Proportional Derivative Controller Research Articles

Synchronous PD Control Using a Time Delay Estimator for a Four-Degree-of-Freedom Parallel Robot in Practice

This paper presents a synchronous proportional derivative (PD) control method using a time delay estimator (SPD-TDE) for a four-degree-of-freedom (DOF) parallel robot in practice. The proposed control is a method that is developed from a synchronous PD control method combined with a time delay estimator to guarantee the tracking objectives and synchronous requirements of the robot. Firstly, the synchronous PD control method is designed by defining cross-coupling errors. A cross-coupling error is determined by incorporating the tracking error and deviation of tracking error among two adjacent joints or synchronous errors. Then, the asynchronous problem between the kinematic chains is solved and guarantees that the goal of synchronicity is achieved. Consequently, to improve the tracking performance of the robot, a time delay estimator is used to estimate and eliminate the uncertainty components of the system, such as modeling errors and actuator faults. In addition, the Lyapunov theory is also used to demonstrate the stability and robustness of the proposed control method. Finally, a testbench 4-DOF parallel robot is built, and the controllers are embedded in the control board from MATLAB Simulink using the Waijung block set library to operate the robot preset trajectory tracking. The experimental results of the proposed control method for the 4-DOF parallel robot are compared with those obtained using other controllers to prove its effectiveness.

Tuning of controller parameters using Pythagorean fuzzy similarity measure for stable and time delayed unstable plants.

This paper proposes a tuning method based on the Pythagorean fuzzy similarity measure and multi-criteria decision-making to determine the most suitable controller parameters for Fractional-order Proportional Integral Derivative (FOPID) and Integer-order Proportional Integral-Proportional Derivative (PI-PD) controllers. Due to the power of the Pythagorean fuzzy approach to evaluate a phenomenon with two memberships known as membership and non-membership, a multi-objective cost function based on the Pythagorean similarity measure is defined. The transient and steady-state properties of the system output were used for the multi-objective cost function. Thus, the determination of the controller parameters was considered a multi-criteria decision-making problem. Ant colony optimization for continuous domains (ACOR) and artificial bee colony (ABC) optimization are utilized to minimize multi-objective cost functions. The proposed method in the study was applied to three different systems: a second-order non-minimum phase stable system, a first-order unstable system with time delay, and a fractional-order unstable system with time delay, to validate its effectiveness. The cost function utilized in the proposed method is compared with the performance measures widely used in the literature based on the integral of the error, such as IAE (Integral Absolute Error), ITAE (Integral Time Absolute Error), ISE (Integral Square Error), and ITSE (Integral Time Square Error). The proposed method provides a more effective control performance by improving the system response characteristics compared to other cost functions. With the proposed method, the undershoot rate could be significantly reduced in the non-minimum phase system. In the other two systems, significant improvements were achieved compared to other methods by reducing the overshoot rate and oscillation. The proposed method does not require knowing the mathematical model of the system and offers a solution that does not require complex calculations. The proposed method can be used alone. Or it can be used as a second and fine-tuning method after a tuning process.

A new seismic control framework of optimal PIλDµ controller series with fuzzy PD controller including soil-structure interaction

A new framework of optimal fractional order proportional-derivative-integral (FOPID) controller series with fuzzy proportional-derivative (PD) controller, namely OFPD-FOPID controller, is proposed in this study for seismic control of structures equipped with active tuned mass damper (ATMD). Three controllers including optimal PID, optimal FOPID, and fuzzy PID (FPID) controllers are also implemented for comparison purposes. Simulation results carried out on a 15-story building show the FOPID controller than the PID and FPID controllers can remarkably reduce the maximum floor displacement, but they represent a poor performance in mitigation of the maximum floor acceleration in different soil conditions, while the proposed OFPD-FOPID controller tracking the amount of the maximum floor acceleration to estimate the optimal control force of the actuator can provide superior performance. An average reduction of 41%, 45%, and 33% in the maximum floor displacement; 36%, 33%, and 20% in the maximum inter-story drift are given by FOPID in the dense, medium, and soft soils, while it results in an increase of 45%, 52% and 24% in the maximum floor acceleration. Similarly, the proposed OFPD-FOPID controller represents an average reduction of 52%, 55%, and 45% in the maximum floor displacement; 42%, 44%, and 28% in the maximum inter-story drift in the dense, medium, and soft soils, while it also slightly reduces the maximum floor acceleration of the studied structure located on different soil conditions.

