Proportional Integral Resonant Controller Research Articles

A Proportional-Integral-Resonant Current Control Strategy for a Wind-Driven Brushless Doubly Fed Generator during Network Unbalance

This article proposes a proportional-integral-resonant (PIR) current control strategy for a wind-driven brushless doubly fed generator (WDBDFG) during network unbalance. Firstly, four control objectives of WDBDFG, including eliminating unbalanced currents of power winding (PW), pulsations of control winding (CW) currents, torque, and PW power, are discussed and different from current controls in which the references to PW currents were computed; the CW current references are derived here. Then, an improved CW current controller using a PIR controller is proposed to achieve different control objectives. In contrast with current controls, CW currents are not involved with sequence extraction in the proposed control and can be totally regulated only in a positive synchronous reference frame. Hence, the system control structure is greatly simplified, and dynamic characteristics are improved. Furthermore, in order to obtain completely decoupled control of current and average power, feedforward control, considering all the couplings and perturbances, is also applied in CW current loops. Simulation results for a 2 MW grid-connected WDBDFG show that the proposed control is capable of achieving four control objectives, including canceling CW current distortion, PW current unbalance, pulsations of PW active power or pulsations of reactive power, and machine torque. Its dynamic process is much more smoothly and quickly than that of current controls, and therefore the proposed control has better dynamic control characteristics during network unbalance.

On the rub-impact force, bifurcations analysis, and vibrations control of a nonlinear rotor system controlled by magnetic actuator integrated with PIRC-control algorithm

This article presents the Proportional Integral Resonant Controller (PIRC-controller) as a novel control strategy to suppress the lateral vibrations and eliminate nonlinear bifurcation characteristics of a vertically supported rotor system. The proposed control algorithm is incorporated into the rotor system via an eight-pole electromagnetic actuator. The control strategy is designed such that the control law (PIRC-controller) is employed to generate eight different control currents depending on the air-gap size between the rotor and the electromagnetic poles. Then, the generated electrical currents are utilized to energize the magnetic actuator to apply controllable electromagnetic attractive forces to suppress the undesired lateral vibrations of the considered rotor system. According to the suggested control strategy, the whole system can be represented as a mathematical model using classical mechanics' principle and electromagnetic theory, in which, the rub-impact force between the rotor and the stator is included in the derived model. Then, the obtained discrete dynamical model is analyzed using perturbation techniques and validated numerically through bifurcation diagrams, frequency spectrums, Poincare maps, time responses, and steady-state whirling orbit. The obtained results illustrate that the proposed control algorithm can mitigate the nonlinear vibration and eliminate the catastrophic bifurcations of the rotor system when the control gains are designed optimally. In addition, the system dynamics are analyzed when the rub-impact occurrence between the rotor and the pole housing is unavoidable. The acquired results revealed that the system may perform periodic-1, periodic-n, or quasiperiodic motion with one of two oscillation modes depending on both the impact stiffness coefficient and the dynamic friction coefficient.Article HighlightsNonlinearity dominates the uncontrolled rotor response, where it suffers from the jump phenomenon and multiple solutions.The proposed controller forces the Jeffcott rotor to respond as a linear system with small oscillation amplitudes.The rotor oscillates with full-annular-rub or partial-rub-impact mode when rub-impact occurs between the rotor and stator.

Comparing Different Resonant Control Approaches for Torque Ripple Minimisation in Electric Machines

Electric machines are highly efficient and highly controllable actuators, but they do still suffer from a number of imperfections. One of them is torque ripple, which introduces high frequency harmonics into the motion. One (cost- and performance-neutral) countermeasure is to apply control that counters the torque ripple. This paper compares several single-input single-output (SISO) control approaches for feedback control of torque ripple of a Permanent Magnet Synchronous Machine (PMSM). The baseline is PI (proportional-integral) control, which does not suppress torque ripple, and the most popular control approach is proportional-integral resonant (PIR) control. Both are compared to an advanced PIR controller (PIRA), frequency modulation, a mixed sensitivity design, and an iterative learning controller (ILC). The analysis demonstrates that PIR control, mixed sensitivity state feedback, and the modulating controller achieve identical behaviour. The choice between these three options is therefore dependent on preferences for the design methodology, or on implementation factors. The PIRA and the ILC on the other hand show more sophisticated behaviour that may be advantageous for certain applications, at the expense of higher complexity.

