Positive Position Feedback Controller Research Articles

ALIPPF-Controller to Stabilize the Unstable Motion and Eliminate the Non-Linear Oscillations of the Rotor Electro-Magnetic Suspension System

Within this work, an advanced control algorithm was proposed to eliminate the non-linear vibrations of the rotor electro-magnetic suspension system. The suggested control algorithm is known as the Adaptive Linear Integral Positive Position Feedback controller (ALIPPF-controller). The ALIPPF-controller is a combination of first-order and second-order filters that are coupled linearly to the targeted non-linear system in order to absorb the excessive vibratory energy. According to the introduced control strategy, the dynamical model of the controlled rotor system was established as six non-linear differential equations that are coupled linearly. The obtained dynamical model was investigated analytically applying the asymptotic analysis, where the slow-flow equations were extracted. Based on the derived slow-flow equations, the bifurcation behaviors of the controlled system were explored by plotting the different bifurcation diagrams. In addition, the performance of the ALIPPF-controller in eliminating the rotor lateral vibrations was compared with the conventional Positive Position Feedback (PPF) controller. The acquired results illustrated that the ALIPPF-controller is the best control technique that can eliminate the considered system’s lateral vibrations regardless of the angular speed and eccentricity of the rotating shaft. Finally, to demonstrate the accuracy of the obtained analytical results, numerical validation was performed for all obtained bifurcation diagrams that were in excellent agreement with the analytical solutions.

Multiple-input multiple-output robust vibration control for constrained gyroelastic solar panel considering parametric and un-modeled dynamic uncertainties

Gyroelastic solar panel is a kind of flexible solar panel structure with variable-speed control moment gyroscopes distributed inside. The torque generated by these variable-speed control moment gyroscopes can be used for active vibration suppression. This paper addresses the vibration suppression problem of gyroelastic solar panel in the presence of parametric uncertainties and un-modeled dynamic uncertainties. A novel μ-synthesis method based on analytical multiple-input multiple-output weights design is proposed, which relates 2-norm of the vector of regulated outputs, closed-loop modal damping, and relative control ability of actuators to each mode to the weights. Based on the idea of collocated control, the full order state-space model of the constrained gyroelastic plate with angle gyros as measuring devices is derived. After model reduction, modeling of un-modeled dynamic, and designing the multiple-input multiple-output weights, μ-controller is solved by the DK-iteration method. Furthermore, a comparative study of the μ-controller designed by the proposed procedure and the Positive Position Feedback (PPF) controller designed by the non-smooth H∞ synthesis method is also presented. The control methods are compared for their vibration attenuation, energy utilization, robustness performance characteristics, and robustness stability characteristics. Results for both time domain and frequency domain simulations are presented. Simulation results show that the designed μ-controller has better vibration attenuation effect and robustness performance characteristics than the PPF controller, and can achieve a better robust vibration suppression of the constrained gyroelastic solar panel in presence of parametric and un-modeled dynamic uncertainties.

NIPPF versus ANIPPF controller outcomes on semi-direct drive cutting transmission system in a shearer

Nonlinear integral positive position feedback (NIPPF) and adaptive nonlinear integral positive position feedback (ANIPPF) controllers are used in a shearer's semi-direct drive cutting transmission system, which is powered by a low speed and high torque permanent magnet synchronous motor (PMSM). The transmission system's torsional vibration characteristics were investigated with internal parameter and external cutting load excitation changes caused by harmonic force. In the case of primary and 1:1 internal resonance, an analytic solution is obtained by employing the averaging technique to solve the nonlinear differential equations and modeling the system with NIPPF and ANIPPF controllers. The Poincare portraits were created to imagine how the PMSM would behave around their fixed points. A good match is found when the approximate solutions are compared to the numerical simulations via the Runge–Kutta method fourth-order (RK4). The linearized stability strategy is used to ensure stability near fixed points in the autonomous system. Before and after control, the steady-state amplitude and stability of nonlinear systems were investigated and analyzed. Optimal system operation conditions and frequency response curves (FRCs) were examined at various controller and system parameter values. Numerous system characteristics were found to have an effect after being combined with NIPPF and ANIPPF. The numerical and analytical solutions at time-history and FRCs were compared using the MATLAB program to confirm their comparability. This study's findings were compared to those found in the literature. We conclude from this analysis that the ANIPPF controller provides the best system control. The calculations also revealed that ANIPPF is the most effective controller. Finally, the controls suppress the system's vibration amplitude and chaos motion. The outcomes of this study were used to develop a theoretical foundation for the shearer semi-direct drive cutting transmission system's design and construction.

