Proportional Differential Controller Research Articles

Dynamics of reconfiguration and assembly of a stacked satellite system

Separation and reconfiguration of stacked satellites in orbit is an effective method for constructing large space structures. This paper investigates the dynamics of a stacked satellite system (SSS) during the separation and reconfiguration process. Firstly, the dynamic model of the SSS is established via the natural coordinate formulation (NCF) to conveniently handle the time-varying constraints between satellites. Then, the separation and reconfiguration strategies are proposed for the SSS including the reconstruction step between two configurations. To ensure collision-free satellite assembly, a proportional differential (PD) controller combined with a potential function is introduced. Additionally, a docking mechanism is designed, considering collision force constraints during satellite docking assembly. Finally, several numerical simulations are conducted to demonstrate the effectiveness of the separation and assembly strategies.

Tracking control for nonlinear high-order fully actuated system with state constraints: an explicit reference governor approach

This paper studies the tracking control problem of nonlinear high-order fully actuated system subject to state constraints. In order to guarantee the stability of the closed-loop system, a generalised nonlinear proportional differential controller is designed to configure the system into a desired linear constant system. Then, an explicit reference governor for high-order system is introduced to modify the reference signal such that the system state and the state derivatives of certain orders always remain within a prescribed constraint set. Furthermore, we prove that the modified reference will converge to the original reference as much as possible. Therefore, the system state can finally track to the original reference by tracking the modified reference. Two numerical examples demonstrate the validity of the proposed method in this paper.

Repetitive Impedance Learning-Based Physically Human-Robot Interactive Control.

Model-based impedance learning control can provide variable impedance regulation for robots through online impedance learning without interaction force sensing. However, the existing related results only guarantee the closed-loop control systems to be uniformly ultimately bounded (UUB) and require the human impedance profiles being periodic, iteration-dependent, or slowly varying. In this article, a repetitive impedance learning control approach is proposed for physical human-robot interaction (PHRI) in repetitive tasks. The proposed control is composed of a proportional-differential (PD) control term, an adaptive control term, and a repetitive impedance learning term. Differential adaptation with projection modification is designed for estimating robotic parameters uncertainties in the time domain, while fully saturated repetitive learning is proposed for estimating time-varying human impedance uncertainties in the iterative domain. Uniform convergence of tracking errors is guaranteed by the PD control and the use of projection and full saturation in the uncertainties estimation and is theoretically proved based on a Lyapunov-like analysis. In impedance profiles, the stiffness and damping are composed of an iteration-independent term and an iteration-dependent disturbance, which are estimated by repetitive learning and compressed by the PD control, respectively. Therefore, the developed approach can be applied to the PHRI where iteration-dependent disturbances exist in the stiffness and damping. The control effectiveness and advantages are validated by simulations on a parallel robot in a repetitive following task.

Parking precise alignment control and cotransporter system for rice harvester and transporter

In autonomous rice harvesting, the use of transporters to assist rice transportation is an effective way to improve efficiency. However, nonlinear systems, such as double Hydraulic Static Transmission (HST)-driven tracked rice harvesters and transporters, make it challenging to control the precise parallel parking alignment during transportation, often leading to rice loss and potential safety hazards. To address this issue, this study established a geometric cotransporter model and used a preset path to decouple a two-dimensional control problem into two sets of one-dimensional controls. Dynamic and kinematic models of the longitudinal drive and steering systems were analyzed. Based on the identified longitudinal drive system transfer function, a predictive model was constructed to predict and compensate for the parking slip caused by system inertia. It was combined with the integrator wind-up protection to improve the pure tracking method and eliminate or reduce system errors in path tracking. A parallel parking alignment control system was designed using these two methods, and comparative experiments were conducted on the road surface. The results demonstrate that the compensated predictor (CP) longitudinal control improves the alignment accuracy compared with the proportional differential (PD) controller, whereas the Improved Pure-Pursuit Control (IPPC) path-tracking slightly enhances the tracking accuracy compared with proportional integral (PI). Moreover, a field-autonomous rice-harvesting cotransporter experiment showed that the longitudinal alignment accuracy of the designed system was less than 0.2 m. The lateral alignment accuracy was less than 0.1 m.

