Proportional Derivative Research Articles

Multiple solitons structures in optical fibers via PNLSE with a novel truncated M-derivative: modulated wave gain

This study introduces a novel truncated Mittage–Leffler (M)- proportional derivative (TMPD) and examines its impact on the perturbed nonlinear Schrödinger equation (PNLSE) that includes fourth-order dispersion and cubic-quintic nonlinearity. The TMPD-PNLSE is used to model light signals in nanofibers. In addition to dispersion and Kerr nonlinearity, which are characteristics of the NLSE, the PNLSE also exhibits self-steepening and self-phase modulation effects. The unified method is implemented to derive exact solutions for the model equation. These solutions provide a variety of phenomena; including breathers, geometric chaos, and complex solitons. The solutions also exhibit numerous structures, such as geometric chaos, where undulated M-shaped and M-shaped solitons are embedded. The modulation instability is analyzed, finding that it is triggered when the coefficient of the fourth-order dispersion surpasses a critical value.

Precision Landing of Unmanned Aerial Vehicle under Wind Disturbance Using Derivative Sliding Mode Nonlinear Disturbance Observer-Based Control Method

Unmanned aerial vehicles (UAVs) are extensively employed in civilian and military applications because of their excellent maneuverability. Achieving fully autonomous quadrotor flight and precision landing on a wireless charging station in the presence of wind disturbance has become a crucial research topic. This paper presents a composite control technique for UAV altitude and attitude tracking in harsh environments, i.e., wind disturbance. A composite controller was developed based on nonlinear disturbance observer (NDOB) control theory to allow the UAV to land in the presence of random external wind disturbances and ground effects. The NDOB estimated the unknown wind disturbance, and the estimation was fed into the derivative sliding mode nonlinear disturbance observer-based control (DSMNDOBC), allowing the UAV to perform autonomous precision landing. Two loop designs were applied: the inner loop for stabilization and the outer loop for altitude tracking. The quadrotor model dynamics and the proposed controller, DSMNDOBC, were simulated employing MATLAB/Simulink®, and the results were compared with the one obtained by the proportional derivative (PD) controller and the sliding mode controller (SMC). The simulation results indicated that the DSMNDOBC has superior altitude and attitude control compared to the PD and SMC controllers and better disturbance estimation and attenuation performance.

Dynamic Response of an Overhead Crane with Anti-Swing Controller in Driving Force and Energy Consumption

Cargo sway caused by overhead crane operation not only reduces crane efficiency and safety but also affects the driving force and energy consumption of the operating mechanism. In this paper, a control scheme based on proportional derivative (PD) control and an input shaping technique is proposed to suppress cargo sway. First, the dynamics model of the crane system is established, and the mathematical expressions of the cargo sway, driving force, and energy consumption are derived. The accuracy of the dynamics model is verified through a comparison between the simulations and experiments. Then, a PD-IS controller is designed based on the dynamics model. Finally, the performance of the designed controller is simulated under four typical excitation signals and compared to that of the standard PD controller.

Optimization of mass and heat flux of MHD viscous fluid flow with constant proportional Caputo derivative by using response surface methodology: Sensitivity analysis

The study of viscous dissipation in the context of unsteady incompressible magnetohydrodynamic viscous fluid flow over a moving plate is a complex and important topic in fluid dynamics and heat transfer. This scenario combines several physical phenomena and has practical applications in various engineering and scientific fields. The fractional mathematical model is proposed by considering the effect of viscous dissipation force of the flowing fluid. For this purpose, fluid is assumed to be lying over a vertical plate that is moving in its own plane. The governing equations are transformed into the dimensionless form and developed fractional model with a new operator Constant Proportional Caputo Derivative. We used the Laplace transform technique to find the solution of the dimensionless governing equation analytically. The transformed solutions for energy and momentum balances developed in terms of series. The validation of the present model comparison graphs is plotted for temperature. The sensitivity of different input parameters on output response are analyzed and displayed the sensitivity results in tabular and graphical form and found that the permeable parameter is most sensitive to skin friction coefficient, and the Eckert number is most sensitive parameter among others to Nusselt Number. The novelty of present work is to develop a correlation between input parameters and output responses by using Response Surface Methodology (RSM). As no such correlation has been developed for optimization of mass and heat flux of MHD viscous fluid flow with Constant Proportional Caputo derivative by using RSM. By using this correlation, we have performed sensitivity analysis for output responses.