A Suitable Active Control for Suppression the Vibrations of a Cantilever Beam

In our consideration, a comparison between four different types of controllers for suppression the vibrations of the cantilever beam excited by an external force is carried out. Those four types are the linear velocity feedback control, the cubic velocity feedback control, the non-linear saturation controller (NSC) and the positive position feedback (PPF) controller. The suitable type is the PPF controller for suppression the vibrations of the cantilever beam. The approximate solution obtained up to the first approximation by using the multiple scale method. The PPF controller effectiveness is studied on the system. We used frequency-response equations to investigate the stability of a cantilever beam. We notified that, there is a good agreement between the analytical solution and the numerical solution.

Feasibility of Active Material Vibration Suppression in a Large Stroke Flexure Hinge

Flexure mechanisms are widely used in precision applications. The finite support stiffness results in parasitic resonance frequencies, typically with low damping, that can be detrimental for positioning performance. Moreover, these resonances may vary over the workspace for mechanisms with moderate or large deflection. In this paper we consider a model of a large stroke flexure hinge that requires accurate end-effector positioning. The feasibility of damping the parasitic resonances using active material is investigated. It is shown that, by placing piezoelectric patches at suitable locations on the flexures, the problematic parasitic resonances can be sensed and actuated. Using modal decoupling the vibration modes are separated, whereafter positive position feedback control is used to suppress the vibration modes. By changing the controller resonance frequency as a function of the nominal deformation, vibration suppression over the entire workspace is achieved. The improved damping in the mechanism is shown using transient simulations.

Fuzzy logic aided PPF controller design to active vibration control of a flexible beam

This paper presents a fuzzy-logic-based observer and a positive position feedback controller to reduce a standard beam's free vibrations using a piezoelectric actuator. It is aimed that fuzzy-logic-based observer is used as feed-through and improves the overall performance of the PPF controller. For this aim, the cantilever beam and a piezoelectric patch are initially numerically modeled using the finite element method considering the close loop control algorithm. The displacement and strain responses results are compared with the experimental model. Then, two controllers are applied to the designed system: positive position feedback (PPF) and fuzzy-logic-based positive position feedback (FLBPPF). The uncontrolled and controlled system responses are investigated and compared in terms of the linear strain and tip displacement results. Using the FLBPPF controller, the settling times of controlled systems are decreased by about 20.7% and 41.6% regarding the linear strain and tip displacement response compared to the PPF controller.

Suppress the vibration of a nonlinear dynamical system subjected to external force using a positive position feedback control.

Suppress the vibration of a nonlinear dynamical system subjected to external force using a positive position feedback control.

Time-delayed positive position feedback control of nonlinear vibrations of continuous rotating shafts

The objective of the present study is to suppress the large amplitudes of a continuous spinning shaft under an active vibration control. For this purpose, the Positive Position Feedback (PPF) control with time-delays are applied to the system via Macro-Fiber-Composite (MFC) sensors and actuators. The nonlinear dynamics of the system is explored analytically utilizing the perturbation method in the primary and one-to-one internal resonances. The steady state solutions of the system and controller in the Cartesian and polar forms are obtained. The effects of the controller gains and time delays on the stability and loci of bifurcations of the system are investigated. The controller shows its feasibility in controlling the system vibrations. Also, it is demonstrated that by increasing the controller gain coefficients the minimum amplitude regions of the system are increased. Furthermore, the safe boundary of the loop delays is studied. The results of the analytical approach are in good agreement with the numerical results of the original system of equations.

