Conventional Proportional Derivative Controller Research Articles

Symmetric Nonlinear Feedback Control and Machine Learning for Sustainable Spherical Motor Operation

This paper presents a comprehensive evaluation of a new control technique for the sphere motor system, aimed at achieving accurate tracking, robust and dispersion of vibrations. Control methods include the determination of a nonlinear model and the application of feedback linearization, followed by the optimization of the proportional derivative (PD) coefficients through the Adaptive Neuro-Fuzzy Inference System. In addition, the system’s reaction to harsh environments is managed using Long Short-Term Memory. In order to gain a deeper understanding, symmetrical environmental disturbances and trajectories are introduced during the testing phase. The results demonstrate the superior performance of the control strategy, with reduced vibrations, faster recovery and confirmed tracking accuracy. In addition, the control method shows its adaptability and reliability, as evidenced by the significant reduction in CO2 emissions compared to conventional PD control methods. The use of symmetric trajectories and visualizations further emphasizes the behavior of the system under symmetric conditions, strengthening the effectiveness and applicability of the control strategy in real-world scenarios. Overall, this study presents a promising solution for converting complex systems under different conditions and making them potentially applicable in various industrial contexts.

Benchmarking Tracking Autopilots for Quadrotor Aerial Robotic System Using Heuristic Nonlinear Controllers

This paper investigates and benchmarks quadrotor navigation and hold autopilots’ global control performance using heuristic optimization algorithms. The compared methods offer advantages in terms of computational effectiveness and efficiency to tune the optimum controller gains for highly nonlinear systems. A nonlinear dynamical model of the quadrotor using the Newton–Euler equations is modeled and validated. Using a modified particle swarm optimization (MPSO) and genetic algorithm (GA) from the heuristic paradigm, an offline optimization problem is formulated and solved for three different controllers: a proportional–derivative (PD) controller, a nonlinear sliding-mode controller (SMC), and a nonlinear backstepping controller (BSC). It is evident through the simulation case studies that the utilization of heuristic optimization techniques for nonlinear controllers considerably enhances the quadrotor system response. The performance of the conventional PD controller, SMC, and BSC is compared with heuristic approaches in terms of stability and influence of internal and external disturbance, and system response using the MATLAB/SIMULINK environment. The simulation results confirm the reliability of the proposed tuned GA and MPSO controllers. The PD controller gives the best performance when the quadrotor system operates at the equilibrium point, while SMC and BSC approaches give the best performance when the system does an aggressive maneuver outside the hovering condition. The overall final results show that the GA-tuned controllers can serve as a benchmark for comparing the global performance of aerial robotic control loops.

A PD-Type State-Dependent Riccati Equation With Iterative Learning Augmentation for Mechanical Systems

This work proposes a novel proportional-derivative (PD)-type state-dependent Riccati equation (SDRE) approach with iterative learning control (ILC) augmentation. On the one hand, the PD-type control gains could adopt many useful available criteria and tools of conventional PD controllers. On the other hand, the SDRE adds nonlinear and optimality characteristics to the controller, i.e., increasing the stability margins. These advantages with the ILC correction part deliver a precise control law with the capability of error reduction by learning. The SDRE provides a symmetric-positive-definite distributed nonlinear suboptimal gain <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{K}(\mathrm{x})$</tex> for the control input law <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{u}=-\mathrm{R}^{-1}(\mathrm{x})\mathrm{B}^{T}(\mathrm{x})\mathrm{K}(\mathrm{x})\mathrm{x}$</tex> . The sub-blocks of the overall gain <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{R}^{-1}(\mathrm{x})\mathrm{B}^{T}(\mathrm{x})\mathrm{K}(\mathrm{x})$</tex> , are not necessarily symmetric positive definite. A new design is proposed to transform the optimal gain into two symmetric-positive-definite gains like PD-type controllers as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{u}= -\mathrm{K}_{\mathrm{SP}}(\mathrm{x})\mathrm{e}-\mathrm{K}_{\mathrm{SD}}(\mathrm{x})\dot{\mathrm{e}}$</tex> . The new form allows us to analytically prove the stability of the proposed learning-based controller for mechanical systems; and presents guaranteed uniform boundedness in finite-time between learning loops. The symmetric PD-type controller is also developed for the state-dependent differential Riccati equation (SDDRE) to manipulate the final time. The SDDRE expresses a differential equation with a final boundary condition, which imposes a constraint on time that could be used for finite-time control. So, the availability of PD-type finite-time control is an asset for enhancing the conventional classical linear controllers with this tool. The learning rules benefit from the gradient descent method for both regulation and tracking cases. One of the advantages of this approach is a guaranteed-stability even from the first loop of learning. A mechanical manipulator, as an illustrative example, was simulated for both regulation and tracking problems. Successful experimental validation was done to show the capability of the system in practice by the implementation of the proposed method on a variable-pitch rotor benchmark.