Anti-Swaying Control Strategy of Ship-Mounted 3-RCU Parallel Platform Based on Dynamic Gravity Compensation

It is essential to ensure stability during marine transportation or the installation of high center of gravity loads. The heavy loads increase gravity disturbance, affecting the steady-state-error control of the multiple degrees of freedom (DOFs) motion compensation platform. In this paper, we propose a proportional derivative (PD) controller with dynamic gravity compensation (PDGC) for a 3-RCU (revolute–cylindrical–universal) parallel platform to improve the control effect of marine motion compensation for high center of gravity loads. We introduce an evaluation parameter of load stability and a weighting coefficient of anti-swaying control to tune the controller performance. The controller can set its control target between the two, keeping the load contact surface level and allowing the load center of gravity with the least movement. By deriving the Jacobian matrix, the gravity disturbance in the joint space is calculated and is compensated in the controller. First, we verify the control superiority of this controller over the PD controller under sinusoidal excitation in simulation and validate the effectiveness of the proposed anti-swing strategy. Then, the experiments are conducted with random excitation. The root mean square (RMS) value of the load’s residual angle with the proposed controller is reduced to 32.2% and 17.6% in two directions, respectively, compared with the PD controller under class 4 sea state excitation. The proposed method is effective for the anti-swaying control of ship-mounted 3-RCU parallel platforms.

Robust Observer-Based Proportional Derivative Fuzzy Control Approach for Discrete-Time Nonlinear Descriptor Systems with Transient Response Requirements

This paper proposes an observer-based proportional Derivative (O-BPD) fuzzy controller for uncertain discrete-time nonlinear descriptor systems (NDSs). Representing NDSs with the Takagi–Sugeno fuzzy model (T-SFM), the proportional derivative (PD) feedback method can be utilized in the fuzzy controller design via the Parallel Distributed Compensation (PDC) concept, such that the noncausal problem and impulse behavior are avoided. A fuzzy observer is proposed to obtain unmeasured states to fulfill the PD fuzzy controller. Moreover, uncertainties and transient response performances are taken into account for the NDSs. Then, a stability analysis process and corresponding stability conditions are derived from the Lyapunov theory with the robust control method and the pole constraint. Different from existing research, the Singular Value Decomposition (SVD) and the projection lemma are utilized to transfer the stability conditions into the Linear Matrix Inequation (LMI) form. Because of this reason, the conservatism of the analysis process can be reduced by eliminating the restriction on the positive definite matrix in the Lyapunov function. By giving the proper center and radius parameters of the pole constraint in the O-BPD fuzzy controller design process, the expected transient responses can be obtained for different designers and different practical applications. Finally, the effectiveness and applicability of the proposed O-BPD fuzzy controller are demonstrated by two examples of the simulation.

Adaptive cruise control system with fractional order ANFIS PD+I controller: optimization and validation

Designing the control structures of fractional order PID controllers has proven to be effective in providing adaptability in set point tracing the performance of a nonlinear cruise control system. Wheel rolling resistance, wind drag force, and road gradient are incorporated into the design to better describe the system under consideration and to show how the nonlinear cruise control system behaves. This study presents a comparative investigation using simulation between control structures such as fractional order proportional–integral–derivative, fractional order integral minus proportional derivative, and fractional order proportional integral minus derivative. By preserving integral error indices as the goal function, a genetic algorithm is used to improve the controller gain parameters and fractional scaling values. To prevent integral windup conflicts and derivative boost issues, both traditional fractional order structures and adaptive neuro-fuzzy-based fractional order structures were used to create the adaptive cruise control system. The FO ANFIS PD plus I controller for the cruise control system exceeds the competition in servo and regulatory difficulties.

Insights on equidistributed real spectral values in second-order delay systems: Perspectives in partial pole placement

In this work, we show that the coexistence of the maximal number of real spectral values of generic single-delay retarded second-order differential equations guarantees the realness of the rightmost spectral value. From a control theory standpoint, this entails that a delayed proportional-derivative (PD) controller can stabilize a delayed second-order differential equation. By assigning the maximum number of negative roots to the corresponding characteristic function (a quasipolynomial), we establish the conditions for asymptotic stability. If the assigned real spectral values are uniformly distributed, we specify a necessary and sufficient condition for the rightmost root to be negative, thus guaranteeing the exponential decay rate of the system’s solutions. We illustrate the proposed design methodology in the delayed PD control of the damped harmonic oscillator. It is worth mentioning that this work represents a natural continuation of Amrane et al. (2018) and Bedouhene et al. (2020), addressing the problem of coexisting real spectral values for linear dynamical systems including delays in their models.