Hybrid rayleigh–van der pol–duffing oscillator: Stability analysis and controller

The current study examines the hybrid Rayleigh–Van der Pol–Duffing oscillator (HRVD) with a cubic–quintic nonlinear term and an external excited force. The Poincaré–Lindstedt technique is adapted to attain an approximate bounded solution. A comparison between the approximate solution with the fourth-order Runge–Kutta method (RK4) shows a good matching. In case of the autonomous system, the linearized stability approach is employed to realize the stability performance near fixed points. The phase portraits are plotted to visualize the behavior of HRVD around their fixed points. The multiple scales method, along with a nonlinear integrated positive position feedback (NIPPF) controller, is employed to minimize the vibrations of the excited force. Optimal conditions of the operation system and frequency response curves (FRCs) are discussed at different values of the controller and the system parameters. The system is scrutinized numerically and graphically before and after providing the controller at the primary resonance case. The MATLAB program is employed to simulate the effectiveness of different parameters and the controller on the system. The calculations showed that NIPPF is the best controller. The validations of time history and FRC of the analysis as well as the numerical results are satisfied by making a comparison among them.

Vibration reduction of a non-linear ship model using positive position feedback controllers

Vibration reduction of a non-linear ship model using positive position feedback controllers

Nonlinear vibration control of smart plates using nonlinear modified positive position feedback approach

In this paper, nonlinear vibration control of a plate is investigated using a nonlinear modified positive position feedback method that is applied through a piezoelectric layer on the plate. Based on the classical theory of displacement and strain relations with von Karman, intended equations of motion for the smart plate have been obtained. In this model, transverse vibrations are studied and stimulations are performed for the primary resonance. Boundary conditions of the smart plate are simply supported. The plate is thickness symmetrical. Using the Galerkin method the temporal nonlinear equations governing the system have been found. Then, the free and forced vibrations of the structure with the nonlinear modified positive position feedback controller have been solved using the Method of Multiple Scales to obtain an analytical solution. Results show that this controller reduces the amplitude of the vibration by inducing an increase in the damping coefficient. In addition, this provides a higher level of suppression in the overall frequency domain response by increasing the compensator gain. Finally, the results of the analytical solution for the closed-loop nonlinear modified positive position feedback controller are presented and compared with the result of the conventional positive position feedback controller and nonlinear integral resonant controller. The results show that the performance of the nonlinear modified positive position feedback controller is better than other controllers and significantly reduces the vibration amplitude.

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

The nonlinear vibration control of a nonlinear dynamical system modeled as the well-known Duffing oscillators is investigated within this article. The conventional Positive Position Feedback (PPF) controller is proposed to mitigate the considered system nonlinear vibrations. The whole system mathematical model is analyzed by applying the multiple time scales perturbation method. The slow-flow modulation equations that govern the oscillation amplitudes of both the main system and controller are derived. The stability analysis is investigated based on Lyapunov’s first method. The effects of the different control parameters on both the main system and controller are explored. The obtained analytical and numerical results illustrated that the PPF controller can eliminate the main system nonlinear vibrations once the controller natural frequency is tuned to be the same value as the external excitation frequency, otherwise, the controller adds excessive vibrational energy to the main system rather than suppressing it. In addition, the PPF controller can destabilize the main system motion when excited by strong excitation force. Therefore, a modified version of the PPF controller named the Adaptive Positive Position Feedback (APPF) controller is proposed to overcome the main drawbacks of the conventional PPF controller. The idea is to track the external excitation frequency using an adaptive frequency measurement technique to update continuously the PPF controller natural frequency to become the same value of the excitation frequency. Based on this strategy, the system mathematical model is analyzed again by making the controller’s natural frequency equal to the external excitation frequency. The obtained analytical and numerical simulations showed that the adaptive positive position feedback controller can suppress the main system nonlinear vibration close to zero regardless of the excitation force amplitude and excitation frequency.

