Linear Velocity Feedback Research Articles

Differentiator‐based bearing‐only formation control of quadrotors

AbstractThis article addresses the leader‐follower formation control problem for a group of quadrotors using only relative bearing measurements. Most existing methods require full position or velocity information, which cis challenging to obtain in harsh environments. In contrast, the proposed control scheme is based on a hierarchical system that does not rely on relative position or velocity measurements. The bearing‐only control law is designed to stabilize the desired formation, and each quadrotor maintains predetermined bearings with its neighbors. The control design relies on a non‐singular extraction algorithm for separate design of translation and rotation control. The outer loop of the control scheme utilizes a filter‐like approach to overcome the lack of bearing rate measurements in the bearing‐only formation controller. Moreover, employing differentiators following the separation principle with properties of asymptotic high accuracy, a uniform differentiator is provided for each following quadrotor to overcome the absence of linear velocity and acceleration feedback in the inner‐loop controller. Ultimately, the efficacy of the proposed control strategy is validated through a combination of Lyapunov stability theory and extensive numerical simulations.

Dynamic modeling and control of hydraulic driven payload anti-swing system for shipborne cranes

Shipborne cranes are widely used in marine engineering and are employed in more diversified working scenes. However, due to the extensive swing range of ships, it is impossible to locate the payload accurately. A constant tension control method of payload anti-swing is proposed based on the principle of linear velocity feedback. This paper establishes a dynamic model of the payload anti-swing system driven by hydraulic motors. The characteristics of the payload swing and the cable tension are obtained through the dynamic simulation. The simulation and experimental results show that the constant tension control method significantly suppresses the shipborne crane’s payload swing, and the payload anti-swing effect reaches 73% and 85.6%. It is also found that the payload swings asymmetrically under external excitation. In addition, the effects of payload asymmetric swing on cable tension, payload swing angle, and the hydraulic pump output oil pressure are studied by a payload asymmetric swing experiment, and the results show that the proposed method also has a good suppression effect on the asymmetric payload swing.

A Homography-Based Visual Servo Control Approach for an Underactuated Unmanned Aerial Vehicle in GPS-Denied Environments

This paper proposes a homography-based visual servo control approach for the stabilization of underactuated unmanned aerial vehicles in GPS-denied environments. A virtual homography matrix is proposed, and a new visual error vector is defined to obtain the passivity-like visual error equation. In addition, a homography-based online translation velocity estimator and a nonlinear backstepping visual servo control approach are addressed to promote fast maneuvering without linear velocity feedback. Unlike conventional homography-based visual servo control solutions that only guarantee the local stability in the equilibrium, the proposed control scheme can get the global stability in large offset. Simulation and experimental tests with a realistic quadrotor subject to the measurement noise are carried out to verify the robustness and performance of the control approach. In addition, the autonomous tracking experiment when the target speed is unpredictable are also reported.

Scalable all-optical cold damping of levitated nanoparticles.

Motional control of levitated nanoparticles relies on either autonomous feedback via a cavity or measurement-based feedback via external forces. Recent demonstrations of the measurement-based ground-state cooling of a single nanoparticle employ linear velocity feedback, also called cold damping, and require the use of electrostatic forces on charged particles via external electrodes. Here we introduce an all-optical cold damping scheme based on the spatial modulation of trap position, which has the advantage of being scalable to multiple particles. The scheme relies on programmable optical tweezers to provide full independent control over the trap frequency and position of each tweezer. We show that the technique cools the centre-of-mass motion of particles along one axis down to 17 mK at a pressure of 2 × 10-6 mbar and demonstrate its scalability by simultaneously cooling the motion of two particles. Our work paves the way towards studying quantum interactions between particles; achieving three-dimensional quantum control of particle motion without cavity-based cooling, electrodes or charged particles; and probing multipartite entanglement in levitated optomechanical systems.

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.

Distributed Formation Control of Quadrotor UAVs Based on Rotation Matrices without Linear Velocity Feedback

Distributed Formation Control of Quadrotor UAVs Based on Rotation Matrices without Linear Velocity Feedback

Modeling and Simulation of Feedback based Linear Electromechanical actuator

An actuator is a device that which provides control over certain automation systems and also provides tuning in movement or positioning in various applications like manufacture of valves, motor, wastewater treatment plants, onboard electronics based on the type of configuration of type of actuators. Out of the available types of actuators, linear Electro Mechanical Actuators (EMA) is a powerful and advanced tool which provides optimal solution for the field of automation, various applications where high speed, high precision with control are required. This paper proposes to have velocity feedback system to entire function of EMA’s in order to improve its functionality, and thus enhances the efficiency. This paper also proposes modeling and simulation of normal conventional linear Electro Mechanical Actuator and velocity feedback controlled EMA and compares the results in MATLAB/SIMULINK.