Disturbance observer‐based control for cable‐driven parallel robots with external disturbance using deep reinforcement learning

AbstractIn cable‐driven parallel robots (CDPRs) practical applications, external disturbances inevitably influence the actuator performance, leading to low positioning accuracy of end‐effector (EE), and even system crashes. This paper addresses a disturbance observer‐based control scheme using deep reinforcement learning (RL) to suppress the effect of external disturbances. A controller via the non‐singular terminal sliding mode (NTSM) is proposed to enhance the system robustness. The estimation of the disturbance is investigated, and the deep RL is employed to enhance the model‐based disturbance observer, namely, the RLDO, and a corresponding controller via NTSM (RLDO‐NTSMC) is proposed. Simulations and experimental results validate that the RLDO effectively improves the estimation accuracy, and the RLDO‐NTSMC significantly increases the control accuracy of CDPRs. The root mean square errors of the EE's positioning errors controlled by the RLDO‐NTSMC decreased by over 93% compared with the classical augmented proportional–derivative (APD) controller.

Soret Effect on MHD Casson Fluid over an Accelerated Plate with the Help of Constant Proportional Caputo Fractional Derivative.

Non-Newtonian fluid flow is significant in engineering and biomedical applications such as thermal exchangers, electrical cooling mechanisms, nuclear reactor cooling, drug delivery, blood flow analysis, and tissue engineering. The Caputo operator has emerged as a prevalent tool in fractional calculus, garnering widespread recognition. This research aims to introduce a novel derivative by merging the proportional and Caputo operators, resulting in the fractional operator known as the constant proportional Caputo. In order to demonstrate this newly defined operator's dynamic qualities, it was employed in the analysis of the unsteady Casson flow model. In addition, the current work shows an analytical analysis to determine the Soret effect on the fractionalized MHD Casson fluid over an oscillating vertical plate. Fractional partial differential equations (PDEs) are used to formulate the problem along with IBCs. The introduction of appropriate nondimensional variables converts the PDEs into dimensionless form. The precise solutions to the fractional governing PDEs are then determined by the Laplace transform method. Velocity, concentration, and temperature profiles; the impacts of the Prandtl number; fractional parameter β and γ; and Soret and Schmidt numbers are graphically depicted. The profiles of temperature, concentration, and velocity rise with rising time and fractional parameters. Interestingly, as the Casson flow parameter is higher, fluid velocity decreases closest to the plate but increases away from the plate. Tables showing the findings for the skin-friction coefficient, Sherwood, and Nusselt numbers for a range of flow-controlling parameter values are provided. Furthermore, an investigation is undertaken to compare fractionalized and ordinary velocity fields. The results suggest that the fractional model employing a constant proportional derivative exhibits a quicker decay than the model incorporating conventional Caputo and Caputo-Fabrizio operators.

PD-Based Iterative Learning Control for the Nonlinear Low-Speed-Jitter Vibration of a Wind Turbine in Yaw Motion

Aiming at the nonlinear low-speed-jitter (LSJ) vibration suppression for a yaw system of a megawatt wind turbine, a kinematics mechanism of the yaw system is investigated from the perspective of tribology, and a kinematics model of the yaw system based on an equilibrium position is established. On the basis of the dynamic modeling of the yaw system, a nonlinear mathematical model of the LSJ system is deduced. Based on the two lead motors’ driving of the conventional yaw motion, an innovative design with a special installation of two auxiliary motors for yaw transmission is carried out, which is integrated with a matching centralized lubrication system (CLS). Based on open-loop proportional-derivative (PD) control and the iterative learning control methods of the time-varying continuous system, the stability control and jitter amplitude suppression of the yaw system are realized by using a combined driving torque provided by the lead and auxiliary gears. From the stability and convergence of the time-domain response and the convergence of the iterative error, the effectiveness of the iterative learning control method with the PD-based regulation is verified, and its advantages for engineering applications are shown based on the algorithm solver improvement. The feasibility of the physical realization and engineering application of the control methodology is verified by using controller-hardware-in-the-loop (C-HITL) simulation technology.

Stabilization and tracking control of underactuated ball and beam system using metaheuristic optimization based TID-F and PIDD2-PI control schemes.