An adaptive proportional-integral-resonant controller for speed ripple suppression of PMSM drive due to current measurement error

An adaptive proportional-integral-resonant (PIR) controller with piecewise phase compensation is proposed to suppress the steady-state speed ripple of permanent magnet synchronous motor (PMSM) drive due to current measurement error. The frequency-varying characteristic of PMSM drive makes the parameters determination of the resonant controller more complicated when considering frequency adaptation. In this paper, after theoretical analysis on the current measurement error, the resonant controller is added in the speed PI loop of the PMSM vector control system, which makes the system more prone to instability. In order to ensure the stability of the system at different speeds, the resonant gain is firstly restricted by root locus method to get a stable system in the full speed range. Then, the resonant gain and the phase angel are further designed to obtain a robust vector margin by Nyquist diagram in different speed ranges. Such piecewise phase compensation method can achieve good stability margin and harmonic suppression ability by making a trade-off between them, avoiding the complicated calculation of the trigonometric functions for compensation in real time. Both steady and transient experiment results indicate that the proposed PIR controller can well restrain the frequency-varying speed ripples caused by current measurement error.

Torque Ripple Suppression of PMSM Using Fractional-Order Vector Resonant and Robust Internal Model Control

Periodic torque ripples caused by current harmonics seriously affect the control accuracy of the Permanent magnet synchronous motors (PMSMs). A conventional approach to reducing current harmonics is the use of a proportional-integral resonant controller in the current loop. Nonetheless, harmonics can still cause steady-state errors. Furthermore, the PI-based control structure is sensitive to parameter mismatches and uncertain disturbances, which will decrease the tracking performance of the current loop. To overcome the drawbacks of the traditional control method, a hybrid robust resonant control strategy was developed in this study. First, a vector resonant controller was enhanced by introducing fractional-order calculus (denoted as the fractional-order vector resonant (FOVR) controller in this article) so that it can suppress harmonic components more effectively. Then, a robust internal mode controller (Robust-IMC) was designed to improve the robustness and dynamic response and further reduce the current harmonics. Finally, by combining the FOVR controller and Robust-IMC, a control method-FOVR-Robust-IMC was designed as the robust control law to ensure satisfactory robustness and harmonics suppression performance. Meanwhile, the stability and robust stability of the developed control strategy were also analyzed. The results demonstrated that the proposed FOVR-Robust-IMC effectively reduced the harmonic components and improved the robustness to parameter mismatch.

Mitigating the Torque Ripple in Electric Traction Using Proportional Integral Resonant Controller

There is increasing popularity of using permanent magnet (PM) machines in vehicle propulsion systems. Due to the pre-excitation of PM, the machines could offer higher efficiency and torque density. However, their inherent torque ripple could be problematic for electric vehicles (EVs) due to low damping of torsional vibration which may affect passenger comfort. This can prohibit the use of PM machines to improve vehicle energy efficiency. This paper presents the application of resonant control (RC) to suppress the impact of the PM torque ripple, which aims to reduce the vibration of a vehicle. A prototype PM machine and driveline have been fitted to a light-duty off-road vehicle. Firstly, the drivetrain frequency response was analyzed. The main source of the vibration is identified as the 24th harmonic torque ripple of the 12-slot/8-pole PM machine, which originates from the cogging torque and air-gap flux harmonics. The vibration becomes more severe when the torque ripple frequency is close to the natural frequency of the drivetrain. Then, the RC in conjunction with PI controller (PIR) was introduced to be used at the outer speed loop, so that an accurate current reference signal can be generated for the inverter to mitigate the speed ripple. When compared to the conventional Proportional-Integral (PI) controller, PIR controller has demonstrated over 80% reduction in speed ripple, even when the torque ripple frequency is close to the natural frequency of the vehicle.

An Improved Sensorless Vector Control Method for IPMSM Drive with Small DC-Link Capacitors

In this paper, an improved sensorless vector control method for an interior permanent magnet synchronous motor (IPMSM) drive with small DC-link capacitors is proposed. First, a fast sliding-mode observer was applied, to enlarge the observer bandwidth. Then, an improved estimator based on a proportional integral resonant controller was designed for the estimate speed shaping, which means the actual speed can be tracked. This not only reduces the position estimate error, but also enhances the grid power factor and suppresses the input current harmonics. Simulation and experiments were conducted on a sensorless IPMSM drive system with a small film capacitor. The effectiveness of the proposed estimation method was verified by the simulation and experimental results. The estimated error was reduced and the grid current harmonics satisfy the requirements of EN61000-3-2.

