Positive Position Feedback Controller Research Articles

Controller synthesis for negative imaginary systems using nonlinear optimisation and H 2 performance measure

ABSTRACT Negative imaginary (NI) systems theory has attracted considerable attention in the area of robust control of highly resonant flexible structures systems and nano-positioning systems, where the NI property is naturally satisfied. In this paper, we present a control synthesis methodology for NI systems based on nonlinear optimisation techniques. In the presented method, a parametrised library of strictly negative imaginary (SNI) controllers is created and used in a standard numerical nonlinear optimisation setup. The SNI controller library contains generic controllers that are widely used in the control highly resonant flexible structures such as positive position feedback (PPF) and integral resonant control (IRC). Sequential quadratic programming (SQP) techniques are used in the numerical optimisation problem. The synthesised controller satisfies the SNI property as well as optimising performance. As an application of these results, an example of controlling a Euler–Bernoulli beam with piezoelectric actuator and sensor is presented.

Utilizing the time delayed PPF controller to suppress vibrations of a nonlinear system containing real power exponents in damping and restoring forces

The time delayed Positive Position Feedback (PPF) controller is utilized to suppress the primary resonance of vibrations of an excited base oscillator by real power exponents of the restoring and damping forces. Multiple scales method is conducted to get the frequency response equations. The stability of the system is studied by using the Lyapunov first method. The influences of system parameters and time delay on the system response are investigated to avoid the jump phenomenon for better system performance. Time margin is deduced for most possible values of controller gain. Analytic results are verified by numerical integration of the original system equations.

Positive Position Feedback Controller for Nonlinear Beam Subject to Harmonically Excitation

In this paper, the vibration reduction of the harmonically excited nonlinear beam is introduced using positive position feedback controller (PPF). The multiple-scale perturbation techniques (MSPT) up is applied to second-order to obtain the analytic results. Numerical simulations are used to compare between time-history and the analytical solution. The frequency response equation (FRE) is studied to illustrate the steady state solutions near the simultaneous resonances. The influences of the different parameters and the system behavior at resonance case are studied to show the optimum conditions of decreasing the vibration. A comparison between the numerical and analytical solutions is presented to appear the validity of the results.

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.

The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances

In this paper, we applied three different control methods; Positive Position Feedback (PPF), Integral Resonance Control (IRC) and Nonlinear Integrated Positive Position Feedback (NIPPF) added to a Duffing oscillator system subjected to harmonic force. An analytic solution is introduced using the multiple scales perturbation technique (MSPT) to solve the nonlinear differential equations, which simulate the system with NIPPF controller. Before and after control at the primary and superharmonic resonances, the nonlinear systems’ steady-state amplitude and stability are studied and examined. The influences of various parameters of the system after being connected to NIPPF are illustrated. Optimum working conditions for the NIPPF controller are obtained at internal resonance ratio 1:1. A Comparison is also made to validate the closeness between the numerical solution and the analytical perturbative one at time-history and frequency response curves (FRC). Finally, a comparison with the available results in the literature is presented. From this comparison, we find that the best control to the system is via the NIPPF controller.

Vibration control of a circular plate using parametric controller with phase shift adjustment

The article presents a vibration control method of a circular plate based on a controller with phase shift adjustment in the feedback loop (PSAF). The proposed controller combines the structures of the positive position feedback and strain rate feedback controllers, which are often used in vibration reduction systems. Additionally, the PSAF controller allows the adjustment of the phase shift of the controller to the object changes by tuning its parameters. An analytical model of bending vibration of the thin plate as well as the estimated model based on the autoregressive identification method with exogenous terms (ARX) is introduced. These two methods of obtaining the mathematical model are applied to develop the control algorithm for vibration cancellation. Vibrations of the plate are measured using a noncontact method – laser vibrometer. This method renders it easy to change the position of the beam on the test surface and ensures the high precision of the measurements. The control input is applied to the plate by an MFC disk that is attached to the plate at its center. The plate vibrations were excited by a loudspeaker located inside a cast iron cylinder. The designed controller was implemented and tested on a realtime platform - PowerDAQ with xPC Target environment. This article presents the concept, results of simulation tests, and implementation for the PSAF controller. Finally, the obtained results confirm the possibility of using the proposed solution to reduce the vibration of plates, indicating significant suppression of the targeted modes.