Synchronization of reaction–diffusion neural networks with random time-varying delay via intermittent boundary control

Under boundary measurement (BM), this paper solves the synchronization problem via intermittent boundary proportional–derivative (PD) control of delayed reaction–diffusion neural networks (RDNNs), where the random time-varying delay (RTVD) belongs to two intervals and is considered by a probabilistic way to take the influence of uncertain factors. The intermittent boundary PD synchronization scheme, which considers the inevitable actuator limitations, is based on BM and only available at some specified boundary position. By using the inequality techniques and switching Lyapunov functional, the mean square exponential stability (MSES) of the synchronization error system (SES) containing the response and drive dynamics is ensured by some synchronization criteria, which are established via an intermittent boundary PD controller under BM and expressed as linear matrix inequalities. Lastly, the proposed intermittent boundary PD synchronization approach is verified by a numerical example.

Neuro-fuzzy-based anti-swing control of automatic tower crane

Controlling the position of the final load and the anti-swing control of the loads during the operation of the tower crane are challenging tasks. These are the most important control issues for safe operation, which are difficult to achieve easily with conventional control systems. Hence, the need to integrate the concepts of soft-computing into the tower crane control system. The aim of this research work is to design an adaptive-network-based fuzzy inference system (ANFIS) controller to move the payload to the final position with the lowest possible swing angle. To evaluate the ability of the proposed controller to meet the control requirements, its performance was compared to three other controllers: a conventional proportional derivative (PD) controller, a fuzzy-tuned PD controller and a fuzzy controller. MATLAB-based computer simulations of the crane and controllers were carried out to verify and compare the performance of the proposed controllers. The obtained results show the effectiveness of the ANFIS-based controller in adjusting the load position while keeping the load fluctuations small at the final position. The load oscillation angle is about ±2.28° with the ANFIS controller while it is about ±10° when using the PD controller. In addition, only one ANFIS controller is used for both load position and swing angle control.

A time-delayed proportional-derivative controller for a dielectric elastomer circular membrane

• In this paper, an internal resonance of a circular DE membrane is investigated within mechanical and electrical excitations in order to find internal resonances for improving its performance for future applications. • This work proposes a time-delayed proportional-derivative (TDPD) controller for decreasing the oscillations of a DE system with quadratic and cubic nonlinearities. • Averaging method is used to solve the controlled system to obtain the first-order approximation solutions and response equations for the DE system. • The TDPD controller is the best control strategy that can reduce the framework vibrations regardless of the excitation frequency. Due to the substantial deformation generated by voltage excitation, the dielectric elastomer (DE) is a new type of functional polymer that can be employed as a smart actuator. In this paper, an internal resonance of a circular DE membrane is investigated within mechanical and electrical excitations in order to find internal resonances for improving its performance for future applications. All programs that contain DE will perform flawlessly if DE is managed. This work proposes a time-delayed proportional-derivative (TDPD) controller for decreasing the oscillations of a DE system with quadratic and cubic nonlinearities. The system is researched and investigated when using a Proportional–derivative (PD) controller to apply time-delayed control on displacement and velocity. Stability is improved, maximum peak overshoot is reduced, settling time is reduced, and the framework transient response is recovered using this control method. The first-order approximation solutions for the DE system are calculated using the averaging method. Simultaneous resonance is regarded as the worst type of resonance. To obtain the dynamic solution of the device with TDPD controllers, analytical and numerical approaches are used. The Routh-Huriwitz approach is used to review and analyze the consistency of the steady state solution in the near-resonance case. The effects of various factors on the steady-state solution are identified and discussed. The effects of time delay are investigated in order to determine the most stable range of time delays for the best performance. The MATLAB software package is used to generate simulation effects. When the results are compared to the numerical simulations, they show that the approximate solution and the control algorithm used in this paper are well validated. At the end, there is a comparison with previously published work. The focus of this paper is on using a TDPD controller to manage the nonlinear dynamic response and probable internal resonances of a circular DE membrane under mechanical and electrical excitations. The approximate solution of a nonlinear system of differential equations is investigated using the averaging technique in the cases of primary and 1:2 internal resonance, which are the worst-case scenarios that should be avoided. To display and compare controller effects at various system settings, several response curves are used. The TDPD controller is used to research nonlinear dynamics control of the DE system with harmonic force. The stability analysis and the effects of parameter behavior are tested using MATLAB program. To examine the controller effect, several response curves are used. The collected findings demonstrated that the TDPD control efficiency in reducing the system's nonlinear oscillations. The frequency response curves of the system were studied at various uncontrolled and regulated coefficients. Before and after control, response curve diagrams employing frequency response equations are created. Finally, validation curves are shown to measure the degree of similarity between analytical and numerical simulation predictions. At the end, there is a comparison with previously published works.

