Integral Resonant Control Research Articles

Model reference adaptive damping control for a nanopositioning stage with load uncertainties.

In this paper, a scheme of model reference adaptive integral resonant control (MRAIRC) is presented for adaptive precision motion control of a piezo-actuated nanopositioning platform. The major advantage of the proposed scheme lies in the adaptivity for dynamic changes resulting from load uncertainties. Existing standard integral resonant control (IRC) with constant controller gains is normally designed based on the identified system model under no external load. For the proposed MRAIRC, a standard IRC is first designed using an analytical approach, assuming that a second-order system model is obtained in advance. Afterwards, the designed closed-loop is utilized as a reference model for systems with model uncertainties. The adaptive laws of the controller gains are determined according to the well-known MIT rules. An offline trail-and-error operation is conducted for adaption gains' tuning. The stability of this adaptive control system is proved through Lyapunov stability analysis. Simulation and experimental studies demonstrate that the proposed MRAIRC is superior to the standard IRC in terms of the tracking errors for commonly used raster scanning signals at 5, 10, and 20 Hz with load variations of the platform ranging from 0 to 1000 g.

A Robust Resonant Controller for High-Speed Scanning of Nanopositioners: Design and Implementation

This brief presents a novel damping control scheme for piezoactuated nanopositioning platforms with robust resonant control (RRC). The RRC is developed to attenuate the resonant-vibrational modes of the lightly damped dynamics of the stage in an inner positive feedback loop. The parameters in the proposed RRC are determined through an analytical approach. Indeed, the controller gains constrained by both the robustness and the damping ratio of the inner loop are tuned based on the small gain theory. Then, a high gain integral tracking controller is applied in the outer loop to minimize the tracking errors due to unmodeled nonlinearity and uncertainties. To validate the effectiveness of the proposed RRC, comparative experiments with conventional positive position feedback (PPF) and integral resonant control (IRC) are conducted on a piezoactuated nanopositioning stage. Results demonstrate that the proposed RRC improves the closed-loop bandwidth from 67 Hz with PPF and 135 Hz with IRC to 176 Hz. Moreover, better robustness against load variations with a range of 0–1000-g loading under 0–20-Hz input raster scanning signals are obtained by RRC compared with PPF as well as IRC.

Vibration suppression of a viscoelastic isolation system by nonlinear integral resonant controller

The nonlinear integral resonant controller (NIRC) is implemented and analyzed to control the vibration of a viscoelastic isolation system under harmonic excitation. The NIRC consists of a first-order resonant integrator, which provides additional damping in the closed-loop system to reduce the high-amplitude vibration near the resonance frequency. The method of multiple scales is applied to analytically find the relationship of the amplitude–frequency response of the viscoelastic isolation system. Besides, the equation of the backbone curve satisfied is derived. Meanwhile, the suppression performance is verified based on time-domain analysis. It is found that the NIRC can effectively suppress vibration and improve stability of the viscoelastic isolation system. Furthermore, the influence of the detuning parameters, the real-power exponent, the viscoelastic damping, and the external excitation amplitude on the stability regions is investigated. Overall, the vibration reduction mechanism of the NIRC on the viscoelastic isolation system is revealed.

A Fast Algebraic Estimator for System Parameter Estimation and Online Controller Tuning—A Nanopositioning Application

Parameter uncertainty is a key challenge in the real-time control of nanopositioners employed in scanning probe microscopy. Changes in the sample to be scanned introduces changes in system resonances, requiring instantaneous online tuning of controller parameters to ensure stable, optimal scanning performance. This paper presents a method based on the frequency-domain algebraic derivative approach for the accurate online identification of the nanopositioner's parameters. The parameter estimates are produced within a fraction of one period of the resonant mode frequency, allowing almost instantaneous tuning of controller parameters. Experimental results show that the proposed method can be utilized to automatically tune an integral resonant control scheme that combines both damping and tracking actions, and consequently deliver positioning performance far superior to that achieved solely due to the scheme's inherent robustness properties. It is further shown that the achieved performance compares favorably with an optimally designed control scheme of the same type.

