Positive Position Feedback Research Articles

Positive Position Feedback Controllers for Reduction the Vibration of a Nonlinear Spring Pendulum

In this paper, the two positive position feedback controllers (PPF) are proposed to reduce the longitudinal and angular vibrations of the nonlinear spring pendulum system which simulated the ship roll motion. This described by a four-degreeof- freedom system (4-DOF) which subjected to the external excitation force at simultaneous primary and internal resonance case. The method of multiple scale perturbation technique (MSPT) is applied to study the approximate solution of the given system. The stability of the system is investigated near the resonance case applying the frequency-response equations. Numerically, the effects of different controllers parameters on the basic system behavior are studied.

Model-based active control of a continuous structure subjected to moving loads

Modelling of a structure is an important preliminary step of structural control. The main objectives of the modelling, which are almost always antagonistic are accuracy and simplicity of the model. The first part of this study focuses on the experimental and theoretical modelling of a structure subjected to the action of one or two decelerating moving carriages modelled as masses. The aim of this part is to obtain a simple but accurate model which will include not only the structure-moving load interaction but also the actuators dynamics. A small scale rig is designed to represent a four-span continuous metallic bridge structure with miniature guiding rails. A series of tests are run subjecting the structure to the action of one or two minicarriages with different loads that were launched along the structure at different initial speeds. The second part is dedicated to model based control design where a feedback controller is designed and tested against the validated model. The study shows that a positive position feedback is able to improve system dynamics but also shows some of the limitations of state- space methods for this type of system.

Hybrid Position Feedback Controller for Inducing Cross-Well Motion of Bistable Structures

A hybrid position feedback controller based on the well-known positive position feedback controller for bistable structures is presented. The proposed controller is a hybrid unstable-then-stable position feedback controller, which is a second-order single-degree-of-freedom system in nature. The controller takes advantage of the resonant mode of a bistable system about one equilibrium position, destabilizes the system, and dynamically induces snapthrough between the two equilibria. The proposed method is demonstrated on a bistable unsymmetric cross-ply composite platelike structure with surface-bonded piezoelectric actuators. The control scheme is shown to eliminate undesirable cross-well oscillations leading to a monotonic state crossover. An experimentally validated parametric analysis is also presented. Essential properties observed in theoretical and numerical analyses, such as the nondynamic stability and stability gain limit for the positive position feedback controller and the wide unstable bandwidth for the negative position feedback controller, are validated with experiments.

Attitude control and sloshing suppression for liquid-filled spacecraft in the presence of sinusoidal disturbance

The attitude regulation for a liquid-filled spacecraft in the presence of low frequency sinusoidal disturbance is considered in this paper. The liquid-filled spacecraft is modelled as a rigid body attached with a simple pendulum. A novel control scheme is proposed, which is composed of Active Disturbance Rejection Control (ADRC), Positive Position Feedback (PPF), Extended State Observer (ESO) and Singular Spectrum Analysis (SSA). The unknown sloshing mode could be estimated from the combined ESO and SSA, and accordingly ADRC and PPF controller is designed for the stabilization of the spacecraft. Particularly, the parameters of the disturbance are not required as long as its frequency is lower than the sloshing one. The proposed approach could provide stabilization for the spacecraft, rejection for the disturbance, and active damping for the sloshing. Its effectiveness is validated by numerical simulations.

Effects of time delay on an active vibration control of a forced and Self-excited nonlinear beam

Loop delays are taken into our consideration when positive position feedback controller is used to control the vibrations of forced and self-excited nonlinear beam. External excitation is a harmonic excitation caused by support motion of the cantilever beam. Self-excitation is caused by fluid flow and modeled by a nonlinear damping with a negative linear part (Rayleigh’s function). The multiple timescales perturbation technique is applied to obtain a first-order approximate solution. Effects of time delay on the system are extensively studied, and optimal conditions for the system operation are deduced. The equilibrium solution curves are plotted for several values of controller parameters. The stability of the steady-state solution is investigated using frequency-response equations. The analytical results are validated by numerical integration of the original closed-loop system model equations, time histories and Poincare map for the system. We realized that all predictions from analytical solutions are in good agreement with the numerical simulation.

