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This paper describes a novel time-delayed control scheme for suppressing the body-freedom flutter of a flexible flying-wing drone and verifies its robustness. The simple formulation and strong robu...

The roll-to-roll (R2R) web printing system is a complex coupling system, in which tension fluctuation is caused by upstream register control, thus results in downstream register errors. Therefore, it is indispensable to compensate for the couplings in order to improve the register precision in R2R printing systems. However, existing control methods do not realize complete decoupling due to their indirect calculation of compensations for the register errors. In this article, a mechanical model is set up to represent the direct relationship between the downstream register errors and all their upstream register controls. According to the model, compensation is calculated on the basis of the Lyapunov stability theorem to converge the register errors to zero. Then, a direct-decoupling closed-loop control method with first-order compensation terms, i.e., the direct-decoupling proportional derivative control (DDPD), is proposed to completely compensate for the couplings between all upstream register controls and downstream register errors. In addition, the first-order expression of the compensation makes it easy to implement in industrial applications. An industrial example indicates that the proposed control method eliminates the couplings and maintains the range of register errors within ±0.06 mm. Note to Practitioners —This article proposes a control strategy for the roll-to-roll (R2R) printing system, particularly for printing systems with electronic line shafts. Few existing studies have been done in detailedly analyzing the upstream register controls and the downstream register errors. This article establishes a mechanical model of printing registration and gives a systematic analysis of the complete relationship between upstream register controls and downstream register errors and then proposes a control strategy based on the Lyapunov stability analysis. The proposed method can be extended to other similar R2R systems. Simulation and industrial examples show that the control method is more feasible and effective compared with the existing methods. In future work, we will study a control method combined with the mechanical model and data model in different R2R systems.

This paper presents a proportional-derivative protocol for the consensus problem of a class of linear second-order multi-agent systems with local information transmission. The communication topology among the agents is switching and agents receive information within a critical bounded distance. As new observations, we show that the desired protocol system undergoes consensus and swarming behaviours when 1 is a simple eigenvalue of the adjacency matrix. In this case, both final velocity and final relative position are formulated. Simulation results show the effectiveness of the proposed protocol.

A robust landing control algorithm is proposed for a quadcopter, as well as for a landing platform to land on an inclined or problematic surface. To use the quadcopter for outdoor application, it is necessary to design a landing platform that can withstand environmental obstacles such as wind and weight load during landing. Conventional retractor landing platforms are not suitable for achieving a stable landing on inclined surfaces or obstacles. Therefore, in this paper, 2-link structured landing legs are applied to stably land on an inclined surface or obstacle with a suitable control algorithm. To achieve stable landing on a slanted surface, a cooperative control algorithm of the quadcopter and the landing platform has been proposed. The proposed robust landing system comprises two controllers, i.e., a high-speed proportional derivative control for the landing platform and a neural network-based proportional–integral–derivative control for controlling the quadcopter in real time. A quadcopter with a robust landing platform has been implemented, and the performance of the robust landing control algorithm has been demonstrated with the system.

A rotating beam at varying speed mathematical model is studied. Multiple time scales method is applied to the nonlinear system of differential equations and investigated the system behavior approximate solution in the instance of resonance case. We studied the system in case of applying the delayed control on the displacement and the velocity with Proportional–derivative (PD) controller. The consistency of the steady state solution in the near-resonance case is reviewed and analyzed using the Routh-Huriwitz approach. The factors on the steady state solution of the various parameters are recognized and discussed. Simulation effects are obtained using MATLAB software package. Different response curves are involved to show and compare controller effects at various system parameters.

In this paper, we aim to propose a novel $ q $-fractional derivative in the Caputo sense included proportional derivative. To this end, we firstly introduced a new concept of proportional $ q $-derivative and discussed its properties in detail. Then, we add this definition in the concept of Caputo derivative to state a new type of dynamical system with $ q $-calculus. For analytically solving this system, $ q $-Laplace transform has been successfully applied to obtain the solutions. Indeed, the bivariate Mittag-Leffler function has an essential role in this regard. Two illustrative examples are also given in detail.