Effect of time delay on the generation of oscillation in a single degree-of-freedom mass-spring-damper system by nonlinear velocity feedback

The present paper investigates the effect of time delay in a particular type of single degree-of-freedom self-excited oscillator. The self-excited vibration is generated in the system by using linear velocity feedback (to destabilize the static equilibrium of the system) with a nonlinear Rayleigh type feedback (to limit the growth of the instability into a stable limit cycle). The general method of describing function is employed to study the dynamics with the presence of time delay. Also, the analytical results are verified with the simulation result. Without time delay, the control law can generate a stable limit cycle with the proper choice of control parameters. However, the presence of time delay introduces a globally unstable limit cycle in the system with a stable one. Though the amplitude of the stable limit cycle dies down with the increase of time delay and finally vanishes by stabilizing the static equilibrium of the system. The effect of control parameters is also studied.

Measurement of added mass for an object oscillating in viscous fluids using nonlinear self-excited oscillations

In this study, a method of measuring the added mass for an object oscillating in a viscous fluid using nonlinear self-excited oscillations was developed. The added mass produces an additional inertial effect on the vibrating object. In previous methods, the added mass is obtained experimentally from the response frequency and amplitude at the peak in the frequency response curve under a harmonically forced excitation. However, such methods cannot be utilized in highly viscous environments because the peak becomes ambiguous as a result of damping. Moreover, in very high-viscosity environments, the resonance peak ceases to exist in the frequency response curves. To solve this problem, self-excited oscillations were induced in the system using linear velocity feedback. Because linear velocity feedback can be used to eliminate the viscous damping effect when the linear feedback gain is set near the Hopf bifurcation point related to self-excited oscillations, the object becomes self-excited at a frequency equal to the natural frequency of the object oscillating in a vacuum, i.e., the undamped natural frequency. What distinguishes the proposed method from the abovementioned previous methods is that the value of the response is not needed; however, a reduction in the oscillation amplitude is required to obtain accurate measurement results. In the proposed method, to avoid an increase in the response amplitude under the applied linear velocity feedback, nonlinear feedback is also applied to produce a limit cycle similar to that produced in a van der Pol oscillator. A prototype of the measurement system was constructed based on the proposed method. A comparison of the experimentally and theoretically obtained added mass values confirmed the validity of the proposed method for added mass sensing.

Identification method for backbone curve of cantilever beam using van der Pol-type self-excited oscillation

This study presents an experimental method for identification of the backbone curves of cantilevers using the nonlinear dynamics of a van der Pol oscillator. The backbone curve characterizes the nonlinear stiffness and nonlinear inertia of the resonator, so it is important to identify this curve experimentally to realize high-sensitivity and high-accuracy sensing resonators. Unlike the conventional method based on the frequency response under external excitation, the proposed method based on self-excited oscillation enables direct backbone curve identification, because the effect of the viscous environment is eliminated under the linear velocity feedback condition. In this research, the method proposed for discrete systems is extended to give an identification method for continuum systems such as cantilever beams. The actuation is given with respect to both the linear and nonlinear feedbacks so that the system behaves as a van der Pol oscillator with a stable steady-state amplitude. By varying the nonlinear feedback gain, we can produce the self-excited oscillation experimentally with various steady-state amplitudes. Then, using the relationship between these steady-state amplitudes and the corresponding experimentally measured response frequencies, we can detect the backbone curve while varying the nonlinear feedback gain. The efficiency of the proposed method is determined by identifying the backbone curves of a macrocantilever with a tip mass and a macrocantilever subjected to atomic forces, which are representative sources of hardening and softening cubic nonlinearities, respectively.