A Fault-Tolerant FOC Strategy for Five-Phase SPMSM With Minimum Torque Ripples in the Full Torque Operation Range Under Double-Phase Open-Circuit Fault

This article proposes a fault-tolerant field-oriented control strategy for five-phase surface-mounted permanent magnet synchronous machine with non-sinusoidal back electromotive force under double-phase open-circuit fault, where the failure phases are either adjacent or nonadjacent. Based on the decoupled mathematical model after failure, the optimum current references which satisfy the zero-torque-pulsation constraint at the synchronous frame are presented. However, the torque operation range is small. So a full-range minimum torque ripples post-fault strategy is proposed. This strategy extends the torque operation range by gradually relaxing the zero-torque-pulsation constraint. And it can minimize the torque ripples for each torque reference value in the whole torque operation range. The synchronous frame proportional integral resonant controllers and carrier-based pulsewidth modulation are employed to implement the proposed post-fault strategy. The experimental results are provided to verify that the proposed strategy can achieve wider torque operation range and smaller torque ripples compared with the conventional fault-tolerant strategies.

Analysis of the performance characteristics and arm current control for modular multilevel converter with asymmetric arm parameters

In this paper, the performance characteristics analysis and an improved arm current control of modular multilevel converter (MMC) with asymmetric arm parameters are presented. The performance characteristics analysis of MMC is conducted based on the average switching function current model, which demonstrates that fundamental and double frequency ripples exist in the arm circulating current under asymmetric arm parameter conditions. Besides, there will be dc and double frequency components in the ac side current, while fundamental and double frequency ripples also appear in the dc side current. According to the analysis results, the arm current control based on an improved PIR (Proportional Integral-Resonant) controller via the FAC (feedback adjustment control) method is proposed to suppress the asymmetric components with significantly enhanced dynamic response. Theoretical analysis shows that by introducing the integration and feedback loops of the FAC method to the conventional PIR controller, the inertia and damping effects are emerged in the system, which can help to enhance the system dynamic response during transient and achieve better suppression performance of the asymmetric components. Simulation cases verify the correctness of the theoretical analysis and the validity of the proposed control.

Investigation of Spatial Harmonic Magnetic Field Coupling Effect on Torque Ripple for Multiphase Induction Motor Under Open Fault Condition

This paper investigates spatial harmonic magnetic field coupling effect on torque ripple for multiphase induction motor under open fault condition. The coupling results in severe torque ripple generated by ellipse asynchronous magnetomotive force, and the current space vectors are utilized for coupling phenomenon analysis in the multiple planes. The optimal current space vector is proposed to achieve the minimum torque ripple, and the traditional method is used for comparison. Both fundamental and harmonic current space vectors are derived, when single-phase and two-phase open fault conditions are analyzed, respectively. Furthermore, the proportional integral resonant controller is used to realize zero-error tracking, and proper values of parameters in the transfer function are derived. Finally, a five-phase variable speed drive system is constructed and the proposed method is validated by experiments.

Combined parameters selection of a proportional integral plus resonant controller for harmonics compensation in a wind energy conversion system

This paper introduces the use of the Naslin polynomial technique in order to tune a proportional integral resonant (PIR) controller for the rotor-side converter of a grid-connected wind energy conversion system (WECS), which is based on a back-to-back converter and a doubly fed induction generator (DFIG). The objective of the proportional integral part of the PIR controller is to control the active and reactive power of the rotor-side converter, while the resonant part of the PIR controller deals with the stator current harmonics of the generator due to grid voltage distortions. Most papers that use PIR controllers for WECS often carry out the separated tuning of the PI part and then the tuning of the resonant part without any guide. In this paper, the tuning of the PIR controller as a single controller is proposed taking into account the mathematical base of the Naslin polynomial technique. The case of study is a WECS based on a 50 HP DFIG, and the considered grid voltage harmonics are the fifth and seventh. Simulations were implemented to evaluate the compensation of the current harmonics with the selected PIR controller values.

Periodic Control of Power Electronic Converters [Book News

The emergent topic of periodic control (PC) is the subject of this book. The explanation of PC starts with the application of the internal model principle (IMP) control solutions for power electronics converters to track periodic inputs. The first IMP based PC solutions, called repetitive control, appeared in the 1980s and achieved an exact regulation of periodic inputs having a known period. The book includes the most significant theoretical advancements and practical applications, mainly to electronic power conversion, made by scientists and engineers since then. Well-known examples of PC are the so-called proportional-integral resonant controllers characterized by a theoretical infinite gain at the resonant period. The book chapters begin with an abstract, end with a summary, and list dozens of references. A table of contents, preface, and index are also included.

