Proportional Derivative Control Scheme Research Articles

Decentralized Control and Obstacle Avoidance in Autonomous Cooperative Transport System

Autonomous cooperative transport has been a receptive research hotspot for decades. The main concern is to find the effective coordination among autonomous agents to perform the task in order to achieve overall performance accuracy. In this paper, a multi-robot system performing a payload manipulation task where the participating robots do not have any knowledge regarding other robots in the system or the payload dynamics is considered. A decentralized proportional-derivative control strategy by which the multi-robot system can organize itself and adapt dynamically to changing circumstances is proposed. The decentralized controller is augmented with an orientation control by which the payload in transport attains a desired angular orientation at the target location. An obstacle avoidance strategy using an artificial potential field method is incorporated to avoid any obstacle in its transport path. The transport systemis simulated with uniform and non-uniform distributions of robots around the payload, for transportation as well as obstacle avoidance scenarios.

Spatiotemporal dynamics optimization of a delayed reaction–diffusion mussel–algae model based on PD control strategy

The dynamic control over time evolution of ordinary differential systems has developed rapidly in recent years, but how to control the spatiotemporal evolution dynamics of partial differential systems is still an open question. Turing pattern is a major spatiotemporal evolution behavior in mussel-algal ecosystems and its control can pull the ecosystem back from the borderline of collapse and make it more stable. However, there has been relatively little research on the optimal control of Turing pattern in the mussel-algal system. In this paper, we first attempt to propose a proportional-derivative (PD) control strategy for the reaction–diffusion mussel–algae model under the influence of time delays. Turing instability driven by diffusion occurs in the diffusive mussel–algae model without control. The introduction of PD control can effectively suppress the occurrence of Turing instability and keep the ecological model stable in both time and space. When the time delay exceeds a critical value, the diffusive mussel–algae model will lose stability and undergo a Hopf bifurcation. PD controller can make Hopf bifurcation occur in advance or in hysteresis by changing the threshold point of Hopf bifurcation. The intrinsic mechanism of Hopf bifurcation is analyzed by means of the formal theory and the central manifold theorem. The numerical simulations demonstrate the efficiency and feasibility of the PD control scheme.

PID Control for Output Synchronization of Multiple Output Coupled Complex Networks

This article attempts to address output synchronization and <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> output synchronization problems for multiple output coupled complex networks (MOCCNs) under proportional-derivative (PD) and proportional-integral (PI) controllers. Firstly, two classes of MOCCNs without and with external disturbances are separately put forward. Secondly, based on the PD and PI control schemes, several output synchronization criteria for MOCCNs are formulated by using the Lyapunov functional method and inequality techniques. Thirdly, <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> output synchronization for MOCCNs is also studied with the help of the PD and PI controllers. Finally, two numerical examples are separately presented to demonstrate the validity of acquired theoretical results.

PD control for passivity of coupled reaction-diffusion neural networks with multiple state couplings or spatial diffusion couplings

This paper studies the passivity for coupled reaction-diffusion neural networks with multiple state couplings (CRDNNMSCs) or spatial diffusion couplings (CRDNNMSDCs) by employing the proportional-derivative (PD) control method. Firstly, a PD control strategy is presented for the sake of ensuring the passivity of CRDNNMSCs, and a synchronization condition is also given by utilizing the output-strict passivity of CRDNNMSCs. In addition, some corresponding conditions for guaranteeing the passivity and synchronization of CRDNNMSDCs are also developed in virtue of PD controller. Lastly, the correctness of the obtained passivity and synchronization criteria for the proposed models is verified by two numerical examples.

Robust adaptive fault‐tolerant proportional‐derivative tracking control for six‐degrees of freedom unmanned aerial vehicles

AbstractThis article presents a robust adaptive control scheme for six‐degrees of freedom (DOF) unmanned aerial vehicles (UAVs) in the presence of modeling uncertainties and actuation faults. The proposed control is in proportional‐derivative (PD) form, and is able to tolerate actuation faults yet ensure stability and transient performance without the need for the detail model information of UAV. Furthermore, the PD control scheme exploited adaptively self‐tuning PD gains, which avoids the ad‐hoc and time‐consuming trial and error process for gain determination as commonly required in traditional PD control, thus is design‐friendly and low‐cost, rendering the control algorithms easy and straightforward for programming and implementation. Both theoretical analysis and numerical simulation validate the effectiveness of the proposed control method.