A Feedback Controlled MEMS Probe Scanner for On-chip AFM

Atomic force microscope (AFM) provides a unique possibility in nanoscience research and development for interrogation and manipulation of matter at nanoscale. Miniaturization of AFM significantly reduces the manufacturing cost and breaks the barrier to widespread adoption of this scientific instrument. This paper presents the characterization and control of a novel microelectromechanical system (MEMS)-based AFM. For in-plane motion, the device is equipped with a micro stage with integrated electrostatic actuators and electrothermal sensors. For use in taping-mode AFM imaging, a microcantilever is embedded within the device, featuring a piezoelectric layer for actuation. Positive position feedback (PPF) controller is used to attenuate the highly resonant dynamics of the stage. Scanning performance of device is evaluated by tracking a raster pattern where a 50 Hz triangular signal is applied to the actuators along the X axis. To reduce the tracking error, turnaround points of triangular signal are smoothed by using an optimization method. Moreover, the closed-loop bandwidth is increased with inversion-based feedforward technique. A 50Hz optimal reference signal combined with an inversion-based feedforward technique results in a fivefold decrease in root mean square of tracking error compared with triangular reference signal.

Positive Position Feedback Control of a Galloping Structure

In this study, the suppression of wind-induced oscillations of a D-shaped prism mounted on a cantilever beam by means of a positive position feedback (PPF) controller is investigated. The assumed mode method is applied to determine the stiffness, mass and non-linear force matrixes of a second order ordinary differential equation system. The positive position feedback control by use of a sensor-actuator piezoelectric is implemented on the galloping system to suppress the mechanical oscillations. The results show that the PPF controller is a powerful method to decrease the galloping amplitude of the D-shaped prism. The numerical results are in a good agreement with experimental results.

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.

Optimization of PPF Control of a Building-like Structure for Vibration Control

This work presents a research on intelligent civil structures, like bridges and buildings, which consists in the use of sensors and actuators to monitor and control some specific parameters of the structures. A recent technological breakthrough has been the development of piezoelectric actuators or sensors using special materials, such as Lead Zirconate Titanate (PZT), magnetorheological dampers, shape memory, and others. In particular, the use of smart materials in the structural control of buildings is an interesting and promising subject in civil engineering. The method of active control is used to reduce the negative effects of external forces or perturbations on the performance of the overall system. These forces can be expressed mainly in terms of the effects of winds or earthquakes. This article presents a case of study of a building-like structure perturbed in the ground-borne by an external force and controlled through an active control applied with a PZT actuator joined in a column of the structure. The scheme of control consists in a modal control known as Positive Position Feedback (PPF), which aims to reduce the vibrations in the building-like structure. The gains of PPF control are tuned using an optimization method known as Differential Evolution combined with the Interior Point Algorithm. Experimental and numerical results are shown with the purpose of analyzing the efficiency of the control in the presence of an exogenous force in the dynamics of the system. The numerical results of the optimized PPF control are interesting and promising, reducing the vibrations and lateral displacements by around 97% of the building-like structure.

Multimodal suppression of vibration in smart flexible beam using piezoelectric electrode-based switching control

This paper describes an active vibration control system combining a piezoelectric electrode configured with a novel switching control system to achieve multimodal vibration suppression in smart flexible structures embedded with only a single piezoelectric actuator. The fact that high-frequency vibrations attenuate more rapidly than do low frequency vibrations motivated the development of a novel scheme in which the resonant excitation of coupled bending and lateral vibrations is applied to a cantilever beam. Switching times are determined using time-frequency analysis of modal responses. A smoothing function was applied to alleviate the effects of high-frequency oscillations during the switching control transition in order to facilitate the suppression of bending mode vibrations. Algorithms for proportional derivative (PD) control and positive position feedback (PPF) control can be tailored specifically for the target vibration modes and implemented in a variety of switching control schemes. The vibration responses induced by various switching control schemes was analyzed in order to derive appropriate control parameters for the development of an efficient switching control system aimed at suppressing multimodal vibrations. Experiment results demonstrate the effectiveness of the proposed piezoelectric electrode configuration in suppressing lateral mode vibrations. The proposed switching control system also proved highly satisfactory in suppressing vibrations in a system subject to simultaneous bending mode excitation.