Dynamic velocity error based trajectory tracking for space robotic manipulator

In this paper, proportional derivative control has been explored further to devise dynamic velocity error-based controller for trajectory tracking of space robotic manipulator. The dynamic velocity error is defined using the difference between current velocity and dynamic desired velocity, which is calculated based on the current position and successive desired position. The dynamic velocity error-based controller consists only of the derivative term, unlike conventional proportional derivative control which consists of both proportional as well as derivative terms. Although proposed dynamic velocity error-based controller is simple and robust, the modified versions of direct and indirect adaptive controllers are also presented utilizing dynamic velocity error to handle external disturbances and internal uncertainties in non linear dynamics. Lyapunov theory is employed to prove the stability of the closed-loop system. The main advantage of the dynamic velocity error based controller is that it is as simple as a proportional derivative controller and as robust as adaptive controllers. Finally, the effectiveness of the proposed control designs is validated using numerical simulations, and a comparative study of various control designs has also been provided to substantiate the claims further.

Dynamical Sliding Mode Control for Robust Dynamic Positioning Systems of FPSO Vessels

The conventional proportional derivative (PD) control algorithm with appropriate gain scheduling is generally applied to a dynamic positioning (DP) system. However, finding appropriate gains through gain scheduling makes the DP system more complicated. A sliding-mode control algorithm controls an arbitrary point, such as the turret system on a floating production storage and offloading (FPSO) vessel. This algorithm was developed for DP and can be applied to FPSO vessels considering the uncertainty of the vessel dynamics, unknown time-varying environmental disturbances, and transient performance. To control an arbitrary point on the FPSO vessel using a DP controller, the Jacobian matrix in the kinematic equation is modified to present the arbitrary point in the control. The Lyapunov stability theory is applied in the design of the SM control algorithm to provide robustness to the control system. A time-domain simulation tool was developed to verify the effectiveness of the proposed SM control algorithm. The performance of the control algorithm was evaluated numerically to address its efficacy. The results were compared with those obtained using the conventional PD control algorithm.

A Low-Complexity PD-Like Attitude Control for Spacecraft With Full-State Constraints

The problem of attitude control for rigid spacecraft under the attitude and angular velocity constraints is investigated in this study. Particularly, a simple structure constrained proportional-derivative (PD)-like control is proposed which contains two portions. The first portion is a conventional PD control to provide convergence of the system states; whereas the second portion provides the desired performance specifications such as convergence rate, overshoot and steady-state bound for attitude and rotation velocity to improve the attitude pointing accuracy and pointing stability. The distinctive property of the suggested constrained control method is to ensure the desired performance in transient and steady-state phases for all the system states. It also possesses much simpler structure compared to the existing constrained control techniques since it is based on a new methodology. The simulation results conducted on a rigid spacecraft verify the efficiency of the proposed approach.

2-DOF robot modelling by SimMechanics and PD-FL integrated controller for position control and trajectory tracking

Background Due to the high demand of robots to perform several industrial tasks, such as welding, machining, pick and place, position control in robotics has attracted high attention recently. Controllers’ improvement is also continuous specifically in terms of design simplicity and performance accuracy. This research plans to obtain the SimMechanics model of a two-degree of freedom (DOF) robot and to propose an integrated controller of a proportional–derivative (PD) controller and a fuzzy logic (FL) controller. Methodology The SimMechanics model of the 2-DOF robot is obtained using MATLAB SimMechanics toolbox from a CAD assembly design of the 2-DOF robot. Then, the proposed PD-FL integrated controller is designed and simulated in MATLAB Simulink. The PD controller is widely used for its simplicity, but it doesn’t have a satisfactory performance in difficult tasks. Furthermore, the FL controller is also easy for design and implementation even by non-experts in control theory, but it has the disadvantage of long computational time for multi-input systems due to the increased fuzzy rules. Results The FL controller is integrated with the PD controller for enhanced performance of the 2-DOF robot. The PD-FL integrated controller is developed and tested to control the 2-DOF robot for point-to-point position control and also tip trajectory tracking (TTT) such as triangular TTT and rhombic TTT. Conclusion The PD-FL integrated controller demonstrates enhanced performance compared to the conventional PD controller in both point-to-point position control and TTT. Furthermore, the PD-FL integrated controller has the advantage of less fuzzy rules which helps to overcome the computational time issue of the FL controller.