Two-degrees-of-freedom PI[formula omitted]D controller for precise nanopositioning in the presence of hardware-induced constant time delay

The fast and accurate tracking of periodic and arbitrary reference trajectories is the principal goal in many nanopositioning applications. Flexure-based piezoelectric stack driven nanopositioners are widely employed in applications where accurate mechanical displacements at these nanometer scales are required. The performance of these nanopositioners is limited by the presence of lightly damped resonances in their dynamic response and actuator nonlinearities. Closed-loop control techniques incorporating both damping and tracking are typically used to address these limitations. However, most tracking schemes employed use a first-order integrator where a triangular trajectory commonly used in nanopositioning applications necessitates a double integral for zero-error tracking. The phase margin of the damped system combined with the hardware-induced delay deem the implementation of a double-integrator unstable. To overcome this limitation, this paper presents the design, analysis and application of a new control scheme based on the structure of the traditional Two-Degrees-of-Freedom PID controller (2DOF-PID). The proposed controller replaces the integral action of the traditional 2DOF-PID with a double integral action (2DOF-PI2D). Despite its simplicity, the proposed controller delivers superior tracking performance compared to traditional combined damping and tracking control schemes based on well-reported designs such as positive position feedback (PPF), Integral resonant control (IRC), and Positive Velocity and Position Feedback (PVPF). The stability of the control system is analyzed in the presence of a time delay in the system. Experimental results validating the efficacy of the proposed chattering-free control of a piezo-driven nanopositioning system are included.

Enhanced Positioning Bandwidth in Nanopositioners via Strategic Pole Placement of the Tracking Controller

Tracking triangular or staircase trajectories is a challenge for a piezo-driven nanopositioner due to vibration problems. The piezo-driven nanopositioner is a lightly-damped system because of its mechanical construction. These reference trajectories are high-frequency components that tend to excite the mechanical resonance of the nanopositioner, causing vibration and thus affecting the accuracy. The Integral Resonant Controller (IRC) is employed to damp the resonance and thereby furnish a larger gain margin for a high-gain tracking controller to be implemented. The IRC, however, introduces a low-frequency pole. Due to other control issues, such as hysteresis nonlinearity, Integral (I) or Proportional Integral (PI) tracking control is used as a tracking loop to address uncertainties (hysteresis). The traditional method using a PI controller has a limited positioning bandwidth. This paper presents the strategic zero placement of the PI controller to enhance the positioning bandwidth, thereby overcoming the limitations of tracking error. Using experimental validations to confirm the feasibility of the proposed method, it is shown that significant improvement regarding bandwidth and disturbance rejection are reported.

Shunt Active Power Filter Based on Proportional Integral and Multi Vector Resonant Controllers for Compensating Nonlinear Loads

The current tracking control strategy determines the compensation performance of shunt active power filter (SAPF). Due to inadequate compensation of the main harmonic by traditional proportional integral (PI) control, a control algorithm based on PI and multi vector resonant (VR) controllers is proposed to control SAPF. The mathematical model of SAPF is built, and basic principle of VR controller is introduced. Under the synchronous reference frame, the proposed control method based on pole zero cancellation is designed, which narrows the order of the control system and improves the system dynamic response and the control accuracy. Then the feasibility of the method is demonstrated by analyzing the closed loop frequency characteristics of the system. Finally, the simulation and experimental results are carried out to verify the performance of the proposed method.

Outcome of special vibration controller techniques linked to a cracked beam

• Analytical solution and numerical simulation of non-linear differential equations. • Multiple scale perturbation technique is used to obtained the first order approximation. • PPF, IRC and NIPPF controllers to reduce the vibration. • Stability study subjected to external excitation. • Effect of different parameters in the system. This paper presents a comparison between three different controller methods added to a cracked beam under the action of a harmonic excitation. Those three controllers are Positive Position Feedback (PPF), Integral Resonant Control (IRC) and Nonlinear Integral Positive Position Feedback (NIPPF) which be added to the measured system. The multiple scales method (MSM) is applied for getting the approximate solution on behalf of measured design. This method is effective to solve the major equations of measured system. Stability and effect of different coefficients of the system are demonstrated. The approximate solution response is established via numerical simulation outcome. NIPPF controller is the best one gives better results compared to the other two controllers in decreasing the high amplitude of the system. Comparison between mathematical solution and numerical simulation are considered. Relationship of formerly available papers is considered.