Integrated Control of Thermally Induced Vibration and Quasi-Static Deformation of Space Truss

Dynamic vibration and quasi-static deformation will occur simultaneously for flexible space structures subjected to sudden thermal loads. In this paper, the integrated controller based on modified positive position feedback (PPF) compensator is proposed as an innovative controller for active deformation reduction in flexible space trusses. The controller uses the concept of positive acceleration feedback combined with integral position feedback to provide effective vibration suppression of multiple modes and compensator of quasi-static deformation. To solve the problem of placement optimization for both sensors and actuators, the discrete glowworm swarm optimization (GSO) algorithm based on genic binary coding is suggested. A cantilevered truss is taken as an example for numerically evaluating the performance of the controller for thermally induced deformation control. Numerical results demonstrate that the discrete GSO algorithm is feasible in solving the combinatorial optimization problem. And the proposed controller is significantly effective in controlling both steady-state deformation and transient vibration.

Experiments on vibration control of a piezoelectric laminated paraboloidal shell

A paraboloidal shell plays a key role in aerospace and optical structural systems applied to large optical reflector, communications antenna, rocket fairing, missile radome, etc. Due to the complexity of analytical procedures, an experimental study of active vibration control of a piezoelectric laminated paraboloidal shell by positive position feedback is carried out. Sixteen PVDF patches are laminated inside and outside of the shell, in which eight of them are used as sensors and eight as actuators to control the vibration of the first two natural modes. Lower natural frequencies and vibration modes of the paraboloidal shell are obtained via the frequency response function analysis by Modal VIEW software. A mathematical model of the control system is formulated by means of parameter identification. The first shell mode is controlled as well as coupled the first and second modes based on the positive position feedback (PPF) algorithm. To minimize the control energy consumption in orbit, an adaptive modal control method is developed in this study by using the PPF in laboratory experiments. The control system collects vibration signals from the piezoelectric sensors to identify location(s) of the largest vibration amplitudes and then select the best two from eight PVDF actuators to apply control forces so that the modal vibration suppression could be accomplished adaptively and effectively.

Adaptive robust attitude control and active vibration suppression of flexible spacecraft

This paper presents the large angle attitude manoeuvre control design of a single-axis flexible spacecraft system that consists of a central rigid body and a cantilever beam with bonded piezoelectric sensor/actuator pairs as a flexible appendage. The proposed control strategy combines the attitude controller designed by the adaptive robust control technique with the active vibration controller designed by the positive position feedback control method. The desired angular position of the spacecraft is planned and an adaptive robust attitude control approach based on a projection type adaptation law is proposed to track the planned path and to achieve precise attitude manoeuvre control. Meanwhile, the positive position feedback control method is applied to actively increase the damping of the flexible appendage and to suppress the residual vibration induced by manoeuvre. Improved transient and steady state performance during and after large angle attitude manoeuvre can be both achieved by integration of the technical merits of all these control methods. Analytical and numerical results illustrate the effectiveness of this approach.

Embedded explicit model predictive vibration control

This article presents an embedded active vibration suppression system featuring real-time explicit model predictive control (EMPC) that is implemented on a microcontroller unit (MCU). The EMPC controller minimizes the tip deflection of an aluminum cantilever beam driven by piezoceramic actuators, gaining its feedback from direct position measurements. The output and input performance of the EMPC method is compared to an analogously tuned positive position feedback (PPF) controller. An extensive analysis is provided on the cycle timing and memory needs of the explicit predictive vibration control scheme. The results demonstrate that the EMPC controller may achieve the same vibration suppression results compared to PPF with less input effort, while inherently respecting process constraints. Furthermore, we show that EMPC task execution timing is comparable in the random access memory (RAM) and read only memory (ROM) alternatives, suggesting that numerous current microcontrollers are suitable for EMPC-based active vibration control, in case the prediction model is kept simple.