Finite-time robust formation control of multiple aerial robotic vehicles with uncertainties and time-varying complex perturbations

Formation control of aerial robotic vehicles (ARVs) has a wide range of applications in the battlefield reconnaissance, medical rescue and load transportation, etc. System parameter variations and complex disturbances are inevitable in the formation control of ARVs, and the effects of them on the formation stability control of ARVs are unnegligible. This paper addresses the robust formation control problem of finite-time leader–follower for multiple ARVs suffering from parameter uncertainties and time-varying perturbations. To ensure the states (e.g. position and velocity) of all followers to converge to leader in finite time, a novel finite-time high-order sliding mode consensus control (HOSMCC) scheme is designed. To better cope with the parameter uncertainties and time-varying disturbances, improve formation control accuracy and achieve the robust formation control of finite-time leader–follower in multiple ARV systems, a new finite time high-order sliding mode formation control (HOSMFC) scheme on the basis of finite-time HOSMCC is proposed. The finite-time stability of multi-ARV formation control system is guaranteed, and the desired formation pattern of multi-ARV systems is achieved using Lyapunov stability theorem. Performance comparisons with proportional differential formation controller (PDFC) and sliding mode formation controller (SMFC) are studied on a four-ARV formation control system. The results validate the designed formation control scheme.

A time-delay-based sliding mode controlling method for reducing contour errors of machine tools

This article presents a time delay-based sliding mode controller to reduce contour errors for machine tools subject to friction and model error. Through decoupling the actual dynamic model of machine tools into a nominal component and an error component, a proportional differential (PD) controller, which is mathematically deduced from the sliding mode controller (SMC), is designed for the nominal model. A time delay estimation (TDE) strategy that considers the friction effect is designed to compensate for the error component. Therefore, tracking accuracy is guaranteed. Based on TDE results, a Kalman state prediction method that considers model error is developed to make a high state prediction accuracy even if the model error is large. By adding the predicted contour errors of the next sampling time into the command trajectory, the pre-compensation of contour errors is realized. Moreover, a new contour error estimation (CEE) method that can improve computing efficiency is proposed. Experiments and comparisons are conducted to verify the effectiveness of proposed method.

Whole-Body Dynamics-Based Aerial Fall Trajectory Optimization and Landing Control for Humanoid Robot.

When humanoid robots work in human environments, falls are inevitable due to the complexity of such environments. Current research on humanoid robot falls has mainly focused on falls on the ground, with little research on humanoid robots falling from the air. In this paper, we employ an extended state variable formulation that directly maps from the high-level motion strategy space to the full-body joint space to optimize the falling trajectory in order to protect the robot when falling from the air. In order to mitigate the impact force generated by the robot's fall, during the aerial phase, we employ simple proportion differentiation (PD) control. In the landing phase, we optimize the optimal contact force at the contact point using the centroidal dynamics model. Based on the contact force, the changes to the end-effector positions are solved using a dual spring-damper model. In the simulation experiments, we conduct three comparative experiments, and the simulation results demonstrate that the robot can safely fall 1.5 m from the ground at a pitch angle of 45°. Finally, we experimentally validate the methods on an actual robot by performing a side-fall experiment. The experimental results show that the proposed trajectory optimization and motion control methods can provide excellent shock absorption for the impact generated when a robot falls.

Bounding gait control of a parallel quadruped robot

PurposeThe computing power of the legged robot is not enough to perform high-frequency updates for the full-body model predictive control (MPC) of the robot, which is a common problem encountered in the gait research of the legged robot. The purpose of this paper is to propose a high-frequency MPC control method for the bounding gait of a parallel quadruped robot.Design/methodology/approachAccording to the bounding gait characteristics of the robot, the quadruped robot model is simplified to an equivalent plane bipedal model. Under the biped robot model, the forces between the robot’s feet and the ground are calculated by MPC. Then, the authors apply a proportional differential controller to distribute these forces to the four feet of the quadruped robot. The robot video can be seen at www.bilibili.com/video/BV1je4y1S7Rn.FindingsTo verify the feasibility of the controller, a prototype was made, and the controller was deployed on the actual prototype and then fully analyzed through experiments. Experiments show that the update frequency of MPC could be stabilized at 500 Hz while the robot was running in the bounding gait stably and efficiently.Originality/valueThis paper proposes a high-frequency MPC controller under the simplified model, which has a higher working efficiency and more stable control performance.