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.

Control the Three-level Rectifier Under Unbalanced Grid Conditions

This paper proposes a novel control method for Three-level rectifier under unbalanced grid conditions. An average model is established to analyze the influence of the unbalanced factor. It can be seen that the unbalanced factor will generate the negative-sequence current. The negative-sequence current can be suppressed by a proportional integral resonant (PIR) controller. Additionally, the unbalance of neutral-point (NP) voltage will generate in the three-level rectifier. Therefore, this paper proposes a space vector modulation for balancing the NP voltage. The simulation results confirm the performance and effectiveness.

High-Precision Control of a Piezo-Driven Nanopositioner Using Fuzzy Logic Controllers

This paper presents single- and dual-loop fuzzy control schemes to precisely control the piezo-driven nanopositioner in the x- and y-axis directions. Various issues are associated with this control problem, such as low stability margin due to the sharp resonant peak, nonlinear dynamics, parameter uncertainty, etc. As such, damping controllers are often utilised to damp the mechanical resonance of the nanopositioners. The Integral Resonant Controller (IRC) is used in this paper as a damping controller to damp the mechanical resonance. A further inherent problem is the hysteresis phenomenon (disturbance), which leads to degrading the positioning performance (accuracy) of the piezo-driven stage. The common approach to treat this disturbance is to invoke tracking controllers in a closed-loop feedback scheme in conjunction with the damping controllers. The traditional approach uses the Integral Controller (I) or Proportional Integral (PI) as a tracking controller, whereas this paper introduces the Proportional and Integral (PI)-like Fuzzy Logic Controller (FLC) as a tracking controller. The effectiveness of the proposed control schemes over conventional schemes is confirmed through comparative simulation studies, and results are presented. The stability boundaries of the proposed control schemes are determined in the same way as with a conventional controller. Robustness against variations in the resonant frequency of the proposed control schemes is verified.

Fractional order implementation of Integral Resonant Control – A nanopositioning application

By exploiting the co-located sensor-actuator arrangement in typical flexure-based piezoelectric stack actuated nanopositioners, the polezero interlacing exhibited by their axial frequency response can be transformed to a zero-pole interlacing by adding a constant feed-through term. The Integral Resonant Control (IRC) utilizes this unique property to add substantial damping to the dominant resonant mode by the use of a simple integrator implemented in closed loop. IRC used in conjunction with an integral tracking scheme, effectively reduces positioning errors introduced by modelling inaccuracies or parameter uncertainties. Over the past few years, successful application of the IRC control technique to nanopositioning systems has demonstrated performance robustness, easy tunability and versatility. The main drawback has been the relatively small positioning bandwidth achievable. This paper proposes a fractional order implementation of the classical integral tracking scheme employed in tandem with the IRC scheme to deliver damping and tracking. The fractional order integrator introduces an additional design parameter which allows desired pole-placement, resulting in superior closed loop bandwidth. Simulations and experimental results are presented to validate the theory. A 250% improvement in the achievable positioning bandwidth is observed with proposed fractional order scheme.

Application of a Fractional Order Integral Resonant Control to increase the achievable bandwidth of a nanopositioner.

This paper proposes a Fractional-order modification of the traditional Integral Resonant Controller named as FIRC. The fractional integral action utilised in the proposed FIRC is a simple, robust, and well-performing technique for vibration control in smart structures with collocated sensor-actuator pairs such as nanopositioning stages. The proposed control scheme is robust in the sense of being insensitive to spillover dynamics and maintaining closed-loop stability even in the presence of model inaccuracies or time-delays in the system. The experimental and simulated results have showed that the proposed FIRC can provide a closed-loop bandwidth which spans up to a 95.2% of the first resonant mode of the experimental system, thus improving the bandwidth achieved by classical integer-order IRC implementations.

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.