2-DOF robot modelling by SimMechanics and PD-FL integrated controller for position control and trajectory tracking

Background Due to the high demand of robots to perform several industrial tasks, such as welding, machining, pick and place, position control in robotics has attracted high attention recently. Controllers’ improvement is also continuous specifically in terms of design simplicity and performance accuracy. This research plans to obtain the SimMechanics model of a two-degree of freedom (DOF) robot and to propose an integrated controller of a proportional–derivative (PD) controller and a fuzzy logic (FL) controller. Methodology The SimMechanics model of the 2-DOF robot is obtained using MATLAB SimMechanics toolbox from a CAD assembly design of the 2-DOF robot. Then, the proposed PD-FL integrated controller is designed and simulated in MATLAB Simulink. The PD controller is widely used for its simplicity, but it doesn’t have a satisfactory performance in difficult tasks. Furthermore, the FL controller is also easy for design and implementation even by non-experts in control theory, but it has the disadvantage of long computational time for multi-input systems due to the increased fuzzy rules. Results The FL controller is integrated with the PD controller for enhanced performance of the 2-DOF robot. The PD-FL integrated controller is developed and tested to control the 2-DOF robot for point-to-point position control and also tip trajectory tracking (TTT) such as triangular TTT and rhombic TTT. Conclusion The PD-FL integrated controller demonstrates enhanced performance compared to the conventional PD controller in both point-to-point position control and TTT. Furthermore, the PD-FL integrated controller has the advantage of less fuzzy rules which helps to overcome the computational time issue of the FL controller.

An active force controlled of small CMG-based satellite

Purpose This paper aims to investigate the attitude control pointing improvement for a small satellite with control moment gyroscopes (CMGs) using the active force control (AFC) method. Design/methodology/approach The AFC method is developed with its governing equations and integrated into the conventional proportional-derivative (PD) controller of a closed-loop satellite attitude control system. Two numerical simulations of an identical attitude control mission namely the PD controller and the PD+AFC controller were carried out using the MATLAB®-SimulinkTM software and their attitude control performances were demonstrated accordingly. Findings Having the PD+AFC controller, the attitude maneuver can be completed within the desired slew rate, which is about 2.14 degree/s and the attitude pointing accuracies for the roll, pitch and yaw angles have improved significantly by more than 85% in comparison with the PD controller alone. Moreover, the implementation of the AFC into the conventional PD controller does not cause significant difference on the physical structure of the four single gimbal CMGs (4-SGCMGs). Practical implications To achieve a precise attitude pointing mission, the AFC method can be applied directly to the existing conventional PD attitude control system of a CMG-based satellite. In this case, the AFC is indeed the backbone for the satellite attitude performance improvement. Originality/value The present study demonstrates that the attitude pointing of a small satellite with CMGs is improved through the implementation of the AFC scheme into the PD controller.

PD Control Compensation Based on a Cascade Neural Network Applied to a Robot Manipulator.

A Proportional Integral Derivative (PID) controller is commonly used to carry out tasks like position tracking in the industrial robot manipulator controller; however, over time, the PID integral gain generates degradation within the controller, which then produces reduced stability and bandwidth. A proportional derivative (PD) controller has been proposed to deal with the increase in integral gain but is limited if gravity is not compensated for. In practice, the dynamic system non-linearities frequently are unknown or hard to obtain. Adaptive controllers are online schemes that are used to deal with systems that present non-linear and uncertainties dynamics. Adaptive controller use measured data of system trajectory in order to learn and compensate the uncertainties and external disturbances. However, these techniques can adopt more efficient learning methods in order to improve their performance. In this work, a nominal control law is used to achieve a sub-optimal performance, and a scheme based on a cascade neural network is implemented to act as a non-linear compensation whose task is to improve upon the performance of the nominal controller. The main contributions of this work are neural compensation based on a cascade neural networks and the function to update the weights of neural network used. The algorithm is implemented using radial basis function neural networks and a recompense function that leads longer traces for an identification problem. A two-degree-of-freedom robot manipulator is proposed to validate the proposed scheme and compare it with conventional PD control compensation.