Physical based motion reconstruction from videos using musculoskeletal model

AbstractWe propose a novel method that combines human pose estimation and physical simulation of character animation. Our approach allows characters to learn from the actor's skills captured in videos and subsequently reconstruct the motions with high fidelity in a physically simulated environment. Firstly, we model the character based on the human musculoskeletal system and build a complete dynamics model of the proposed system using the Lagrange equations of motion. Next, we employ the pose estimation method to process the input video and generate human reference motion. Finally, we design a hierarchical control framework consisting of a trajectory tracking layer and a muscle control layer. The trajectory tracking layer aims to minimize the difference between the reference motion pose and the actual output pose, while the muscle control layer aims to minimize the difference between the target torque and the actual output muscle force. The two layers interact by passing parameters through a proportional differential controller until the desired learning objective is achieved. A series of complex experimental results demonstrate that our proposed method can learn to produce comparable high‐quality motions with high similarity from videos of different complexity levels and remains stable in the presence of muscle contracture weakness perturbations.

A Decoupling Matrix-Based Learning Control Scheme for the Machine Directional Register of Roll-to-Roll Systems

Roll-to-Roll (R2R) printing systems are complex MIMO systems, which makes it difficult to design a register control scheme for them, much less high-precision learning control scheme. In this paper, a decoupling matrix-based simplification scheme is proposed to transform the complex MIMO system to be a simple one. According to the transformed system and the Lyapunov stability theory, a decoupling matrix-based learning control (DMBLC) scheme is proposed for the register control of R2R printing systems, while a data-based evaluation index is designed to assist DMBLC to achieve high register precision through continuous learning. The effectiveness of DMBLC is verified by simulations and experiments. Comparisons among DMBLC, dynamic matrix control and fully decoupled proportional differential control are carried out to show the superior performance of DMBLC.

Frequency Domain Analysis of Load Frequency Control Using PIDTune Model Standard

The load frequency control system aims to regulate the frequency in the electric power system at a normal value with a predetermined tolerance limit. In practice, the load frequency control system does not always operate optimally, therefore a controller is needed to be added to the load frequency control system. The controller designed is a variation of the combination of Proportional-Integral-Differential (PID) controllers with the standard model PIDTune method consisting of proportional (P) controller, proportional integral (PI) controller, proportional differential (PD) controller, Proportional Integral Differential (PID) controller, Proportional Differential controller with first-order filter on differential section (PDF), and Proportional Integral Differential controller with first-order filter on differential section (PIDF). This study is aiming to carry out simulation and analysis in the frequency domain and then analyze the robustness of the reheat type power frequency control system and then design a PID controller for the reheat type power frequency control system in basic configuration, filter configuration, feedback configuration, feedforward configuration, and cascade configuration using PIDtune Model Standard on Matlab software. From the results of simulation and analysis, the controller that complies the design criteria and can make the reheat type of load frequency control system work optimally based on frequency domain analysis and robustness analysis is a proportional-integral (PI) controller in a feedback configuration with gain margin (Kg) equals to 38.11 dB, phase margin equals to 59.6°, infinity bandwidth, peak resonance value (Mr) equals to 1.19, maximum sensitivity peak value (MS) equals to 1.24, and complementary maximum sensitivity peak value (MT) equals to 1,17.

African vulture optimizer algorithm based vector control induction motor drive system

<span lang="EN-US">This study describes a new optimization approach for three-phase induction motor speed drive to minimize the integral square error for speed controller and improve the dynamic speed performance. The new proposed algorithm, African vulture optimizer algorithm (AVOA) optimizes internal controller parameters of a fuzzy like proportional differential (PD) speed controller. The AVOA is notable for its ease of implementation, minimal number of design parameters, high convergence speed, and low computing burden. This study compares fuzzy-like PD speed controllers optimized with AVOA to adaptive fuzzy logic speed regulators, fuzzy-like PD optimized with genetic algorithm (GA), and proportional integral (PI) speed regulators optimized with AVOA to provide speed control for an induction motor drive system. The drive system is simulated using MATLAB/Simulink and laboratory prototype is implemented using DSP-DS1104 board. The results demonstrate that the suggested fuzzy-like PD speed controller optimized with AVOA, with a speed steady state error performance of 0.5% compared to the adaptive fuzzy logic speed regulator’s 0.7%, is the optimum alternative for speed controller. The results clarify the effectiveness of the controllers based on fuzzy like PD speed controller optimized with AVOA for each performance index as it provides lower overshoot, lowers rising time, and high dynamic response.</span>

Adaptive Tracking of Large-Angle Maneuvers for Spacecraft Equipped with an Active Pointing Ultraquiet Platform

An adaptive controller for the tracking of large-angle maneuvers is proposed for spacecraft equipped with an active pointing ultraquiet platform (AQP). The inertial parameters of the spacecraft and the payload (supported by the AQP) are estimated online, whereas the parameters of the AQP are assumed to be precisely known. To enable the derivation of the proposed controller, a novel dynamic model of AQP spacecraft was derived, which employs relative motion variables for the payload and is linear in the unknown inertial parameters. A Lyapunov-like argument was used to prove the local asymptotical stability of the closed-loop system, and the original controller was simplified further to a physically more intuitive proportional-differential (PD) plus adaptive feed-forward controller. The superior tracking performance of the proposed controller compared with that of a standard PD plus nonadaptive feed-forward controller was shown via numerical simulation. It also was shown that the estimates of a selected set of unknown inertial parameters will converge to their true values if a certain kind of maneuver trajectory is tracked.