Mass sensing using a virtual cantilever virtually coupled with a real cantilever

Mass measurements based on the eigenmode shift of coupled cantilevers provide much higher sensitivity than the method based on the natural frequency shift of a single cantilever. The essence of the former method is that the two cantilevers are identical and are weakly coupled. However, in practical coupled cantilevers, these requirements cannot be satisfied completely because of the limitations of machining accuracy. To realize the advantages of this method fully, we propose the concepts of a “virtual cantilever” and “virtual coupling.” In the proposed method, one of the real cantilevers is replaced with a virtual cantilever that is virtually coupled with the remaining real cantilever. The virtual cantilever dynamics and the effect of coupling on the real cantilever are thus calculated in real-time using a digital computer, and the real cantilever is also actuated in real-time based on the coupling effect obtained. By adjusting the virtual cantilever's physical parameters to match those of the real cantilever while tuning the virtual coupling stiffness to be low in the digital scheme, identical real and virtual cantilevers and the weak coupling required can be realized. Additionally, to produce self-excitation with a steady-state amplitude, we apply the linear and nonlinear velocity feedback control technique that was proposed in our previous study for the above system. We confirm the validity of the virtual cantilever and virtual coupling concepts proposed for mass sensing experimentally using a real single macrocantilever and a virtual cantilever virtually coupled with the real cantilever as a prototype.

Two-dimensional vortex-induced vibration suppression through the cylinder transverse linear/nonlinear velocity feedback

Suppressing vortex-induced vibration (VIV) has recently attracted numerous researchers due to its practical significance in many engineering applications. Most of the previous studies have focused on a passive or active flow control. A structurally active control approach to mitigate a two-dimensional, nonlinear coupled, cross-flow/in-line VIV has not been well studied. This paper presents a reduced-order fluid-structure dynamic model and combined analytical–numerical solutions for the efficient suppression of two-dimensional VIV of a flexibly mounted circular cylinder in uniform flows. The theoretical model is based on the use of coupled Duffing–Rayleigh oscillators with three variables describing the cylinder cross-flow/in-line displacements and the strength of the fluid vortex circulation in the cylinder wake. These equations of fluid-structure motions contain geometric and hydrodynamic nonlinearities. Closed-loop linear and nonlinear velocity feedback controllers are implemented in the transverse direction governing the larger cross-flow response than the associated in-line counterpart. Approximated analytical expressions are derived by using the harmonic balance to explicitly capture the system nonlinear dynamic features and the effects of key dimensionless parameters. Parametric investigations are carried out to evaluate the linear versus nonlinear controller performance in terms of the maximum response suppression capability and the power requirement in a wide range of reduced flow velocities, mass ratios, and control gains. Over the main lock-in resonance region with coupled cross-flow/in-line responses, the linear controller is found to be more efficient in suppressing the two-dimensional VIV by also modifying the system frequencies and phase relationships. Nevertheless, based on the power comparison, the nonlinear control is superior to the linear control for very small targeted controlled amplitudes of a very low-mass cylinder. These active control strategies may be further applied to the multimode VIV suppression of a long flexible cylinder with multi degrees of freedom.

Four-wheel Rover’s Motion Control and Modeling Method

The control and modeling problem of four-wheel rover is studied under lunar soft soil and low gravity. The Newton - Euler dynamic model of the four-wheel rover is established by constructing the D-H coordinate system of the rover and gets the value of the wheel angular velocity, and the steering angle is determined by the method of non-holonomic constraints. A closed-loop motion control system for linear velocity and angular velocity feedback regulation of rover is designed and realized by combining the model of wheel terrain mechanics. The experimental results show that the dynamic characteristics of the rover in the process of cruise and the designed motion control system can effectively reduce the disturbance of the external terrain environment and realize the tracking control of the rover linear velocity and angular velocity.

Suppression of two-dimensional vortex-induced vibration with active velocity feedback controller

Vortex-induced vibrations (VIV) establish key design parameters for offshore and subsea structures subject to current flows. Understanding and predicting VIV phenomena have been improved in recent years. Further, there is a need to determine how to effectively and economically mitigate VIV effects. In this study, linear and nonlinear velocity feedback controllers are applied to actively suppress the combined cross-flow and in-line VIV of an elastically-mounted rigid circular cylinder. The strongly coupled fluid-structure interactions are numerically modelled and investigated using a calibrated reduced-order wake oscillator derived from the vortex strength concept. The importance of structural geometrical nonlinearities is studied which highlights the model ability in matching experimental results. The effectiveness of linear vs nonlinear controllers are analysed with regard to the control direction, gain and power. Parametric studies are carried out which allow us to choose the linear vs nonlinear control, depending on the target controlled amplitudes and associated power requirements.