Direct Tilt Controller Design with Disturbance Compensation and Implementation for a Narrow Tilting Electric Vehicle

Three-wheeled electric city vehicles are becoming popular because they have lower cost and enable motorcycle driving feeling with electric powertrain performance. These vehicles need a driver assistant system, also known as an active tilting stability controller, to provide a safe cornering manoeuvre. Active tilt control methods are direct tilt control (DTC), steering tilt control (STC) and a combination of these methods. In this study, DTC system design with a servo motor actuator with simulation and experimental results are presented. State feedback control with pole placement design has been improved with disturbance compensation control. This novel controller structure enhances the response of DTC and enables a faster-tilting response. Simulation results are given up to 10 m/s speed. Experimental results of the developed method are given up to 3.05 m/s (11 km/h) speed on a three-wheeled electric vehicle. The speed control loop of the servo motor drive unit (SMDU) stabilizes the DTC system. In the state of the art, a proportional derivative controller is commonly used as a tilt controller. By including the speed control loop of SMDU in the tilt control system, the use of the derivative term can be eliminated. The stability effect of the speed control loop is shown by MATLAB analysis, simulations in Simulink and experimental step response test as well.

Designing and Implementing a Versatile Agricultural Robot: A Vehicle Manipulator System for Efficient Multitasking in Farming Operations

This paper presents a detailed design of a skid-steering mobile platform with four wheels, along with a Cartesian serial (PPP) manipulator. The aim of this design is to enable the platform to perform various tasks in the agricultural process. The parallel manipulator designed can handle heavy materials in the agricultural field. An experimental robotic harvesting scenario was conducted using parallel manipulator-based end-effectors to handle heavy fruits such as watermelon or muskmelon. The conceptual and component design of the different models was carried out using the Solidworks modeling package. Design specifications and parametric values were utilized during the manufacturing stage. The mobile manipulator was simulated on undulating terrain profiles using ADAMS software. The simulation was analyzed for a duration of 15 s, and graphs depicting the distance, velocity, and acceleration were evaluated over time. Proportional derivative control and proportional derivative-like conventional sliding surface control were applied to the model, and the results were analyzed to assess the error in relation to the input and desired variables. Additionally, a structural analysis was performed to ensure minimal deformation and the highest safety factor for the wheel shaft and L bracket thickness. Throughout the fabrication and prototype development, calibration tests were conducted at various X-, Y-, and Z-axis frame mounting stages. The objective was to minimize the lateral and longitudinal deviation between the parallel linear motion (LM) rails. Once the fabrication and prototype construction was completed, field testing was carried out. All mechanical movements in the lateral and longitudinal directions functioned according to the desired commands given by the Arduino Mega, controlled via a six-channel radio frequency (RF) controller. In the context of agriculture, the grippers utilizing parallel mechanisms were also subjected to testing, demonstrating their ability to handle sizable cylindrical and spherical fruits or vegetables, as well as other relevant objects.

Robust trajectory tracking control for collaborative robots based on learning feedback gain self-adjustment

Abstract. A robust position control algorithm with learning feedback gain automatic adjustment for collaborative robots under uncertainty is proposed, aiming to compensate for the disturbance effects of the system. First, inside the proportional-derivative (PD) control framework, the robust controller is designed based on model and error. All of the model's uncertainties are represented by functions with upper bounds in order to surmount the uncertainties induced by parameter changes and unmodeled dynamics. Secondly, the feedback gain is automatically adjusted by learning, so that the control feedback gain is automatically adjusted iteratively to optimize the desired performance of the system. Thirdly, the Lyapunov minimax method is used to demonstrate that the proposed controller is both uniformly bounded and uniformly ultimately bounded. The simulations and experimental results of the robot experimental platform demonstrate that the proposed control achieves outstanding performance in both transient and steady-state tracking. Also, the proposed control has a simple structure with few parameters requiring adjustment, and no manual setting is required during parameter setting. Moreover, the robustness and efficacy of the robot's trajectory tracking with uncertainty are significantly enhanced.

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.

Automated Laser-Fiber Coupling Module for Optical-Resolution Photoacoustic Microscopy.