Response analysis and energy transmissibility of a vibration isolation system with real-power nonlinearities under a NMPPF controller

In this paper, the nonlinear modified positive position feedback (NMPPF) scheme and the real-power form of restoring and damping forces are combined to improve the response performance of a vibration isolation system. Based on the method of multiple scales, the frequency response, the stability and the energy transmissibility of the real-power vibration isolation system are studied. It is found that the controlled isolation system exhibits a softening behavior for sub-linear restoring force, while it exhibits the two peak response characteristic rather than a hardening behavior for over-linear restoring force. Further, the sensitivity of the feedback parameters on the responses is discussed. The results, compared to the conventional PPF and IRC methods, show that the proposed method is significantly more effective in controlling the steady-state response, and slightly advantageous for the steady-state dynamics control. The effectiveness of this method is also verified by time domain analysis. Then, the suitable feedback and controller parameters are derived by simulation results in which the amplitude peak is suppressed and the resonance stability is maintained. Finally, the energy transmissibility of the vibration isolation system is investigated. The results show that the feedback gain can reduce the whole transmissibility level and greatly suppress vibration in the resonance region, and the existence of the nonlinear real-power stiffness term leads to the critical value for the appearance of the negative value become larger.

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.

Active vibration control of plates using positive postion feedback control with PZT actuators

In this study, the active vibration control of clamped plates using a positive position feedback (PPF) controller with a sensor/moment pair actuator (non-collocation configuration) is considered. To identify the characteristics of the PPF control system, a numerical parametric studies is conducted. The design parameters (gain and damping ratio) of the PPF controller are shown to have a significant effect on the stability and performance of the control system. Using these results, a multi-mode (first and second mode) single-input single-output (SISO) PPF controller is implemented. Two PPF controllers are connected in parallel with the SISO configuration. The final designed multi-mode PPF controller showed good conditional stability and high performance. The vibration levels at the tuned modes are reduced by about 5 dB. Finally, the performance of the PPF controller is experimentally verified. The disturbance levels at the target modes can be reduced by about 5 dB, nearly the same as the theoretical result.

Active vibration control of structures using a leader–follower-based consensus design

This paper proposes a new leader–follower-based consensus vibration controller to actively suppress unwanted oscillations in distributed-parameter flexible structures. Actuation and sensing is performed via piezoelectric layers in a collocated sense. The actuator/sensor patches for the vibration control system are considered to collaborate in a network, and follow a virtual leader which is accessible to all agents. Hence, a vibration controller law is defined, to remove disagreement between agents and force the agents to follow the virtual leader. The proposed approach is an observer-based design, in which an optimal consensus state estimator is initially designed. Stability of the closed-loop system is investigated and the optimality conditions of the system are derived. Although the designed vibration controller could be implemented for suppression tasks in different distributed-parameter systems, a flexible clamped-clamped beam is used here for equation derivation and numerical performance verification. According to the results, the optimal observer estimates the system states in a finite time, as expected, and the vibration controller suppresses unwanted oscillations, either in resonant or arbitrary form, to a much lower level; while the disagreement between agents converges to zero. Additionally, suppression performance and robustness of the controller to failure in control system elements is investigated in comparison with a conventional positive position feedback controller, and its superiority is illustrated and discussed.

Suppression of Vibrations of a Forced and Self-excited Nonlinear Beam by Using Positive Position Feedback Controller PPF

Suppression of Vibrations of a Forced and Self-excited Nonlinear Beam by Using Positive Position Feedback Controller PPF

Multi positive feedback control method for active vibration suppression in flexible structures

This paper presents a novel controller for active vibration reduction in piezoelectric-actuated flexible structures. The new Multi Positive Feedback (MPF) control consists of two sections where each operates using a set of actuators. One section uses position and the other uses velocity feedback to perform real-time vibration control. The 90° phase difference between the feedbacks leads to non-zero resultant control output. This property results in a more effective operation of the available actuators. Sections of the MPF controller are designed based on the concept of the Modified Positive Position Feedback (MPPF) control approach, where the damping of the control system is increased by addition of a first-order term parallel to a second-order compensator. The controller is designed to simultaneously control single or multi resonant frequency vibrations. Due to the high influence of gain values on the control performance, H2 and H∞ norms are used to optimize these gains. For validation purposes, the controller is verified here numerically and experimentally for vibration control of a clamped–clamped beam and a cantilever at resonance. According to the results, the MPF controller has a superior performance compared to the MPPF controller, in addition to effective suppression on both vibration displacement and velocity. Using the MPF controller in multimode and by utilizing the H∞ gain optimization method, vibration displacement amplitudes were reduced to 19.4% of the uncontrolled state for the beam.