Controlling self-excited vibration of a nonlinear beam by nonlinear resonant velocity feedback with time-delay

In this paper, the efficacy of velocity feedback based nonlinear resonant controller is proposed to control the free and forced self-excited vibration of a nonlinear beam. The velocity signal obtained from the sensor is fed through a second-order filter and the nonlinear function of the derivative of the filter variable is used to obtain the control force. The resulting control system being a band-pass one, is believed to be superior to other resonant control schemes like Positive Position Feedback (PPF) control and Acceleration Feedback Control (AFC). To the best of the authors’ knowledge, it is the first attempt to explore the efficacy of resonant nonlinear velocity feedback controller for mitigating self-excited vibration. Analytical results are obtained using multiple time-scale method, are validated with the data obtained from direct numerical simulation carried out in Matlab Simulink model. Analytical results of the uncontrolled system show the periodic, quasi-periodic as well as chaotic behavior. It is observed that the proposed controller can reduce the amplitude of vibration by a significant level near primary resonance. Moreover, the Hopf bifurcations are eliminated by the control action. It is also observed that the proposed controller can reduce the amplitude of the chaotic oscillation significantly. The effect of the actuation delay in the feedback loop is also explored. It is observed that the effect of time delay is detrimental to system performance.

Modern Semi-Active Control Schemes for a Suspension with MR Actuator for Vibration Attenuation

This article describes semi-active modern control schemes for a quarter-vehicle suspension with a magnetorheological damper (MRD) to attenuate vibrations and simultaneously improve the passenger comfort and the vehicle road-holding. The first solution is a multiple positive position feedback (MPPF) control scheme to attenuate the vibration amplitude at the two modal frequencies. The second solution is based on elementary passivity considerations on the exact regulation error dynamics passive output. The passive output feedback is used to improve the control aims. Finally, the third solution deals with a disturbance rejection control (DRC) based on an extended state observer. The three proposed control schemes consider an inverse polynomial model of a commercial MRD for numerical implementation and are evaluated by comfort and road-holding performance indexes proposed in the literature. Furthermore, the effects of variation in the sprung mass (emulating different number of passengers) on the controllers’ performance is analysed. The numerical results show in both scenarios (constant and variable sprung mass) that passivity based control (PBC) and DRC improve the performance indexes compared with the classical sky-hook control and the open-loop systems with a different constant current input for the MRD. Obtained results for damping force and power consumption are within the operation range of the considered commercial MRD showing the viability for experimental implementation of the proposed control schemes.

2D and 3D Visualizations of the Mass-Damper-Spring Model Dynamics Controlled by a Servo-Controlled Linear Actuator

This paper focuses on controlling the dynamics of a mass-damper-spring model via a servo-controlled linear actuator (SCLA). The displacements of the mass are sensed and measured by a linear variable differential transformer (LVDT) whose output electrical signal is proportional with the position of the mass. Furthermore, a positive position feedback (PPF) controller is then provided with this signal to be processed and to generate the suitable control signal. The control signal itself is applied to the actuator which in turn controls the mass position. The whole system dynamical equations for the amplitudes and phases are derived with the aid of Krylov-Bogoliubov averaging perturbation method. 2D and 3D visualizations are included to give the reader a wider aspect of the system behavior before and after control.

Tuned Positive Position Feedback Control of an Active Magnetic Bearings System With 16-Poles and Constant Stiffness

This paper presents a tuned positive position feedback controller (TPPF) to overcome the dual high peaks of the classical PPF. This control signal is merged with a proportional-derivative (PD) control signal to suppress the vibrations of a constant-stiffness 16-poles rotor active magnetic bearings (AMBs) system. Another benefit of the applied TPPF is turning the rotor’s quasiperiodic unstable motion into a periodic stable motion by eliminating both saddle-node and Hopf points. The whole group equations of motion are derived and their approximate solutions are sought with the aid of the multiple scales method. Different response curves are plotted to clarify the difference between the rotor’s vibratory behaviors before and after PPF and also with TPPF.