Photoacoustic imaging has emerged as a promising biomedical imaging technique that enables visualization of the optical absorption characteristics of biological tissues in vivo. Among the different photoacoustic imaging system configurations, optical-resolution photoacoustic microscopy stands out by providing high spatial resolution using a tightly focused laser beam, which is typically transmitted through optical fibers. Achieving high-quality images depends significantly on optical fluence, which is directly proportional to the signal-to-noise ratio. Hence, optimizing the laser-fiber coupling is critical. Conventional coupling systems require manual adjustment of the optical path to direct the laser beam into the fiber, which is a repetitive and time-consuming process. In this study, we propose an automated laser-fiber coupling module that optimizes laser delivery and minimizes the need for manual intervention. By incorporating a motor-mounted mirror holder and proportional derivative control, we successfully achieved efficient and robust laser delivery. The performance of the proposed system was evaluated using a leaf-skeleton phantom in vitro and a human finger in vivo, resulting in high-quality photoacoustic images. This innovation has the potential to significantly enhance the quality and efficiency of optical-resolution photoacoustic microscopy.

Proportional-Derivative Control of Cortisol for Treatment of PTSD.

Mental illnesses, such as depression or post-traumatic stress disorder (PTSD), often impact an individual's physiological reaction to stress via their cortisol response. We examine the regulation of cortisol within the hypothalamic-pituitary-adrenal (HPA) axis as a dynamic biosystem. We investigate the difference between the cortisol regulation of people with PTSD and healthy controls. Additionally, we investigate models for potential therapies based on proportional-derivative (PD) control to normalize and improve the stress response of those with PTSD. Such a design may be relevant to improving the treatment of PTSD, as current medical interventions are frequently imprecise and may result in unwanted side effects. The use of a PD controller in administration of hormone therapy, in contrast, can be highly measurable and patient specific.Clinical Relevance- This paper offers an approach to treating post-traumatic stress disorder (PTSD) via stabilizing an individual's endocrinal regulation as a potential future alternative to current pharmaceutical practices.

Hybrid Controller for a Single Flexible Link Manipulator

In this study, the dynamic modeling and step input tracking control of single flexible link is studied. The Lagrange-assumed modes approach is applied to get the dynamic model of a planner single link manipulator. A Step input tracking controller is suggested by utilizing the hybrid controller approach to overcome the problem of vibration of tip position through motion which is a characteristic of the flexible link system. The first controller is a modified version of the proportional-derivative (PD) rigid controller to track the hub position while sliding mode (SM) control is used for vibration damping. Also, a second controller (a fuzzy logic based proportional-integral plus derivative (PI+D) control scheme) is developed for both vibration damping and hub position tracking. A comparison is made between the performances of these two controllers. The Hybrid controller with PD and SM shows better tracking behavior than obtained from the suggested fuzzy (PI+D)2 controller for a single link flexible manipulator.

Dynamic Reliability Analysis of Running Safety and Stability of a High-Speed Maglev Train on a Guideway Bridge

The dynamic performance of high-speed maglev trains, a next-generation rapid transit system, has received continuous attention in recent years. In this study, a dynamic reliability analysis method for a high-speed maglev train–guideway coupled system was proposed. First, a refined model of the maglev vehicle–bridge interaction system was established, where the vehicle subsystem was simulated as a rigid body-spring-damper model with 101 degrees of freedom. The guideway subsystem was simulated as a finite element model, and these two subsystems were coupled as an entire system through a magnet–rail interaction model with a proportional-derivative (PD) controller. Second, a dimension-reduction method for the simulation of representative samples of track irregularities was developed, and thus the number of random variables in the system was reduced to four. Finally, an efficient method for the calculation of the dynamic reliability of a maglev train–guideway coupled system was proposed using the probability density evolution method-based equivalent extreme value principle. With numerical examples, the accuracy of the maglev train–guideway interaction model was verified by comparing it with field measurement data from the Shanghai high-speed maglev line. The accuracy of the proposed dynamic reliability analysis method was confirmed by comparing three types of results, that is, the mean value time-history curve, the probability density function, and the cumulative distribution function of extreme values, obtained by the Monte Carlo method. Finally, the dynamic reliability of the running safety and stability of the maglev vehicle at a speed of 430 km/h and the variation laws of the dynamic reliabilities with train speed were examined in detail.

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.

Fractional multi-loop active disturbance rejection control for a lower knee exoskeleton system

Rehabilitation Exoskeleton is becoming more and more important in physiotherapists’ routine work. To improve the treatment performance, such as reducing the recovery period and/or monitoring and reacting to unpredictable situations, the rehabilitation manipulators need to help the patients in various physical trainings. A special case of the active disturbance rejection control (ADRC) is applied to govern a proper realisation of basic limb rehabilitation trainings. The experimental study is performed on a model of a flexible joint manipulator, whose behaviour resembles a real exoskeleton rehabilitation device (a one-degree-of-freedom, rigid-link, flexible-joint manipulator). The fractional (FADRC) is an unconventional model-independent approach, acknowledged as an effective controller in the existence of total plant uncertainties, and these uncertainties are inclusive of the total disturbances and unknown dynamics of the plant. In this work, three FADRC schemes are used, the first one using a fractional state observer (FSO), or FADRC1, second one using a fractional proportional-derivative controller (FPD), or FADRC2, and the third one a Multi-loop fractional in PD-loop controller and the observer-loop (Feedforward and Feedback), or FADRC3. The simulated Exoskeleton system is subjected to a noise disturbance and the FADRC3 shows the effectiveness to compensate all these effects and satisfies the desired position when compared with FADRC1 and FADRC2. The design and simulation were carried out in MATLAB/Simulink.

