to counteract communication and control delays. A sliding mode assist disturbance observer compensates for load torque variations. The approach aims to ensure stability and transparency by handling time-varying delays. The system model comprises two interconnected direct-drive motors, simulating robotic configurations without a physical robot. The nonlinear controller framework simplifies the complex bilateral control problem, significantly improving stability and transparency performance. Computer simulations with step and sinusoidal inputs demonstrate the effectiveness of the approach, providing a satisfactory level of accuracy and transparency between estimated and actual slave positions, even with varying delays and load variations. The research contributes to control engineering by offering a robust method to enhance bilateral system performance, ensuring stable and transparent communication between the master and slave, particularly suitable for real-time internet-based bilateral control systems.

Passivity-Based Trajectory Tracking and Formation Control of Nonholonomic Wheeled Robots Without Velocity Measurements

This note proposes a passivity-based control method for trajectory tracking and formation control of nonholonomic wheeled robots without velocity measurements. Coordinate transformations are used to incorporate the nonholonomic constraints, which are then avoided by controlling the front end of the robot rather than the center of the wheel axle into the differential equations. Starting from the passivity-based coordination design, the control goals are achieved via an internal controller for velocity tracking and heading control and an external controller for formation in the port-Hamiltonian framework. This approach endows the resulting controller with a physical interpretation. To avoid unavailable velocity measurements or unreliable velocity estimations, we derive the distributed control law with only position measurements by introducing a dynamic extension. In addition, we prove that our approach is suitable not only for acyclic graphs but also for a class of non-acyclic graphs, namely, ring graphs. Simulations are provided to illustrate the effectiveness of the approach.

An Adaptive Controller Based on Interconnection and Damping Assignment Passivity-Based Control for Underactuated Mechanical Systems: Application to the Ball and Beam System

In this paper, an adaptive technology and the interconnection and damping assignment passivity-based control method are combined to solve the stabilization problem for underactuated mechanical systems with uncertainties (including matched and unmatched). These uncertainties include unknown friction coefficients and unknown terms in kinetic energy and potential energy. A novel adaptive interconnection and damping assignment passivity-based control scheme is proposed and an adaptive stabilization controller is designed to make the closed-loop system locally stable. Verification is conducted on the ball and beam system. The locally asymptotic stability is demonstrated using the LaSalle’s invariance principle and approximate linearization. The effectiveness of the proposed control law is verified through numerical simulations.

Passivity-Based Control Method for Three-Level Photovoltaic Inverter to Mitigate Common-Mode Resonant Current

In transformerless three-level photovoltaic inverter systems, the modified LC filter, which directly connects the dc-side neutral point to the common point of filter capacitors, is considered to be an ideal scheme to suppress the troublesome leakage current. However, a new common-mode (CM) resonant current is emerged, which leads to inverter-side current distortion and even system instability. Therefore, a second-order passivity-based controller in time domain featuring with excellent system stability is proposed for the CM resonant current mitigation. First, the reason of CM resonant current generation with the modified LC filter is analysed in detail. Then, the CM current model is derived, which reveals that it is a second-order system. The passivity of this second-order model is strictly proved. Moreover, based on the passive control theory, zero state detectable theory and Lyapunov stability theorem, a second-order passivity-based controller is designed step by step to suppress the CM resonant current, and the system global asymptotic stability is also proved. The proposed controller is based on time domain, which is more intuitive and avoids the error amplification in the conversion from frequency domain to time domain. Finally, the effectiveness and the correctness of theoretical derivation of the passivity-based control method are validated by experiments. Compared with passive damping resistor method, the proposed method not only has better performance, but also avoids the use of real resistor and reduces the cost by using software instead of hardware.

A new robust SIDA-PBC approach to control a DFIG

Credible control and overall stabilization of closed-loop nonlinear systems presented in a port-controlled hamiltonian structure (PCH-D) were forever the development of the simultaneous interconnection and damping assignment passivity-based control (SIDA-PBC) method. The robustness and reliability of the method called into question against noise and certainly modelling errors. Indeed, a new scheme has been presented to control a doubly fed induction generator (DFIG) based on the energy form and exploiting the electrical parameters of the closed loop system. The results obtained provide a new technique and implement more freedom when designing the diagram of the advanced controller during the production of active power. The contribution of this paper is researching on the advanced nonlinear methodes used, many simulations were carried out in simulation using the MATLAB/Simulink environment under important operating conditions, allowing to demonstrate the feasibility of the proposed method and verify the performance considering the robustness.