Friction drag reduction based on a proportional-derivative control scheme

Dielectric barrier discharge plasma actuators (DBD-PAs) are deployed experimentally for the first time in a feed-forward proportional-derivative (PD) control system, where the fluctuating wall-pressure Pw is demonstrated to be an effective feed-forward signal, to manipulate a turbulent boundary layer for drag reduction. A floating-element force balance with an area of 50 mm (streamwise length) × 200 mm (spanwise length) is deployed to capture the spatially averaged drag variation behind the DBD-PAs. The DBD-PAs generate streamwise vortices, whose occurrence synchronizes with the output signal of the controller with a predominant frequency of 40 Hz under the optimally tuned PD control. The control system proves to be effective, achieving a spatially averaged drag reduction by 16%, and efficient, cutting down its energy consumption by 30% at a negligibly small expense of drag reduction compared with the open-loop control. It has been found that the optimally tuned PD control aptly increases the voltage applied to the DBD-PAs upon detecting large Pw fluctuations or coherent structures, accounting for the savings in input power, Pinput. The experimental data have been carefully analyzed, which cast light upon the underlying physical mechanism behind the drag reduction. The reason behind the efficient control is also clearly elaborated.

Stability and control of radial deployment of electric solar wind sail

The paper studies the stability and control of radial deployment of an electric solar wind sail with the consideration of high-order modes of elastic tethers. The electric solar wind sail is modeled by combining the flexible tether dynamics, the rigid-body dynamics of central spacecraft, and the flexible-rigid kinematic coupling. The tether deployment process is modeled by the nodal position finite element method in the arbitrary Lagrangian–Eulerian framework. A symplectic-type implicit Runge–Kutta integration is proposed to solve the resulting differential–algebraic equation. A proportional–derivative control strategy is applied to stabilize the central spacecraft’s attitudes to ensure tethers’ stable deployment with a constant spinning rate. The results show the electric solar wind sail requires thrust at remote units in the tangential direction to counterbalance the Coriolis forces acting on the tethers and remote units to deploy tethers radially successfully. The parametric analysis shows the tether deployment speed and the thrust magnitude significantly impacts deployment stability and tether libration, which opens the possibility of successful deployment of tethers by using optimal control. Finally, the analysis results show that radial deployment is advantageous due to the isolated deployment mechanism, and a jammed tether can be isolated from affecting the deployment of rest tethers.

A six-degree-of-freedom proportional-derivative control strategy for bumblebee flight stabilization

A six-degree-of-freedom proportional-derivative control strategy for bumblebee flight stabilization

Integrated vibration suppression attitude control for flexible spacecrafts with internal liquid sloshing

Vibration suppression during attitude control is a fundamental research topic whenever control of the rotational motion of a spacecraft with flexible appendages and internal liquid sloshing is of interest. The proposed method is based on an attitude control system with centralized sensors and actuators, without the usage of collocated devices for vibration management. In this way, it is possible to develop and implement a computationally efficient real-time control system that is suitable for any kind of spacecraft, even with advanced control capabilities. An integrated vibration suppression attitude control is designed and analyzed, exploiting also a numerical simulation verification procedure based on validated code. The developed attitude control system applies two fundamental control schemes: classical proportional-derivative (PD) control, with nonadaptive band-stop filters, and wave-based control. The proposed wave-based control implementation allows managing three-dimensional attitude dynamics in steady state pointing, without cross-coupling between the separate body axes. To overcome this limitation, the paper presents the integration of the wave-based control with the filtered PD control scheme, allowing us to have a complete three-dimensional real-time MIMO controller, with vibration suppression capabilities and robustness to system uncertainties. The paper also presents the development of an accurate dynamical model of a generic flexible spacecraft with internal liquid sloshing based on a multibody formulation.

Optimizing the Torque Distribution of a Redundantly Actuated Parallel Robot to Study the Temporomandibular Reaction Forces During Food Chewing