Data-Driven Virtual Reference Set-Point Learning of PD Control and Applications to Permanent Magnet Linear Motors

In this work, a data-driven virtual reference setting learning (DDVRSL) method is proposed to enhance the proportional-derivative (PD) feedback controller of the repetitive nonlinear system. First, an ideal nonlinear virtual reference setting learning law is presented in the outer loop of the control system to tune the reference setting. Such an ideal nonlinear learning law exists theoretically and is transferred to a linear parametric DDVRSL via iterative dynamic linearization (IDL). Next, an iterative adaptation law is proposed for the estimation of the parameters in the DDVRSL law subject to the nonlinear system which is also transferred into a linear form by using the IDL method. The iterative adaptation algorithm tunes the learning gains of DDVRSL law using input and output measurements, therefore improving the robust ability against uncertainties. The proposed DDVRSL-based PD control method does not require any exact mechanistic model knowledge. The convergence is proved via the contraction mapping principle, mathematical induction, and time-weighted norm. Further, the theoretical results are verified through simulations.

Design and Control of Autonomous Rover for Foliage Navigation

Implementation of UGV in civilian applications is getting trendy and normalized due to its solid achievement in executing mission under harsh environments. The UGV foliage environment-oriented applications even attracted the people’s attention in correspond sectors to ease their tasks with guaranteed performance. Given this, the development of the autonomous rover from sensors and control aspects with the consideration of foliage environment interest people to enhance its functionality. To ensure the sensor is not easily affected by the environment factor, the radar and the camera are selected to provide the environment perception to the rover. The approach for a linear Proportional-Derivative (PD) controller with the dynamic modelling of the UGV is also discussed in this paper. The study shows preliminary results that are working.

Optimized FSF Controller for Bulk Power Control of Large-Core PHWRs

This paper considers an optimized full state feedback (FSF) optimal controller for bulk power control of a 700-MW(electric) pressurized heavy water reactor (PHWR) that minimizes the controller norm to reduce the effect of disturbances. Lyapunov’s linear matrix inequalities (LMIs) have been considered for stability of the model. For the closed loop, these inequalities, which become nonlinear in the unknowns, are converted to LMIs by a suitable variable substitution. The controller’s optimization is achieved by minimizing the upper bound of the state feedback vector’s norm. As a result of this optimization, the controller gain is reduced, which reduces the effect of the disturbance input to the system. We study the stability of the closed loop system and the nonlinear transient performance using the state feedback. We demonstrate that the proposed controller’s transient performance is superior to that of a nonoptimized controller when compared to a conventional proportional-derivative controller. The designed controller has a norm that is about five orders lower than that obtained without optimization while still providing acceptable transient performance.

Vibration Control and Ride Comfort Analysis of a Full Car with a Driver Model Using Big-Bang Big-Crunch Optimized FLC

The main motive of the active suspension system is to enhance the ride comfort by suppressing the vibrations induced due to road irregularities. The actuator is getting more significance in the automotive industry due to its superior ride comfort for passengers. In this study, an eight Degrees of Freedom (DOF) full car with a driver model is considered for the ride comfort analysis (ISO2631 Standard) and vibration control. The real road terrain is not uniform in nature. Hence an effective intelligent control technology is required to improve the quality of travel. Initially, a conventional Proportional Integral and Derivative (PID) controller is designed for the system. Then a Fuzzy Logic Controller (FLC) is designed for the 8 DOF vehicle model to control the unwanted vibration produced in the vertical and angular directions. The FLC is designed with suitable firing rules, membership functions, and scaling factors using MATLAB/Simulink 2019 environment. The performance of FLC is further enhanced by the Big Bang Big Crunch (B3C) optimization technique, and it can suppress vibrations when the vehicle is travelling over bumpy and imperfect random road terrain as per ISO 8608. The Root Mean Square (RMS), Frequency Weighted RMS (FWRMS), and Vibration Dose Value of seat acceleration are the performance indices to investigate the potency of B3C-tuned FLC against the PID controller, FLC and passive suspension system.