Modified passivity-based control method for three-phase cascaded unidirectional multilevel converters

Modified passivity-based control method for three-phase cascaded unidirectional multilevel converters

Non-Linear Control of Fuel Cell/Ultra-Capacitor Hybrid Electric Vehicle Using Comprehensive Function Algorithm Based on IDA-PBC

Hybrid electric vehicles (HEVs) have become increasingly popular due to their high fuel economy performance and low greenhouse gas emissions. HEVs that use fuel cells produce fewer emissions and are more efficient than many other types of cars. Accordingly, many researchers are significantly interested in applying a combination of the fuel cell (FC) and the ultra-capacitor (UC) for HEVs. This study proposes a method for improving the control of an FC/UC hybrid electric vehicle, also analyzing its performance. In the HEV used, the fuel cell provides the main power, but in transient situations where the FC cannot support the vehicle alone, the UC gives the stored energy to the system to solve the energy deficiency. In this study, the interconnection and damping assignment passivity-based control (IDA-PBC) method is applied and regulates the system performance under nonlinear operation. In addition, a comprehensive energy management strategy proposes to cover all driving cycle situations. The main control objective is to keep the system voltage within an acceptable range despite the appropriate dynamic behavior. To increase the accuracy of the results, in system structure modeling, energy losses are considered. In the case study part, a standard Japanese driving cycle (SJDC) uses, which comprises different practical conditions such as off-load, overload, uphill, and downhill. The simulation results using MATLAB/Simulink show the effectiveness of the proposed algorithm and control method.

A control-theoretic approach for input saturated linear systems: Integration of phase-shaping and gain-scheduling

Saturation is mainly characterized by its passivity and magnitude bound. But most of the saturation control methods only make use of either of these features. To enhance the performance of saturated systems, this paper develops a novel method capable of fully using both of these two features. This method is a two-stage design scheme which integrates the phase-shaping technique with the gain-scheduled control. The phase-shaping fully uses the passivity of saturation while the gain-scheduling actively utilizes the magnitude bound of saturation. In this way, the design conservatism associated with existing methods is reduced substantially. Specifically, a matrix-type phase-shaping method is developed through the placement of systems’ frequency loci, and a meta-heuristic method is devised for the design of the phase-shaping function. Furthermore, the gain-scheduled control is transformed into the robust performance problem of a passive uncertain system, and designed by the passivity-based robust control method of the authors. Application to two practical control systems validates the effectiveness of the proposed method. The superiority is demonstrated via comparisons with typical saturation control methods.

Modified Passivity-Based Control for LCL-Filtered Grid-Tied Inverter with Output Admittance Reshaping

As a nonlinear control method, the Euler–Lagrange- (EL-) based passivity-based control (PBC) has been studied for grid-tied converters based on energy function to achieve better performance. However, the EL-based PBC method is dependent on an accurate mathematical model. In the traditional EL-based PBC research for LCL-filtered grid-tied inverter, the effect of the digital control delay is rarely considered and the stability under the grid impedance uncertainties is not discussed, especially in the capacitive grid or complex weak grid. To address these concerns, this study proposes a modified EL-based PBC method based on the output admittance reshaping for LCL-filtered grid-tied inverters. The system’ passive region is expanded by adding capacitor current feedback loop up to the Nyquist frequency. The potential resonance is thus eliminated irrespective of the grid impedance. Additionally, the stable region and control parameters design methods of the modified EL-based PBC method with inverter-side control are also carried out. To verify the correctness of the theoretical analysis, both simulation and experimental results are investigated from a 3 kW grid-tied inverter prototype.

An Optimized Coil Array and Passivity-Based Control for Receiving Side Multilevel Connected DC-DC Converter of Dynamic Wireless Charging