Abstract Inverse dynamics solution of redundantly actuated parallel robots (RAPRs) requires redundancy resolution methods. In this paper, the Lagrange’s equations of the second kind are used to derive governing equations of a chewing RAPR. Jacobian analysis of the RAPR is presented. As redundancy resolutions, two different optimization cost functions corresponding to specific neuromuscular objectives, which are minimization of effort of the muscles of mastication and temporomandibular joints (TMJs) loads, are used to find the RAPR’s optimized actuation torque distributions. The actuation torques under the influence of experimentally determined dynamic chewing forces on molar teeth reproduced from a separate chewing experiment are calculated for realistic in vitro simulation of typical human chewing. These actuation torques are applied to the RAPR with a distributed-computed-torque proportional-derivative control scheme, allowing the RAPR’s mandible to follow a human subject’s chewing trajectory. TMJs loads are measured by force sensors, which are comparable with the computed loads from theoretical formulation. The TMJs loads for the two optimization cost functions are measured while the RAPR is chewing 3 g of peanuts on its left molars. Maximum and mean of the recorded loads on the left TMJ were higher in both cases. Moreover, the maximum and mean of the recorded loads on both TMJs were smaller for the cost function minimizing the TMJs loads. These results demonstrate validity of the model, suggesting the RAPR as a potential TMJ loads measurement tool to study the chewing characteristics of patients suffering from pain in TMJs.

Kinematic Control of Serial Manipulators Using Clifford Algebra

Abstract We exploit the potentials of Clifford algebra to present a singularity free, compact, and computationally efficient scheme for kinematic control of serial manipulators. We introduce and implement the new special proportional-derivative control scheme. The introduced control scheme facilitates a fast motion control for the manipulators and enables them to react to the changes in their set points quickly. Such conditions are common in the context of dynamic working environments and collaborative manipulation scenarios. We describe the kinematics of the manipulators with unit dual quaternions using screw theory. The Lie-group properties of quaternions and dual quaternions are presented and discussed. By means of Lyapunov theory, it will be shown that the controller is globally exponentially stable.

Dynamic trajectory-tracking control method of robotic transcranial magnetic stimulation with end-effector gravity compensation based on force sensors

PurposeThis paper aims to propose a dynamic trajectory-tracking control method for robotic transcranial magnetic stimulation (TMS), based on force sensors, which follows the dynamic movement of the patient’s head during treatment.Design/methodology/approachFirst, end-effector gravity compensation methods based on kinematics and back-propagation (BP) neural networks are presented and compared. Second, a dynamic trajectory-tracking method is tested using force/position hybrid control. Finally, an adaptive proportional-derivative (PD) controller is adopted to make pose corrections. All the methods are designed for robotic TMS systems.FindingsThe gravity compensation method, based on BP neural networks for end-effectors, is proposed due to the different zero drifts in different sensors’ postures, modeling errors in the kinematics and the effects of other uncertain factors on the accuracy of gravity compensation. Results indicate that accuracy is improved using this method and the computing load is significantly reduced. The pose correction of the robotic manipulator can be achieved using an adaptive PD hybrid force/position controller.Originality/valueA BP neural network-based gravity compensation method is developed and compared with traditional kinematic methods. The adaptive PD control strategy is designed to make the necessary pose corrections more effectively. The proposed methods are verified on a robotic TMS system. Experimental results indicate that the system is effective and flexible for the dynamic trajectory-tracking control of manipulator applications.

Integrated optimal design of a high-speed planar parallel manipulator

To obtain excellent comprehensive performances of the planar parallel manipulator for the high-speed application, an integrated optimal design method, which integrated dimensional synthesis, motors/reducers selection, and control parameters tuning, is proposed, and the 3RRR parallel manipulator was taken as the example. The kinematic and dynamic performances of condition number, velocity index, acceleration capability, and low-order frequency are taken into accounts for the dimensional synthesis. Then, to match motors/reducers parameters and keep an economical cost, the constraint equations and the parameters library are built, and the cost is chosen as one of the optimization objectives. Also, to get high tracking accuracy, the dynamic forward plus proportional–derivative control scheme is introduced, and the tracking error is chosen as one of the optimization objectives. Hence, the optimization model including dimensional synthesis, motors/reducers selection and controller parameters tuning is established, which is solved by the genetic algorithm II (NSGA-II). The result shows that comprehensive performances can be effectively promoted through the proposed integrated optimal design, and the prototype was constructed according to the Pareto-optimal front.

A proportional-derivative control strategy for restarting the GMRES(m) algorithm

Restarted GMRES (or GMRES( m )) is normally used for solving large linear systems A x = b with a general, possibly nonsymmetric, matrix A . Although, the restarted GMRES consumes less computational time than its counterpart full GMRES, if the restarting parameter is not correctly chosen its convergence cannot be guaranteed and the method may converge slowly. Unfortunately, it is difficult to know how to choose this parameter a priori. In this article, we regard the GMRES( m ) method as a control problem, in which the parameter m is the controlled variable and propose a new control-inspired strategy for choosing the parameter m adaptively at each iteration. The advantage of this control strategy method is that only a few additional vectors need to be stored and the controller has the capacity to modify the dimension of the Krylov subspace whenever any convergence problem is detected. Numerical experiments, based on benchmark problems, show that the proposed control strategy accelerates the convergence of GMRES ( m ) .