A practical time-delay control scheme for aerial manipulators

In recent years, aerial manipulators consist of unmanned aerial vehicles and robotic manipulators have been widely utilized in aerial operations. The complex dynamic coupling effects between unmanned aerial vehicles and robotic manipulators will bring some issues to the motion control. Therefore, the article proposes a new control scheme for aerial manipulators. The proposed method includes three elements, that is, time-delay estimation, backstepping design, and nonsingular terminal sliding mode. The time-delay estimation technique is adopted to estimate the complex system dynamics and to bring a model-free feature of the system. With the backstepping design, the proposed control strategy can ensure the asymptotic stability of the closed-loop system by recursive procedure. To deal with the unmodelling dynamics and disturbances, and to assure finite-time convergence of the system states, the nonsingular terminal sliding mode is adopted. By combining three elements, the tracking performance of aerial manipulators is improved under unmodelling dynamics and disturbances. Global stability of closed-loop control system is analyzed using Lyapunov stability theory. Finally, comparative simulations are conducted, and the results show that the proposed controller has better performance than a conventional proportional–derivative controller or a nonsingular terminal sliding mode controller.

Linear Quadratic Regulator Method in Vision-Based Laser Beam Tracking for a Mobile Target Robot

SUMMARYThis paper proposes a novel laser beam tracking mechanism for a mobile target robot that is used in shooting ranges. Compared with other traditional tracking mechanisms and modules, the proposed laser beam tracking mechanism is more flexible and low cost in use. The mechanical design and the working principle of the tracking module are illustrated, and the complete control system of the mobile target robot is introduced in detail. The tracking control includes two main steps: localizing the mobile target robot with regards to the position of the laser beam and tracking the laser beam by the linear quadratic regulator (LQR). First of all, the state function of the control system is built for this tracking system; second, the control law is deduced according to the discretized state function; lastly, the stability of the control method is proved by the Lyapunov theory. The experimental results demonstrate that the Hue, Saturation, Value feature-extracting method is robust and is qualified to be used for localization in the laser beam tracking control. It is verified through experiments that the LQR method is of better performance than the conventional Proportional Derivative control in the aspect of converge time, lateral error control, and distance error control.

On the nonlinear dynamics of constant stiffness coefficients 16-pole rotor active magnetic bearings system

The present study is devoted to investigate the oscillatory behaviors of the 16-pole rotor active magnetic bearing system. A controllable electromagnetic force generated via a conventional proportional-derivative controller is utilized to stabilize the system lateral oscillations that excited by the rotating disk eccentricity when the spinning speed (Ω) is close to or equal the system linear natural frequency (ω). The nonlinear dynamical equations governing the controlled system lateral vibrations at constant stiffness coefficients are derived in this article for the first time. Then, four nonlinear autonomous first-order differential equations to describe the considered system oscillation amplitudes and the corresponding phase angles are obtained applying the asymptotic analysis. Bifurcation behavior of the system periodic motions under varying the different control parameters is explored. The main acquired results confirm that the 16-pole rotor-AMB system at constant stiffness coefficients can exhibit one of three oscillatory motions that are periodic, quasiperiodic, or chaotic motions depending on the derivative gain coefficient. Moreover, the system may respond with one-stable solution, bi-stable solutions, tri-stable solutions, or quadri-stable solutions depending on the proportional gain coefficient. Numerical simulations for different system motions are validated via the system time response, Poincare map, orbit plot, and frequency spectrum that are showed an excellent agreement with the obtained analytical results.

Particle swarm optimization based proportional-derivative parameters for unmanned tilt-rotor flight control and trajectory tracking

ABSTRACTThis paper presents the dynamic modelling and control technique for a tilt-rotor aerial vehicle operating in bi-rotor mode. This kind of aircraft combines two flight envelopes, making it ideal for scenarios that require hovering, vertical take-off/landing and fixed-wing capabilities. In this work, a detailed mathematical model is derived using Newton–Euler formalism. Based on the obtained model, a new control scheme that incorporates six Proportional-Derivative (PD) controllers is proposed for the attitudes (roll (φ), pitch (θ), yaw (ψ)) and the positions (x, y, z) of the aircraft. Then, intelligent Particle Swarm Optimization (PSO) and conventional Reference Model (RM) techniques are applied for optimal tuning of the controllers' parameters. The stability analysis is developed using the Lyapunov approach and its application to the tilt-rotor system in the case of intelligent and conventional PD controllers. Numerical results of two scenarios prove the efficiency of the controllers tuned using the PSO method. Indeed, its ability to track the desired trajectories is demonstrated through 3D path tracking simulations, even in the presence of wind disturbances. Finally, experimental tests of stabilization and trajectory tracking are carried out on our prototype. These testing showed that our tilt-rotor was stable and suitably follows the imposed trajectories.