트랙터 자율주행을 위한 영상 기반 경작지 경계 인식 알고리즘

To utilize autonomous driving tractors for precision agriculture, the cultivable farmland area and its boundary information must be determined. Currently, autonomous driving is performed using the global positioning system (GPS) data of four boundary points; however, the operator must drive and obtain the boundary information. In this study, a vision-based autonomous driving algorithm was developed. A stereo camera and a MobileNetV3-based segmentation algorithm were used to segment the cultivable area and boundary, perform autonomous driving, and store the boundary information. Inverse perspective mapping was performed to store the farmland information in a two-dimensional space, and occupancy grid mapping was performed according to the heading angle of the tractor obtained from Inertial Measurement Unit (IMU) and GPS. By using the preview distance concept, a target heading angle of the tractor was generated at a point away from the boundary, and Proportional-Differential controller was used for the path-tracking algorithm.

Adaptive nonsingular terminal sliding mode control of robot manipulator based on contour error compensation

To achieve accurate contour tracking of robotic manipulators with system uncertainties, external disturbance and actuator faults, a cross-coupling contour adaptive nonsingular terminal sliding mode control (CCCANTSMC) is proposed. A nonsingular terminal sliding mode manifold is developed which eliminates the singularity completely. In order to avoid the demand of the prior knowledge of system uncertainties, external disturbance and actuator faults in practical applications, an adaptive tuning approach is proposed. The stability of the proposed control strategy is demonstrated by the finite-time stability theory. Then, the developed controller combines adaptive nonlinear terminal sliding mode control (ANTSMC) of joint trajectory tracking and proportion–differentiation control of end-effector contour tracking by introducing the coupling factor between multiple axes based on Jacobian. Moreover, a unified framework of cross-coupling contour compensation and reference position pre-compensation is built. Finally, numerical simulation and experimental results validate the effectiveness of the proposed control strategy.

Autonomous Control of the Underwater Remotely Operated Vehicle in Collision Situation with Stationary Obstacle

Abstract The article considers the problem of autonomous control of the underwater remotely operated vehicle mini Remotely Operated Vehicle (ROV) in a collision situation with a stationary obstacle. The control of the collision avoidance process is presented as a synthesis of fuzzy proportional-differential controllers for the control of distance and orientation concerning the detected stationary obstacle. The control of the submergence depth of the underwater vehicle has been adopted as a separate control flow. A method to obtain the main motion parameters of the underwater vehicle relative to the detected stationary obstacle using a Laser-based Vision System (LVS) and a pressure sensor coupled to an Inertial Measurement Unit (IMU) is described and discussed. The result of computer implementation of the designed fuzzy controllers for collision avoidance is demonstrated in simulation tests and experiments carried out with the mini ROV in the test pool.

Fractional-Order Active Disturbance Rejection Control with Fuzzy Self-Tuning for Precision Stabilized Platform.

In this paper, a novel fractional-order active disturbance rejection control with fuzzy self-tuning method (FSFOADRC) is proposed for photoelectric tracking system (PTS). Firstly, aiming at the internal uncertainty of PTS and external disturbance, a fraction-order extended state observer (FOESO) is designed, and the FOESO can transform the plant into a simple form, which greatly simplifies the mathematical model. Secondly, a fuzzy regulator is applied to the proportion-differentiation controller (PD), increasing the flexibility and adaptivity of the controller. In addition, the stability of the whole control system can be guaranteed. Eventually, numerical comparative simulations are implemented to verify the feasibility and superiority of the proposed method. Compared with the integral-order active disturbance rejection control (IOADRC), fractional-order active disturbance rejection control (FOADRC) without the fuzzy regulator and proportion-integration-differentiation (PID) controller, the proposed method performs better with faster response, smaller overshoot, and stronger disturbance suppression capability.