In this paper, we propose two different control strategies for the position control of the ball of the ball and beam system (BBS). The first control strategy uses the proportional integral derivative-second derivative with a proportional integrator PIDD2-PI. The second control strategy uses the tilt integral derivative with filter (TID-F). The designed controllers employ two distinct metaheuristic computation techniques: grey wolf optimization (GWO) and whale optimization algorithm (WOA) for the parameter tuning. We evaluated the dynamic and steady-state performance of the proposed control strategies using four performance indices. In addition, to analyze the robustness of proposed control strategies, a comprehensive comparison has been performed with a variety of controllers, including tilt integral-derivative (TID), fractional order proportional integral derivative (FOPID), integral-proportional derivative (I-PD), proportional integral-derivative (PI-D), and proportional integral proportional derivative (PI-PD). By comparing different test cases, including the variation in the parameters of the BBS with disturbance, we examine step response, set point tracking, disturbance rejection analysis, and robustness of proposed control strategies. The comprehensive comparison of results shows that WOA-PIDD2-PI-ISE and GWO-TID-F- ISE perform superior. Moreover, the proposed control strategies yield oscillation-free, stable, and quick response, which confirms the robustness of the proposed control strategies to the disturbance, parameter variation of BBS, and tracking performance. The practical implementation of the proposed controllers can be in the field of under actuated mechanical systems (UMS), robotics and industrial automation. The proposed control strategies are successfully tested in MATLAB simulation.

Limited Integrator Antiwindup-Based Control of Input-Constrained Manipulators

The limited integrator anti-windup (LIAW) is a helpful method that can be applied to improve performance in systems with constrained inputs. However, the use of this technique has relied on no formal stability framework but on intuition. To the best of our knowledge, Lyapunov's theory has yet to be applied to study the advantages of the LIAW when used in an adaptive control scheme. This paper introduces an adaptive gravity compensation proportional-derivative (PD) plus LIAW algorithm to solve the joint position regulation of input-constrained robot manipulators. Moreover, this paper also reports the real-time experimental comparison among three control strategies: An adaptive nonlinear proportional-integral-derivative (PID) controller without any anti-windup extension, an adaptive PID scheme with a nonlinear anti-windup augmentation already reported in the literature, and the proposed adaptive PD plus LIAW algorithm. The experimental comparison departs from the idea of using PID-type controllers tuned with the same gains but without any special care for the input limitations. The advantages of the LIAW extension are then observed. Better performance results are obtained for the proposed adaptive PD plus LIAW solution.

Controlling temperature using proportional integral and derivative control algorithm for hybrid forced convection solar dryer

Drying is one of the crucial processes in agricultural production, especially in grain processing. The drying process can improve grain quality and affect the grain content. However, maintaining the temperature is a challenge in the drying process. Because it can influence the drying performance and produce a low-efficiency reduction of water content, in this study, the hybrid drying system is proposed to improve the performance of the forced convection dryer system. The proposed system used a proportional integral and derivative (PID) control system to obtain the optimal temperature. The proposed system was compared with natural drying and forced convection methods. The experimental result showed that the proposed system performed excellently for three performance evaluations. The average temperature was obtained as the highest of the other methods, with 54.68 °C and 54.55 °C for coffee and cocoa beans. The water content can be reduced by an average of 27.38% and 42.67% for coffee and cocoa beans. Then, the proposed system also had the highest reduction efficiency of water content than the other methods, with 62.71% and 36.94% reductions for coffee and cocoa beans, respectively. The results indicate that the proposed hybrid system performs better than the other methods.

Forecasting and dynamical modeling of reversible enzymatic reactions with a hybrid proportional fractional derivative

Chemical kinetics is a branch of chemistry that investigates the rates of chemical reactions and has applications in cosmology, geology, and physiology. In this study, we develop a mathematical model for chemical reactions based on enzyme dynamics and kinetics, which is a two-step substrate–enzyme reversible reaction, applying chemical kinetics-based modeling of enzyme functions. The non-linear differential equations are transformed into fractional-order systems utilizing the constant proportional Caputo–Fabrizio (CPCF) and constant proportional Atangana–Baleanu–Caputo (CPABC) operators. The system of fractional differential equations is simulated using the Laplace–Adomian decomposition method at different fractional orders through simulations and numerical results. Both qualitative and quantitative analyses such as boundedness, positivity, unique solution, and feasible concentration for the proposed model with different hybrid operators are provided. The stability analysis of the proposed scheme is also verified using Picard’s stable condition through the fixed point theorem.

Analysis of the proportional Caputo-Fabrizio derivative

Analysis of the proportional Caputo-Fabrizio derivative

An innovative fuzzy logic based controller for solid oxide fuel cells

The solid oxide fuel cell (SOFC) stands out as a vital component in sustainable distributed generation systems, thanks to its reliability and adaptable power generation capabilities. This adaptability allows the SOFC to efficiently balance grid power by adjusting its power output. Nevertheless, maintaining the desired fuel usage rate and achieving rapid load tracking pose considerable hardships in SOFC control. To deal with these difficulties, this study introduces a novel approach, the Cascaded Double Input Interval Type-2 Fuzzy Logic Controller (C-DIT2-FLC), designed for SOFC control. In this innovative model, the Improved Salp Swarm Algorithm (ISSA) is applied to determine the crucial parameters of Proportional Integral-Proportional Derivative (PI-PD) cascade controllers. The C-DIT2-FLC dynamically adjusts the controller gains, which are optimized using ISSA, to enhance the effectiveness of SOFC operations. The research results substantiate the superior efficacy of the C-DIT2-FLC over conventional controllers, thereby providing enhanced control and performance capabilities for SOFC systems.