Path Following Control Tuning for an Autonomous Unmanned Quadrotor Using Particle Swarm Optimization

The goal of this work is to present the particle swarm optimization application for quadrotor attitude and path following control tuning. To perform this task a path following feed-forward plus proportional-derivative control strategy was implemented, using particle swarm for tuning gains, and root mean square error for validating. The basic of quadrotor kinematics and dynamics model will be presented. Path planning will be executed through Euler-Lagrange equations to minimize the snap cost function and guarantee a soft trajectory through a set of intermediary waypoints. The reliability of this approach will be tested through several simulations.

L 1 adaptive controller design for hypersonic formation flight

The design of an L 1 adaptive controller for hypersonic formation flight is presented. The traditional leader/wingman formation control problem is considered, with focused attention on dealing with the input disturbance and parametric variations, both of which are intrinsic properties of the system that result in undesired control performance. A proportional-derivative control scheme based on nonlinear dynamic inversion is implemented as the baseline controller, and an L 1 adaptive controller is augmented to the baseline controller to attenuate the effects of input disturbance and parametric variations. Simulation results illustrate the effectiveness of the proposed control scheme.

Delay-dependent H ∞ control for a class of uncertain time-delay singular Markovian jump systems via hybrid impulsive control

This paper deals with the problem of robust normalization and delay-dependent H∞ control for a class of singular Markovian jump systems with norm-bounded parameter uncertainties and time delay. A new impulsive and proportional-derivative control strategy with memory is presented, which results in a novel class of hybrid impulsive systems. Sufficient conditions are developed to guarantee that the resultant closed-loop system is not only robust normal and stochastically stable, but also satisfies a prescribed H∞ performance level for all delays no larger than a given upper bound. In addition, the explicit expression of the desired impulsive control gains is also given together with the design approach. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

Reliable Dissipative Control for a Class of Uncertain Singular Markovian Jump Systems via Hybrid Impulsive Control

AbstractIn this paper, the problem of robust normalization and reliable dissipative control is investigated for a class of uncertain singular Markovian jump systems with actuator failures. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional–derivative control strategy is presented. The gain matrices of the impulsive control part can be obtained together with the design approach. Moreover, the dissipative control results obtained in this paper include the results of H‐infinity and passive control as special cases. Finally, two numerical examples are provided to illustrate the effectiveness and applicability of the proposed methods.

Robust gaze-steering of an active vision system against errors in the estimated parameters

Gaze-steering is often used to broaden the viewing range of an active vision system. Gaze-steering procedures are usually based on estimated parameters such as image position, image velocity, depth and camera calibration parameters. However, there may be uncertainties in these estimated parameters because of measurement noise and estimation errors. In this case, robust gaze-steering cannot be guaranteed. To compensate for such problems, this paper proposes a gaze-steering method based on a linear matrix inequality (LMI). In this method, we first propose a proportional derivative (PD) control scheme on the unit sphere that does not use depth parameters. This proposed PD control scheme can avoid uncertainties in the estimated depth and camera calibration parameters, as well as inconveniences in their estimation process, including the use of auxiliary feature points and highly non-linear computation. Furthermore, the control gain of the proposed PD control scheme on the unit sphere is designed using LMI such that the designed control is robust in the presence of uncertainties in the other estimated parameters, such as image position and velocity. Simulation results demonstrate that the proposed method provides a better compensation for uncertainties in the estimated parameters than the contemporary linear method and steers the gaze of the camera more steadily over time than the contemporary non-linear method.

Active Suspension System Based on Linear Switched Reluctance Actuator and Control Schemes

In this paper, an active suspension system utilizing a low-cost high-performance linear switched reluctance actuator with proportional-derivative (PD) control is presented. With the tracking differentiator (TD) calculating the displacement and its derivatives directly under the presence of noise, velocity and acceleration can be evaluated, and accurate position control can be achieved. Comparison is made between linear and nonlinear PD control methods in terms of various system parameters and road profiles. A nonlinear PD controller with better dynamic responses is evaluated and developed for real-time suspension application. The proposed PD control schemes are simulated, tested, and analyzed to prove its robustness and reliability. Finally, a quarter-car active suspension system prototype is built to demonstrate the effectiveness of the proposed control schemes with experiment results.