In view of the problems that the analytical inverse system decoupling method of bearingless induction motor is sensitive to the change of motor parameters and is greatly affected by unmodeled dynamics, and that of traditional proportional–derivative controller lacking the self-adaptive regulation ability, a neural network inverse system decoupling fuzzy self-tuning proportional–derivative control strategy is proposed for a bearingless induction motor system. First, under the conditions of considering the stator current dynamic of torque winding, and by neural network inverse system method, the bearingless induction motor system is decoupled into four pseudo-linear integral subsystems. Second, the traditional proportional–derivative controller is improved, and the fuzzy control algorithm is used to adjust the parameters of improved proportional–derivative controller adaptively. Thus, a neural network inverse system decoupling fuzzy self-tuning proportional–derivative control system is constructed for a bearingless induction motor. The simulation experimental results show that the proposed control strategy not only can effectively improve the stability, robustness and steady-state control accuracy of bearingless induction motor system, but also can significantly improve the dynamic response speed and the ability to resist the influences of motor parameter change and load disturbance.

International audience; This paper deals with the design, improvement, and implementation of a nonlinear control strategy to solve the tra-jectory tracking problem for an autonomous underwater vehicle under model uncertainties and external disturbances. First, a disturbance observer based on high-order sliding mode control is designed to counteract the negative impact of both parametric uncertainties and bounded external disturbances. Then, the nonlinear control is enhanced through injecting the disturbance estimation into the designed controller. The stability of the closed-loop system with the enhanced proposed nonlinear controller is proven by Lyapunov arguments. Finally, real-time experimental results are also provided to demonstrate the effectiveness of the proposed controller.

This paper provides optimum analytical tuning rules to determine tuning parameters of Integral-Proportional Derivative (I-PD) controllers for controlling integrating processes with inverse response and time delay. Integral performance criteria, such as ISTE (integral of squared time error), IST2E (integral of squared time2 error) and IST3E (integral of squared time3 error), are used to derive mentioned optimum tuning rules. The effectiveness of the proposed I-PD controller design method are shown by simulation examples. Comparisons with design methods existing in the literature, in terms of set point tracking and disturbance rejection capability, are performed to see the use of the proposed I-PD controller. Some performance measures are also given to evaluate the closed loop performances. It has been observed that the proposed I-PD controller has some important advantages over design methods used for comparison.

This paper intends to tune fractional order proportional derivative controller for the performance, stability and robustness of second order plus time delay plant. The tuning method is based on the previously proposed “frequency frame” which is a rectangular frame enclosing gain and phase margins limited with gain and phase crossover frequencies in the Bode plot. Edges of the frame are tuned to achieve desired crossover frequencies and margins. By shaping the curves of the Bode plot, improvements are observed in the performance and robustness of the second order plus time delay system controlled by a fractional order proportional derivative controller. Generalized equations to obtain the parameters of the fractional order proportional derivative controller for second order plus time delay plant are given. In contrast to existing studies, this method reduces mathematical complexity when providing desired properties. Three examples are considered and effectiveness of the frequency frame is shown.

The present paper introduces a novel minimal control-effort and control-time, proportional-derivative feedback control theory for second-order dynamical systems on Lie groups. The devised control t...

The present study deals with the nonlinear analysis of electrostatic micro-electro-mechanical systems resonators with two symmetric electrodes and subjected to delayed proportional–derivative controller. After a brief description of the model, the stability analysis of the linearized system is presented to depict the stability charts in the parameter space of proportional gain and time delay. The bifurcation diagram is used to confirm the existence of the delay-dependent and delay-independent regions and to analyze the effect of proportional–derivative gains and time delay on the dynamics of the system. Using Melnikov’s theorem, the criterion for the appearance of horseshoe chaos from homoclinic and heteroclinic bifurcations is presented. Melnikov’s predictions are confirmed by using the numerical simulations based on the basin of attraction of initial conditions. It is found that the increase in proportional gain contributes to increase the region of regular motion in both bifurcations. However, the increase in derivative gain contributes rather to reduce the region of regular motion for homoclinic bifurcation, although it increases rather this region in the case of heteroclinic bifurcation. Moreover, it is also observed, depending on proportional–derivative gains, the existence of a critical value of the delay where before it, the region of regular motion increases and after it, decreases rather.

The proportional-derivative sliding-mode control will be designed and tuned in the trajectory tracking of a robot manipulator which operates on uncertain dynamic environments. For achieving these goals, first, a linear matrix inequality–based framework is suggested to design a robust proportional-derivative sliding-mode control in the presence of external disturbances. Next, the parameters of the proportional-derivative sliding-mode control law will be tuned via another minimization problem subjected to some linear matrix inequality constraints. Thus, the controller parameters can be automatically updated via the solution of the optimization problem. The results are successfully used in the robot manipulator with considering two reference paths and some different loads. The simulation results show the effectiveness of the proposed method in comparison with the same technique.