Active vibration control of a smart beam by a tuner-based PID controller

In this study, a tuner-based Proportional-Integral-Derivative controller is proposed to actively control a smart beam. In numerical simulation environment, the performance of the tuner-based PID and a positive position feedback controller in damping the forced vibrations of a smart beam using a piezoelectric actuator are investigated. The finite element method is used to numerically model the smart beam by exporting the state-space matrices that are characterized with regard to the active vibration control loop. Two types of vibration data with sine tones are comprised in order to stimulate behavior of the proposed system. The first one is the composition of the first and second natural frequencies of smart beam. The second one is the composition of the first to the third natural frequencies of smart beam. In the tuner-based PID, controller design tuner toolbox is used to obtain suitable PID coefficients. In this simulation environment active vibration control based on the proposed tuner-based PID and on positive position feedback controllers is studied and compared. Additionally, the controller power consumption levels are determined for the proposed controller design. Numerical results show that the overall tuner-based PID control performance of flexible smart beam system is more effective than the positive position feedback controlled system for forced vibration control. Also, the tuner-based PID controller provides more energy savings than the positive position feedback controller.

Adaptive positive position feedback control with a feedforward compensator of a magnetostrictive beam for vibration suppression

In this paper, a Fe–Ga alloy magnetostrictive beam is designed as an actuator to restrain the vibration of a supported mass. Dynamic modeling of the system based on the transfer matrix method of multibody system is first shown, and then a hybrid controller is developed to achieve vibration control. The proposed vibration controller combines a multi-mode adaptive positive position feedback (APPF) with a feedforward compensator. In the APPF control, an adaptive natural frequency estimator based on the recursive least-square method is developed to be used. In the feedforward compensator, the hysteresis of the magnetostrictive beam is linearized based on a Bouc–Wen model. The further remarkable vibration suppression capability of the proposed hybrid controller is demonstrated experimentally and compared with the positive position feedback controller. Experiment results show that the proposed controller is applicable to the magnetostrictive beam for improving vibration control effectiveness.

Vibration active control of structure with parameter perturbation using fractional order positive position feedback controller

A Fractional-Order Positive Position Feedback (FOPPF) controller is developed by transforming the integer-order exponent of the Positive Position Feedback (PPF) controller into a fractional format to increase the number of designable parameters. The sensitivity of these fractional-order exponents is investigated to assess their influence on the behavior of the FOPPF controller in frequency domain. An optimal design method of FOPPF controller is presented by taking account of the uncertainty of object structure, and constructing an objective function. This objective function is the weighted sum of the suppression ratio of the peak value of power spectral density and the suppression ratio of the root-mean-square value of the random response in the target frequency band. The performance of this controller is analyzed by numerical simulation and experiment using a vertical tail attaching macro fiber composite piezoelectric actuator. Results indicate that a wider band of effective phase compensation is obtained using the FOPPF controller than using the PPF one, and a higher robustness is achieved as well. The FOPPF controller is more effective on suppressing the both periodic and random vibration responses comparing with the PPF and modified PPF controller.

Investigation of the time delay effect on the control of rotating blade vibrations

Abstract In this paper, a time-delayed positive position feedback (PPF) controller is applied to reduce the nonlinear oscillations of the dynamical system of a rotating blade. The main system is coupled to the controller whose natural frequency is approximately equal to the natural frequency of the main system. The main system has two oscillatory modes that are found to be powerfully linearly coupled. The approximate nonlinear dynamical behavior is studied and analyzed by applying the multiple time scales method. The effects of the time delay are investigated to indicate the safe region of operation. Time history and different curves are included to show the effectiveness of the controller. Eventually, validation curves are given to estimate the degree of closeness between the analytical and numerical solutions.

Experiments study on attitude coupling control method for flexible spacecraft

High pointing accuracy and stabilization are significant for spacecrafts to carry out Earth observing, laser communication and space exploration missions. However, when a spacecraft undergoes large angle maneuver, the excited elastic oscillation of flexible appendages, for instance, solar wing and onboard antenna, would downgrade the performance of the spacecraft platform. This paper proposes a coupling control method, which synthesizes the adaptive sliding mode controller and the positive position feedback (PPF) controller, to control the attitude and suppress the elastic vibration simultaneously. Because of its prominent performance for attitude tracking and stabilization, the proposed method is capable of slewing the flexible spacecraft with a large angle. Also, the method is robust to parametric uncertainties of the spacecraft model. Numerical simulations are carried out with a hub-plate system which undergoes a single-axis attitude maneuver. An attitude control testbed for the flexible spacecraft is established and experiments are conducted to validate the coupling control method. Both numerical and experimental results demonstrate that the method discussed above can effectively decrease the stabilization time and improve the attitude accuracy of the flexible spacecraft.