Application of Constant Proportional Caputo Fractional Derivative to Thermodiffusion Flow of MHD Radiative Maxwell Fluid under Slip Effect over a Moving Flat Surface with Heat and Mass Diffusion

Thermal diffusion is a phenomenon where the concentration gradient or diffusive flux is created due to the temperature gradient. Thermal diffusion is induced because of the higher temperature and uneven distribution of the mixture. Formally, thermal diffusion is called the Soret effect, and it is a crucial factor in a number of natural occurrences like the separation of isotopes technique of purification. In this research paper, Maxwell fluid’s flow in the vicinage of a flat plate is discussed by considering the effect of the thermodiffusion subject to the first-order slip at the boundary with the application of a constant proportional Caputo (CPC) fractional derivative. The effect of heat generation and radiation is also taken into consideration, as well as the effect of a magnetic field of constant magnitude. The generalized heat and mass fluxes are considered, and this generalization of heat and mass fluxes is done by utilizing the CPC fractional derivative. After converting the current model’s governing equations into a dimensionless form, the temperature, concentration, and velocity fields’ analytical solutions are found. By drawing graphs of the temperature, concentration, and velocity fields for the parametric modifications, the results are graphically illustrated. It becomes clear from the results discussion that the outcomes produced by the constant proportional derivative are more decaying than those obtained with the classical differential operator of order one.

Spotted Hyena Optimizer enhances the performance of Fractional-Order PD controller for Tri-copter drone

AbstractIn this study, nonlinear control design is presented for trajectory tracking of Tricopter system. A Fractional Order Proportional Derivative (FOPD) controller has been developed. The performance of controlled Tri-copter system can be enhanced by suggesting modern optimization technique to optimally tune the design parameters of FOPD controller. The Spotted Hyena Optimizer (SHO) is proposed as an optimization method for optimal tuning of FOPD's parameters. To verify the performance of controlled Tricopter system based on optimal SHO-based FOPD controller, computer simulation is implemented via MATLAB codes. Moreover, a comparison study between SHO and Particle Swarm Optimization (PSO) has been made in terms of robustness and transient behavior characteristics of FOPD controller.

Development of a master–slave 3D printed robotic surgical finger with haptic feedback

Robotic surgery started nearly 30 years ago. It has achieved telepresence and the performance of repetitive, precise, and accurate tasks. The “master–slave” robotic system allows control of manipulators by surgeon at distant site. Robotic surgical fingers were developed to allow surgeons to move them with accuracy through sensors fixed on surgeon’s hand. Also, haptic sensors were developed to allow transmission of sensation from robotic finger to surgeon’s finger. A complete system of a, 3D printed by a stereolithography (SLA) 3D printer, robotic surgical finger with haptic feedback system is proposed. The developed system includes a master glove that controls the motion of a 3DOF robotic slave finger while getting haptic feedback of force/pressure exerted on it. The precise control of the slave robotic finger was achieved by applying a Proportional Integral and Derivative (PID), fast and robust, control algorithm using an Arduino based hardware and software module. The individual joint angles, metacarpophalangeal joint (MCP) and proximal interphalangeal joint (PIP), and wrist were measured using rotatory and inertial sensors respectively. The degree of movement for MCP, PIP, and Wrist joints were measured to be 0–86°, 0–71°, and 0–89° respectively. Motion to the robotic finger is mimicked by a glove motion requiring minimal learning curve for the device. The collected data for the slave motion is in good agreement with the master-glove motion data. The vibro-tactile haptic feedback system was developed to distinguish between three different materials to mimic human flesh, tumor, and bone. The master–slave system using robotic surgical finger with good simultaneous movement to surgeon’s finger and good haptic sensation will provide the surgeon with the opportunity to perform finger dissection in laparoscopic and robotic surgery, as it used to be in open surgery. 3D bio printing will make this process even cheaper with the added advantage of making surgical tools locally according to the need of the surgery. An ongoing work is to develop silicone based 8 mm robotic surgical finger with multiple type haptic feedback.