Vibration control of beams subjected to a moving mass using a successively combined control method

This study addresses the vibration control of beams subjected to a moving mass, which represent real applications such as vehicle–bridge interaction. Positive position feedback control (PPF) which has been successfully used in vibration control of flexible structures is found not suitable for the current control problem when the moving mass is travelling on the beam as it makes the structure more flexible but is found capable of reducing free vibration after the moving mass leaves the beam. Sliding mode control (SMC) is known to be a robust method to deal with parameter uncertainties and disturbances in vibration, however it is found to be likely to introduce some higher-frequency vibration which is detrimental to the beam. A method combining SMC and PPF is proposed to suppress the vibration of the beam when the moving mass is on and off the beam, which overcomes the above problems and possesses the benefits of both SMC control and PPF control. Simulated numerical examples demonstrate the effectiveness of the proposed method.

Experiment on vibration control of a two-link flexible manipulator using an input shaper and adaptive positive position feedback

This article presents a novel approach for actively suppressing the vibration within a two-link flexible manipulator to adapt the variation in the model parameters, which is composed of an input shaper and multimode adaptive positive position feedback. Input shaper is applied to shape the command to avoid the flexible vibration in the manoeuvre motion, and the residual vibration can be suppressed by a piezo actuator with the adaptive positive position feedback approach. To demonstrate the approach, two sets of piezoelectric actuator/stain gauge sensor pairs are bonded to the surface of the two-link flexible manipulator; slewing of the flexible link induces vibrations in the link that persist long after the motors stop moving. Vibration suppression is achieved through a combined scheme of input shaper–based motor motion control and an adaptive positive position feedback–based piezo actuator controller. Experimental results show the effectiveness of the proposed approach and its suitability for implementation in an existing robot.

Nonlinear analysis of vertical conveyor with positive position feedback (PPF) controllers

In this paper, the two positive position feedback controllers (PPF) are used to reduce the vertical vibration in the vertical conveyors. An investigation is presented of the response of a four-degree-of-freedom system (4-DOF) with cubic nonlinearities and external excitations at primary resonance $$(\Omega _1 \cong \omega _1 ,\Omega _2 \cong \omega _2)$$ in the presence of 1:1 internal resonance $$(\omega _3 \cong \omega _1 ,\omega _4 \cong \omega _2)$$ . Method of multiple scales is applied to the equations of the system to find approximate analytical solutions. Then, we derived the frequency response equation and the stability criteria for the system. Numerical solution show that the time histories of the main system and the PPF controllers to present the response with and without control. The frequency response curves for the system and the controllers are studied numerically. To discuss the validity of the results, we make comparison between the analytical and numerical solutions and also compared them with the available published work.

Hybrid Positive Feedback Control for Active Vibration Attenuation of Flexible Structures

A new controller is introduced in this paper as a novel method for active vibration suppression in flexible structures. The hybrid positive feedback (HPF) uses a second- and a first-order compensator that are fed by the displacement and velocity feedbacks, respectively. Parallel pairs of the HPF controller are implemented when suppression in multimode condition is issued. Since the controller uses two gains for each pair of the actuator/sensor patch for each mode, a suitable gain optimization method has to be used to ensure the optimum performance. To this end, ${\cal H}_2$ and ${\cal H}_{\infty}$ optimization approaches are utilized. For validation purposes, the controller is verified numerically and experimentally for vibration control of a cantilever beam. System identification is performed, then closed-loop system responses to simultaneous multimode and swept frequency excitations are obtained. According to the results, the HPF controller has a superior performance compared to the conventional method of positive position feedback. Vibration displacement amplitudes were reduced by more than 85% relative to the uncontrolled state. The best performance was achieved by the ${\cal H}_2$ -optimized HPF, as the net value for vibration displacement amplitude reduction in the multimode condition was 90% of the uncontrolled amplitude.

Coupled flexural–torsional vibration of spinning smart beams with asymmetric cross sections

In this paper, the electrical–structural modeling and control electronics of spinning smart beams with distributed piezoelectric sensor and actuator layers are considered. The governing equations of beams with asymmetric cross sections have been formulated incorporating the warping effect and the influence of spinning. For the purpose of verification of the model established, numerical results are compared with those given in relevant literature. Effects of spinning on natural frequencies and mode shapes are investigated for the boom in solar array of Hubble Space Telescope. In order to control the vibration of the spinning beam whose natural characteristics are changed with respect to spinning velocity, the positive position feedback (PPF) compensator is applied. Numerical results showed that the PPF approach is effective in vibration suppression of spinning smart beams.