Experimental study of active vibration control for suppressing impact or moving disturbance-induced vibrations with polyvinylidene fluoride and fiber Bragg grating sensors

In this work, we experimentally study active vibration control of a smart cantilever beam and focus on influences of disturbances to the vibrations and corresponding control performances. The smart cantilever beam is subjected to impacts or moving mass loadings and robust positive position feedback (PPF) control is implemented to suppress the disturbance-induced vibrations. Specifically, we employ high sensitive polyvinylidene fluoride (PVDF) and fiber Bragg grating (FBG) sensors to capture dynamic characteristics of the disturbances. To allow repeatable and controllable experimental conditions for the prescribed disturbances, steel balls or a steel rod are used as the sources of the disturbances applied on the cantilever beam, on which a rail is cut out to guide the motions of the steel ball. Before designing PPF, finite element simulations are carried out to numerically compare sensing performances of the PVDF and FBG sensors. Resonant frequencies of the cantilever beam, including bending, torsional, and lateral modes, are also obtained beforehand numerically and experimentally for understanding behaviors of the disturbance-induced vibrations. By performing fast Fourier transform (FFT) and short-time Fourier transform (STFT) on the detected transient responses, characteristics of the disturbances and their suppressions with the PPF controllers are demonstrated and discussed. The proposed smart cantilever beam with the prescribed repeatable and controllable disturbances serves as a very suitable model in laboratory confirmations for active controller designs. In addition, our experimental work provides suggestions for sensor selections in active vibration control of flexible structures, especially in environments involving impact or moving disturbances.

Robust Positive Position Feedback Controller for Voltage Control of Islanded Microgrid

This paper presents the design of robust positive position feedback (PPF) controller to control the grid voltage for an islanded microgrid. The microgrid consists of several distributed generators (DG) and local loads which is partially unknown and uncertain. The controller is designed in a way that it shows the robustness against unmodeled loads, dynamic loads and harmonic loads. The dynamics of the plant is identified using differential equations. The design of the controller is presented based on negative imaginary approach. The simulation results presented in the paper show that the controller provides extensive improvement in the voltage control of islanded microgrid under different uncertainties.

Controlling quarter car suspension system by proportional derivative and positive position feedback controllers with time delay

The active car suspension system is presented here to suppress the vibration of the car by applying proportional derivative (PD) and positive position feedback (PPF) controllers with time delay. The control signal output of the controller is applied electrically to the magneto-rheological (MR) damper or Electrical-rheological (ER) damper which is attached parallel to the passive components to improve the suppression of the vibration. The electrical control signal is produced by electronic circuits or programmable logic controller and the two-position sensor feedback signal which are connected to the controller. The approximate solutions of PD and PPF suspension systems are obtained by applying multiple time scales perturbation method. The effects of parameters variation of both the system and the controllers are investigated to achieve the best performance. Simulation results show good performance of the designed controllers.

Positive acceleration, velocity and position feedback based damping control approach for piezo-actuated nanopositioning stages

This paper proposes a new damping control approach with positive acceleration, velocity and position feedback (PAVPF) scheme for piezo-actuated nanopositioning stages to implement high-bandwidth operation. To achieve this objective, the intrinsic hysteresis nonlinearity of the piezoelectric actuator is firstly handled by a feedforward compensator with a modified Prandtl–Ishlinskii model. Afterwards, the PAVPF controller with the pole-placement method is implemented to suppress the lightly damped resonant mode of the hysteresis compensated system. With the PAVPF controller, the poles of the damped system in a third-model can be placed to arbitrary positions with an analytical method. Finally, for accurately tracking a predefined trajectory, a high-gain proportional-integral (PI) controller is designed, which could deal with the disturbance and the unmodeled dynamics. For verifying the proposed PAVPF-based control approach, comparative experiments with positive velocity and position feedback controller and with PI controller are conducted on a piezo-actuated nanopositioning stage. Experimental results demonstrate that the developed control approach with PAVPF controller is effective on damping control and improves the control bandwidth of the conventional PI controller from 111 Hz to 766 Hz, which leads to the significant increase of the tracking speed.