Control of Parallel Three-Phase PWM Converters Under Generalized Unbalanced Operating Conditions

This paper proposes a new control scheme for parallel three-phase pulse width modulation converters under generalized unbalanced operating conditions. An average model of the parallel system in positive-sequence synchronous reference frame is derived to analyze the influence of generalized unbalanced operating conditions in ac side. It is seen that the unbalance factors in filter inductance will not only give rise to negative-sequence circulating current, but also contribute to generating zero-sequence circulating current (ZSCC). The negative-sequence circulating current can be inhibited by suppressing the negative-sequence components in ac output currents of parallel modules with a proportional integral resonant (PIR) controller. An improved feed-forward strategy and a PIR controller for ZSCC control are proposed for unbalanced operating conditions. The disturbances in ZSCC caused by unbalance factors in filter inductance can be rejected with feed-forward strategy. Because the disturbance in ZSCC is the fluctuation in grid frequency which can be suppressed by a resonance controller, therefore, a PIR controller is adopted in ZSCC controller. The proposed scheme can effectively suppress the circulating currents between the parallel modules and as a result, the distortions in output currents can be greatly reduced. Experimental results confirm the performance and effectiveness of the proposed method.

Improved Vector Control of Brushless Doubly Fed Induction Generator under Unbalanced Grid Conditions for Offshore Wind Power Generation

Brushless doubly fed induction generators (BDFIGs) are promising alternatives to doubly fed induction generators due to high reliability and low maintenance cost for the absence of brushes and slip rings. As a typical application in offshore wind energy generation, a feedforward method is applied to the grid-voltage oriented vector control to make the active and reactive power decoupled. Another challenge in practice is how to meet the demanding requirements of grid codes. The dynamic behavior of BDFIG is analyzed in detail under unbalanced grid conditions with the proposal of four different targets. To deal with these issues, an improved vector control strategy based on the proportional-integral resonant controller (PI + R) in a single synchronous reference frame is developed. The stability and robustness of the proposed control scheme under parameters uncertainties and variations are discussed as well. The advantage of this control strategy is that it is simple and fast in transient response. The effectiveness of the proposed control strategy is validated by the experiment results of a 3-kW prototype machine.

Unity Power Factor Operation of Indirect Matrix Converter Tied to Unbalanced Grid

This paper presents a new control method for indirect matrix converter operating under unbalanced grid voltages. The proposed method aims to achieve balanced output voltages as well as a near unity input power factor operation. First, an opportune reference current accurately generated, and a proportional integral resonant controller are designed in a dq reference frame that is synchronized with the positive sequence of the grid voltages so as to achieve a perfect tracking of input reactive power reference. Then, a real-time estimator of the virtual dc-link voltage is developed with the aim to provide balanced output voltages; therefore, an almost constant active power free of low frequency ripple is supplied from the grid. Experimental results are presented to verify the feasibility and effectiveness of the proposed control method.

Enhanced Control for a Direct-driven Permanent Synchronous Generator Wind-power Generation System with Flywheel Energy Storage Unit Under Unbalanced Grid Fault

—This article presents an enhanced control strategy for a direct-driven permanent synchronous generator based wind-power generation system with a flywheel energy storage unit. The behaviors of the direct-driven permanent magnet synchronous generator system with a flywheel energy storage unit under unbalanced grid fault conditions are investigated. Three control targets for the grid-side converter during network unbalance conditions are identified, including eliminating the oscillations in the total active power or reactive power or no negative-sequence current injecting into the grid. Meanwhile, the DC-link voltage oscillations can be effectively suppressed during the unbalanced grid fault by controlling the flywheel energy storage unit. Furthermore, a proportional–integral-resonant controller is designed for the flywheel motor to eliminate the oscillations in the DC-link voltage. Finally, the proposed coordinated control strategy for the direct-driven permanent magnet synchronous generator system with a flywheel energy storage unit has been validated by the simulation results of a 1-MW direct-driven permanent magnet synchronous generator wind power generation system with a flywheel energy storage unit under unbalanced grid fault.

Smooth Speed Control for Low-Speed High-Torque Permanent-Magnet Synchronous Motor Using Proportional–Integral–Resonant Controller

This paper proposes a speed and current proportional-integral-resonant (PIR) control strategy to realize smooth speed control of the low-speed high-torque permanent-magnet synchronous motor (PMSM) drive system by minimizing the periodic torque ripples. Some nonideal factors causing periodic torque ripples, such as harmonics of rotor flux, cogging torque, current measurement errors, and dead time of inverter, are mathematically modeled, and their effects on current and speed control are analyzed, according to their locations in the system. Stability analysis is carried out, considering the delays caused by current loop and speed measurement as they may make the whole system unstable under the proposed PIR control strategy, and the optimal phase adjustment parameters for resonant item to keep the system stable are then obtained through theoretical analysis and numerical simulations. Finally, experimental results achieved on a 10-kW setup prove that the proposed strategy effectively minimizes the periodic speed ripples of PMSM drive.