Response Analysis and Controlling the Nonlinear Vibration of Van Der-Pol Duffing Oscillator Connected to the NIPPF Controller

In this paper, we introduced response analysis and controlling the nonlinear vibration of van der pol duffing oscillator subject to parametric and external excitations by connecting the nonlinear integral positive position feedback (NIPPF). The controller combines the characteristics of the positive position feedback controller (PPF) and integral resonant control (IRC) and these controllers are viewed in a blocked scheme for the closed-loop system (system under control). The analytical solution and all resonance cases are obtained by applying the multiple time scales perturbation method (MSPM). The stability analysis is studied using the frequency response equations at the supposed worst resonance case. For numerical simulation, the system is examined before and after connecting the NIPPF controller using Matlab software program (package ode45). The influences of different parameters are examined numerically for the vibrating system and controller. The approximate analysis is confirmed with numerical simulation outcomes. Finally, making a comparison with previously related published work.

Study of Hopf curves in the time delayed active control of a 2DOF nonlinear dynamical system

Within this paper, we are focusing on the time delay effects on the improved positive position feedback (PPF) controller for the oscillations of a 2DOF nonlinear dynamical system which represents a thin-walled pre-twisted rotating blade. Herein, we are improving the performance of the traditional positive position feedback controller (PPF) that suffers from the existence of two high amplitude peaks on both sides of its minimum amplitude point. The improvement involves coupling double nonlinear saturation controllers to the main system to notch down the high peaks. As an active control process, the time delay is inherent in the process which produces a locus of Hopf bifurcation points separating between the stable and unstable regions of operation. Variation of different parameters is studied to relate their effects with time delay on the system operation. To ensure the validity of our proposed work, a comparison between the approached multiple scales analytical solutions and the computed Rung-Kutta numerical solutions is done at the end of this paper.

Nonlinear vibrations control of a contact-mode AFM model via a time-delayed positive position feedback

In this work, the nonlinear vibrations of a contact-mode atomic force microscopy (AFM) model subjected to multi excitations are controlled via a time-delayed positive position feedback (PPF) controller. A perturbation method is implemented to obtain the approximate nonlinear dynamical behavior of the AFM system. Different response curves, before and after control, are included utilizing frequency response equations. At multiple resonance cases (primary, sub-harmonic, and internal), the gain effects on the vibration amplitude and stability behavior of the controlled system are studied. The acquired results revealed that PPF controller is efficient in reducing the studied system oscillations. The efficiency of the controller Ea was about 193, means that the controller reduced the vibration by about 99.5%. For increasing feedback signal gain α2, the stability region in τ1-τ2 plane was shrinking. Finally, verification curves are plotted to depict the degree of closeness between analytical predictions and numerical simulation.

Analysis of Vibration Control of Nonlinear Beam Using a Time-Delayed PPF Controller

This paper presents a study on the performance of a positive position feedback (PPF) controller to suppress the vibration of a horizontal beam under vertical excitation. Time delays in the control loop are taken into consideration to study their effects on the controller performance and the stable region. The integral iterative method is conducted to obtain a second-order approximate solution and the corresponding amplitude equations for the considered system. The stability of the steady-state solutions is ascertained using a combination of Floquet theory and Hill’s determinant. The maximum limits of time delays at which the system remains stable have been determined for different values of control parameters. And the effects of various control parameters on the existence of multiple-solution region are investigated. The analysis illustrates that the appearance of time delay and the elimination of controller damping coefficient are the two main factors to enhance the nonlinear characteristics of the controlled system. The points at which the steady-state amplitude of the main system reaches its minimum are studied analytically. The analyses show that the analytical results are in excellent agreement with the numerical simulations.