Dynamic wireless charging (DWC) is one of the most promising and economical power supply solutions for electric vehicles (EVs), which can address range anxiety and downsize the volume of onboard batteries. To solve the null power phenomenon and transfer power pulsation phenomenon in DWC scheme, this paper proposes a new magnetic coupler array to implement continuous charging and reduce the output power variation. The transmitters are placed with a proper interval to eliminate the adjacent coupling and enlarge the coil array&#x2019;s effective length. ANSYS Maxwell is utilized to demonstrate the finite element analysis (FEA) of the DWC system. A larger receiver coil is designed to significantly mitigate power pulsation and increase the magnetic coupling as the receiver moves along the array. With the well-designed receiver coil, the output power pulsation is <inline-formula><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 1.52<inline-formula><tex-math notation="LaTeX">$\%$</tex-math></inline-formula>. For the high-power capacity scenario, a multilevel connected DC-DC converter is designed on the receiver side to regulate the transfer power. Besides, a passivity-based control (PBC) is developed for the receiving DC-DC converter based on the Euler-Lagrange (EL) model, and a current sharing compensator is employed to balance each phase inductor current. Finally, a 500-<inline-formula><tex-math notation="LaTeX">$\text{W}$</tex-math></inline-formula> prototype is constructed, and experimental results are represented to validate the proposed optimized coil array and the proposed PBC method.

Analysis and design of photovoltaic three-phase grid-connected inverter using passivity-based control

This paper presents photovoltaic three-phase grid-connected inverter with an inductor-capacitor-inductor (LCL)-filter. For robustness against variation of filter parameters and external disturbance, the passivity-based control (PBC) method has been adopted. In this method, there are two interactively coupled feedforward terms and three damping gains in the control loops which are designed to limit the steady state error of grid current. Boost converter with P&amp;amp;O maximum power point tracker (MPPT) is used for each photovoltaic (PV) string to extract maximum power and to raise the PV voltage to a value suitable for the grid-connected inverter. The outputs of all boost converters are connected in parallel and controlled to fixed reference voltage using proportional-integral (PI) controller to make the direct-current (DC) link voltage robust against variations in sun radiation intensity and system parameters change. The suggested system is analyzed, designed and simulated using PSIM program. 1 kW, 2kW, and 3kW PV systems connected to grid of 220V/50Hz are tested and the results show the validity of the suggested grid-connected PV systems and robustness against filter parameters variation.

An Improved Three-Level Cascaded Control for LCL-Filtered Grid-Connected Inverter in Complex Grid Impedance Condition

The passivity-based control (PBC) with Euler&#x2013;Lagrange (EL) model has been used for LCL-filtered grid-connected converter. However, the impacts of the control delay and the interaction resonances under capacitive grid impedance are rarely considered for PBC method. Nonlinear Lyapunov&#x2019;s stability theory is hard to estimate the stability of the system and accurately design the controller parameters considering the control delay. This paper derived the impedance model of LCL-filtered grid-connected inverter with grid current control based on PBC method. The passive theory and the zero-pole maps are applied to reveal the influence of the digital delay and differential item of inverter current loop. A new three-level cascaded control method is then proposed based on traditional PBC method to achieve stability and high robustness in complex grid. Furthermore, controller parameters are designed accurately to maintain passivity within switching frequency ranges and parameter variations of the LCL filter are investigated. Final validation of the effectiveness and performance of the proposed control structure is performed by simulation and experimentation.

An improved IDA-PBC method with link-side damping injection and online gravity compensation for series elastic actuator

Elastic elements in series elastic actuator (SEA) will cause residual vibration in position control. Incorporating link-side damping injection and friction compensation, we propose an improved interconnection and damping assignment passivity-based control (IDA-PBC+) method to suppress residual vibration. Damping on the motor side and link side can be adjusted simultaneously. In addition, the desired motor-side trajectory planning and online gravity compensation are also introduced to improve control performance and steady-state accuracy. The effectiveness of the proposed method in suppressing residual vibration is experimentally verified with a two-degree-of-freedom SEA device.

Passivity-based adaptive trajectory control of an underactuated 3-DOF overhead crane

This paper presents a robust passivity-based adaptive control method for payload trajectory tracking of a three degree-of-freedom overhead crane with a varying-length rigid hoist cable. A reformulation of the overhead crane’s equations of motion is used and an adaptive control law is developed to ensure the system has an output strictly passive (OSP) input–output mapping. The Passivity Theorem is used to prove that the closed-loop system is input–output stable when an OSP negative feedback controller is implemented. Convergence and boundedness of the payload trajectory tracking error is proven with two candidate OSP feedback controllers, including a constant gain and a strictly positive real (SPR) controller. Numerical simulations and experiments are performed with the proposed control method and two state-of-the-art control laws from the literature. The results demonstrate the practicality of the proposed control method and the improved performance of the proposed SPR controller in the experiments compared to the controllers from the literature.

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.