Slamming impact induced hydrodynamic response in wave-piercing catamaran beam elements with controller

When subjected to a slamming load, wave-piercing catamarans may be vulnerable to damage and deck diving. Aluminum beams are one of the key components of catamaran vessels and improving their stiffness and dynamic smart management is crucial to reducing the impact of waves at sea. The numerical analysis and mathematical modeling of the wave-piercing catamaran beam elements are fresh topics that largely depend on smart control issues. Based on a 2D Wanger type impact force model, this work presents a numerical benchmark study for the hydrodynamic analysis and smart control of wave-piercing catamaran beam elements. The Rankine panel approach also takes into account the impact of the wave-piercing catamaran's forward speed. The wave-piercing catamaran's smart control system consists of a proportional-differential (PD) controller with two piezoelectric layers acting as an actuator and a sensor on the top and bottom surfaces of the beams, respectively. Carbon nanotubes (CNTs) are employed as reinforcement to increase the stiffness of porous beams while assuming their agglomeration effects based on the Mori-Tanaka model. Refined zigzag shear deformation beam theory (RZSDBT) is used to mathematically represent the smart structure, and the related motion equations are generated using the energy technique. The differential quadrature method (DQM) and the Newmark method are used to solve the framework in order to capture the dynamic deflection and flexural moment and describe the Gibbs phenomenon. The effects of the controller, externally applied voltage, CNTs as reinforcement, forward speed, modification of shape and pressure distribution, porosity, deadrise angle, and external loads caused by demi-hulls and the cross-deck are all investigated using numerical studies. These studies look at how these factors affect dynamic deflection, flexural moment and Gibbs phenomenon. Regarding the primary goal of this work, the findings showed that the harmful effects can be greatly controlled with a PD controller. In other words, we can state unequivocally that the controller's assistance reduces the pressure distribution's discontinuity or spike while enhancing the beam's dry area. Additionally, the dynamic deflection and flexural moment are decreased by 49% and 37%, respectively, by employing the controller. The use of CNTs as beam reinforcement, which can reduce dynamic deflection and flexural moment by around 50% and 33%, respectively, is another goal of this work.

A Training Method for a Sensor-Based Exercise Rehabilitation Robot

In order to solve the problem that the traditional mirror therapy did not take into account the real-time recovery of the affected limb and the training effect was limited, a training method of sports rehabilitation robot based on sensor was proposed. A mirror active rehabilitation training system was proposed, which was composed of four steps including trajectory acquisition of the limb inertial measurement unit (IMU), fuzzy adaptive proportion differentiation (PD) control in closed-loop variable domain, muscle force estimation of the surface electromyographic signal (sEMG) of the affected limb, and power compensation of the outer ring of the affected limb. The experimental results showed that the sagittal forward flexion angle of the healthy shoulder increased from 0° to 128° at a relatively uniform speed, and the sagittal forward flexion angle of the shoulder was basically consistent with that of the healthy limb after the adaptive power compensation of the affected limb. The calculated trajectory tracking error of the healthy limb controlled by the fuzzy adaptive PD controller in the variable domain was 0.21 ± 1.35 ° . The horizontal backward extension angle of the healthy shoulder joint increased from 0° to 43°, and the following trajectory of the affected limb was roughly consistent with the movement trajectory of the healthy limb. The calculated tracking error of the healthy limb trajectory was 0.39 ± 1.45 ° . It was concluded that the control system could provide the real-time power compensation according to the recovery of the affected limb, give full play to the training initiative of the affected limb, and make the affected limb achieve a better rehabilitation training effect.

Time-Delayed Active Control of Stall Flutter for an Airfoil via Camber Morphing

This paper investigates a time-delayed active control for suppressing the stall flutter via camber morphing. A time-domain fluid–structure–control coupled solver is presented. This solver composes a computational fluid dynamics (CFD)-based flow solver with dynamic mesh techniques, a one- degree-of-freedom structural solver for a pitching airfoil, and a time-delayed proportional–differential controller that actuates the nonlinear camber morphing of the airfoil. The modules of the structural solver and the controller are both implanted into the CFD-based flow solver OpenFOAM. The proposed solver is first validated with the aerodynamic stall and stall-flutter experimental results, and then it is used for investigating the stall-flutter suppression performance in the time domain with nonlinear camber morphing. The numerical results with various time delays in the active control suggest that the time delay significantly impacts the response suppression effect of the stall flutter. The closed-loop controls with time delays ranging from 0.01 to 0.15 s can suppress stall flutter. The suppression effect reaches the best when as it reduces the amplitude of the limit-cycle response by 60%. The active control mechanism of the time-delayed camber morphing is analyzed in terms of the flow pattern and energy transfer in depth.