To suppress the high frequency noise in resonant micro optic gyroscope, this paper proposes a reduced sampling rate proportional-derivative control loop. Simulation results show that the loop bandwidth is broaden to 19.3 kHz.

In this study the nonlinear dynamics of an asymmetrical rotating shaft is investigated. The high-static-low dynamic stiffness are used. Also, the active time-delayed proportional derivative control...

This paper deals with an admissibilization problem of singular systems with uniform input quantization. The aim is to design a controller to guarantee the admissibility of the closed-loop system. To achieve this, this paper proposes a proportional-derivative state-feedback controller which includes non-linear control part to reject the effect of uniform input quantization. Based on the proposed controller, sufficient conditions are obtained in terms of linear matrix inequalities. Two examples show the feasibility of the proposed controller.

Subsystems of Russian automatic excitation regulators that ensure the maximum dynamic stability and effective damping of oscillations in an electric power system are described. They are compared to stabilizers included in international and national standards of other countries. It is shown that the Russian system stabilizer PSS2RU is effective in oscillation damping in various circuits and modes.

This paper deals with analyzing a newly introduced method for tuning of fractional order &#x005B proportional derivative &#x005D &#x0028 FO&#x005B PD &#x005D &#x0029 controllers to be used in motion control. By using this tuning method, not only the phase margin and gain crossover frequency are adjustable, but also robustness to variations in the plant time-constant is guaranteed. Conditions on the values of control specifications &#x0028 desired phase margin and gain crossover frequency &#x0029 for solution existence in this tuning method are found. Also, the number of solutions is analytically determined in this study. Moreover, experimental verifications are presented to indicate the applicability of the obtained results.

Feeding a controller with acceleration signal can improve system robustness and relative stability. However, neither measurements of acceleration signals nor velocity signals are available in most ...

International audience; This article focuses on the root behavior of the characteristic function of some LTI SISO systems controlled by a PD-control when a delay-difference operator is used to approximate the derivative action. We will focus on the cases when the corresponding stability problem is improperly posed for “small” delay values. In this context, we will express the solutions of the corresponding characteristic function as power series and exploit their structure in deriving the asymptotic behavior of the characteristic roots. This analysis will allow detecting and explicitly characterizing the cases when delay-difference approximations lead to improperly posed stability problems. Furthermore, in the case when the derivative approximation guarantees the properly posedness of the closed-loop system, the robustness of the scheme with respect to the delay margin of the delay-difference approximation and control gains parameters are explicitly addressed. More precisely, upper bounds on the delays as well as the robustness of the corresponding controller are computed. Some illustrative examples complete the presentation.

This paper presents the development of vision-based robotic arm manipulator control by applying Proportional Derivative-Pseudoinverse Jacobian (PD-PIJ) kinematics and Denavit Hartenberg forward kinematics. The task of sorting objects based on color is carried out to observe error propagation in the implementation of manipulator on real system. The objects image captured by the digital camera were processed based on HSV-color model and the centroid coordinate of each object detected were calculated. These coordinates are end effector position target to pick each object and were placed to the right position based on its color. Based on the end effector position target, PD-PIJ inverse kinematics method was used to determine the right angle of each joint of manipulator links. The angles found by PD-PIJ is the input of DH forward kinematics. The process was repeated until the square end effector reached the target. The experiment of model and implementation to actual manipulator were analyzed using Probability Density Function (PDF) and Weibull Probability Distribution. The result shows that the manipulator navigation system had a good performance. The real implementation of color sorting task on manipulator shows the probability of success rate cm is 94.46% for euclidian distance error less than 1.2 cm., Comment: The manuscript published in Jurnal Elektronika dan Telekomunikasi (JET), Vol. 21, No. 1, August 2021, pp. 8-18

This paper suggests to replace PIs and PIDs, which play a key role in control engineering, by intelligent Proportional-Derivative feedback loops, or iPDs, which are derived from model-free control. This standpoint is enhanced by a laboratory experiment., Comment: Accepted in "International Journal of Robust and Nonlinear Control"