Synchronization method for grid integrated battery storage systems during asymmetrical grid faults

This paper aims at presenting a robust and reliable synchronization method for battery storage systems during asymmetrical grid faults. For this purpose, a Matlab/Simulink based model for testing of the power electronic interface between the grid and the battery storage systems has been developed. The synchronization method proposed in the paper is based on the proportional integral resonant controller with the delay signal cancellation. The validity of the synchronization method has been verified using the advanced laboratory station for the control of grid connected distributed energy sources. The proposed synchronization method has eliminated unfavourable components from the estimated grid angular frequency, leading to the more accurate and reliable tracking of the grid voltage vector positive sequence during both the normal operation and the operation during asymmetrical grid faults.

Active Power Quality Improvement Strategy for Grid-Connected Microgrid Based on Hierarchical Control

When connected to a distorted grid utility, droop-controlled grid-connected microgrids (DCGC-MGs) exhibit low equivalent impedance. The harmonic and unbalanced voltage at the point of common coupling (PCC) deteriorates the power quality of the grid-connected current (GCC) of DCGC-MG. This paper proposes an active, unbalanced, and harmonic GCC suppression strategy based on hierarchical theory. The voltage error between the bus of the DCGC-MG and the grid’s PCC was transformed to the dq frame. On the basis of the grid, an additional compensator, which consists of multiple resonant voltage regulators, was then added to the original secondary control to generate the negative fundamental and unbalanced harmonic voltage reference. Proportional integral and multiple resonant controllers were adopted as voltage controller at the original primary level to improve the voltage tracking performance of the inverter. Consequently, the voltage difference between the PCC and the system bus decreased. In addition, we established a system model for parameter margin and stability analyses. Finally, the simulation and experiment results from a scaled-down laboratory prototype were presented to verify the validity of the proposed control strategy.

Fractional-order integral resonant control of collocated smart structures

This paper proposes a fractional-order integral controller, FI, which is a simple, robust and well-performing technique for vibration control in smart structures with collocated sensors and actuators. This new methodology is compared with the most relevant controllers for smart structures. It is demonstrated that the proposed controller improves the robustness of the closed-loop system to changes in the mass of the payload at the tip. The previous controllers are robust in the sense of being insensitive to spillover and maintaining the closed-loop stability when changes occur in the plant parameters. However, the phase margin of such closed-loop systems (and, therefore, their damping) may change significantly as a result of these parameter variations. In this paper the possibility of increasing the phase margin robustness by using a fractional-order controller with a very simple structure is explored. This controller has been applied to an experimental smart structure, and simulations and experiments have shown the improvement attained with this new technique in the removal of the vibration in the structure when the mass of the payload at the tip changes.

Nonlinear integral resonant controller for vibration reduction in nonlinear systems

A new nonlinear integral resonant controller (NIRC) is introduced in this paper to suppress vibration in nonlinear oscillatory smart structures. The NIRC consists of a first-order resonant integrator that provides additional damping in a closed-loop system response to reduce high-amplitude nonlinear vibration around the fundamental resonance frequency. The method of multiple scales is used to obtain an approximate solution for the closed-loop system. Then closed-loop system stability is investigated using the resulting modulation equation. Finally, the effects of different control system parameters are illustrated and an approximate solution response is verified via numerical simulation results. The advantages and disadvantages of the proposed controller are presented and extensively discussed in the results. The controlled system via the NIRC shows no high-amplitude peaks in the neighboring frequencies of the resonant mode, unlike conventional second-order compensation methods. This makes the NIRC controlled system robust to excitation frequency variations.

Butterworth Pattern-based Simultaneous Damping and Tracking Controller Designs for Nanopositioning Systems

The Butterworth filter is known to have maximally flat response. Incidentally, the same response is desired in precise positioning systems. This paper presents a method for obtaining a closed-loop Butterworth filter pattern using common control schemes for positioning applications, i.e. Integral Resonant Control (IRC), Integral Force Feedback (IFF), Positive Position Feedback (PPF), and Positive Velocity and Position Feedback (PVPF). Simulations show a significant increase in bandwidth over traditional design methods and verify the desired pole placement is achieved. The simulations also show a significant limitation of the achievable bandwidth in the case of IRC, IFF, and PPF. For this reason, only PVPF is considered in experimental analysis. Experiments are performed using a two-axis serial kinematic nanopositioning stage. The results show a significant improvement in bandwidth and increased positioning accuracy, specifically at the turn-around point. This allows a greater portion of the scan to be used and improved positioning accuracy at high scanning speeds.