Using negative velocity feedback controller to reduce the vibration of a suspended cable

The system of suspended cable with mixed excitation forces is controlled in this paper by using negative linear velocity feedback controller. The equations of motion of this system contain quadratic and cubic nonlinearities. The multiple scale perturbation technique is applied to determine the response of the nonlinear system near the simultaneous sub-harmonic and combined resonance case of this system. The stability of the obtained numerical solution is investigated using frequency response equations. The effect of different parameters on the vibrating system are investigated and reported.

Erratum to: Measurement of softening cubic nonlinear and negative linear stiffness using van der Pol type self-excited oscillation

In this paper, a stiffness sensor for measuring the softening cubic nonlinear and negative linear stiffness is developed. The measurement system consists of a measurement object, an oscillator and a feedback circuit, and achieves the dynamics of van der Pol oscillator by the positive linear velocity feedback and the nonlinear feedback proportional to the squared position and the velocity. Then, the tuning of the nonlinear feedback gain can realize any setting of the magnitude of the response amplitude. Therefore, from the relationship between response amplitudes set by various nonlinear feedback gains and the corresponding response frequencies, we can experimentally describe the backbone curve which exhibits the dependency of the natural frequency on the amplitude in nonlinear mechanical systems. It has been experimentally verified by our research group that the hardening cubic nonlinear and positive linear stiffness can be measured by using the backbone curve. In this research, we assess the potential for measuring the softening cubic nonlinear and negative linear stiffness by employing a magnetic attraction model. The softening cubic nonlinear and negative linear stiffness are also measured by setting the sign of the coefficient of the nonlinear feedback gain appropriately to produce the stable limit cycle.

An improved time-delay saturation controller for suppression of nonlinear beam vibration

In this paper, a nonlinear saturation controller is improved by using quadratic velocity coupling term with time delay instead of the original quadratic position coupling term in the controller and adding a negative time-delay velocity feedback to the primary system. The improved controller is utilized to control the high-amplitude vibration of a flexible, geometrically nonlinear beam-like structure when the primary resonance and the 1:2 internal resonance occur simultaneously. To explain analytically mechanism of the saturation controlled system, an integral iterative method is presented to obtain the second-order approximations and the amplitude equations. It is shown that the quadratic velocity coupling term can enlarge the effective frequency bandwidth and enhance the performance of the vibration suppression by comparison with the quadratic position coupling term, and the linear velocity feedback can suppress the transient vibrations. The effects of different control parameters on saturation control are investigated. We found that time delays can be used as control parameters to change the effective frequency bandwidth and avoid the controller overload risk. The analyses show that numerical simulations are in good agreement with the analytical solutions.

Resonance and vibration control of two-degree-of-freedom nonlinear electromechanical system with harmonic excitation

The dynamics and chaos control of the two-degree-of-freedom nonlinear electromechanical system, in which the magnetic field is modeled as being time-varying (periodic in fact), will be investigated. The system is modeled by a coupled second-order nonlinear ordinary differential equations. Their approximate solutions are sought applying the method of multiple scales. A reduced system of four first-order ordinary differential equations is determined to describe the time variation of the amplitudes and phases of the vibration in the mechanical and electrical components of the considered model. The steady-state response and stability of the solutions for various parameters are studied numerically, using the frequency response function and the time-series solution. Effects of system parameters including external forces and time-varying magnetic field on the solutions of nonlinear equations are investigated numerically. The amplitudes have maximum peaks at the simultaneous primary resonance case $$({\varOmega } = \omega _{1}=\omega _{2}=\omega =1.0)$$ and hence is considered as the worst resonance case of the system behavior. It can be seen that the best control law is the negative linear velocity feedback. Comparison between numerical solution and perturbation solution is obtained.

Erratum to: Active vibration control of a dynamical system via negative linear velocity feedback

Erratum to: Active vibration control of a dynamical system via negative linear velocity feedback

Active vibration control of a dynamical system via negative linear velocity feedback

In this paper, a negative velocity feedback is added to a dynamical system which is represented by second-order nonlinear differential equations having quadratic coupling, quadratic, and cubic nonlinearities. The system describes the vibration of the system subjected to multi-parametric excitation forces. The method of multiple scale perturbation technique is applied to obtain the response equation near the simultaneous internal and super-harmonic resonance case of this system. The stability to the system is investigated applying frequency response equations. The numerical solution and the effects of some parameters on the vibrating system are investigated and reported. The simulation results are achieved using MATLAB 7.0 program. A comparison is made with the available published work.