MRAC-Based Voltage Controller for Three-Phase CVCF Inverters to Attenuate Parameter Uncertainties Under Critical Load Conditions

This paper investigates a robust model reference adaptive control (MRAC) method for a three-phase constant-voltage constant-frequency (CVCF) inverter with an output LC filter. The proposed MRAC method is designed to stabilize the error dynamics of the system by a feedback control term in the steady state and attenuate the parameter uncertainties of the system by an updated MRAC term. Unlike the conventional proportional–derivative control (PDC) scheme, the proposed MRAC scheme ensures the fast convergence of the output errors to the exponential trajectories predefined by the reference models. Furthermore, the adaptive state-feedback mechanism can guarantee the fast dynamic response in the transient state without using load current sensors or observers. The asymptotic stability is mathematically proven by a Lyapunov theory. The feasibility of the proposed controller is confirmed through extensive experimental studies on a prototype three-phase CVCF inverter with a TI TMS320LF28335 DSP. Finally, comparative experimental results of three control methods (i.e., conventional PDC, feedback linearization control, and proposed MRAC) are provided to validate the superior performance of the proposed method such as fast transient response, low total harmonic distortion, and robustness to parameter uncertainties under critical load conditions (i.e., abrupt load changes, unbalanced loads, and distorted nonlinear loads).

Robust Learning Control for Shipborne Manipulator With Fuzzy Neural Network.

The shipborne manipulator plays an important role in autonomous collaboration between marine vehicles. In real applications, a conventional proportional-derivative (PD) controller is not suitable for the shipborne manipulator to conduct safe and accurate operations under ocean conditions, due to its bad tracing performance. This paper presents a real-time and adaptive control approach for the shipborne manipulator to achieve position control. This novel control approach consists of a conventional PD controller and fuzzy neural network (FNN), which work in parallel to realize PD+FNN control. Qualitative and quantitative tests of simulations and real experiments show that the proposed PD+FNN controller achieves better performance in comparison with the conventional PD controller, in the presence of uncertainty and disturbance. The presented PD+FNN eliminates the requirements for precise tuning of the conventional PD controller under different ocean conditions, as well as an accurate dynamics model of the shipborne manipulator. In addition, it effectively implements a sliding mode control (SMC) theory-based learning algorithm, for fast and robust control, which does not require matrix inversions or partial derivatives. Furthermore, simulation and experimental results show that the angle compensation deviation of the shipborne manipulator can be improved in the range of ±1°.

Load frequency control for mini-hydropower system: A new approach based on self-tuning fuzzy proportional-derivative scheme

This paper presents a new method for load frequency control (LFC) based on self-tuning fuzzy Proportional-Derivative method. Under dynamic frequency variations, the proportional-derivative (PD) gains will automatically tuned by the fuzzy rules in order to maintain frequency at nominal value. In this paper, the proposed controller was used to controls the frequency of a high-penetration mini-hydropower system. In the microgrid, both diesel generator and mini-hydropower system were designed to meet the demand at low stream flow. However, the diesel generator will be shut down if hydropower generation surpasses the consumer demand. The frequency was controlled by absorbing excess generation from hydropower system through secondary load bank. The system performance with the new control scheme was assessed by simulation under dynamic frequency variations. The simulation result shows the employment of the proposed load frequency controller demonstrates robust and high-performance frequency control compared to conventional fixed-gain PD controller.

Adaptive robust sliding mode trajectory tracking control for 6 degree-of-freedom industrial assembly robot with disturbances

PurposeThis paper aims to present an adaptive robust sliding mode tracking controller for a 6 degree-of-freedom industrial assembly robot with parametric uncertainties and external disturbances. The controller is used to achieve both stringent trajectory tracking, accurate parameter estimations and robustness against external disturbances.Design/methodology/approachThe controller is designed based on the combination of sliding mode control, adaptive and robust controls and hence has good adaptation and robustness abilities to parametric variations and uncertainties. The unknown parameter estimates are updated online based on a discontinuous projection adaptation law. The robotic dynamics is first formulated in both joint spaces and workspace of the robot’s end-effector. Then, the design procedure of the adaptive robust sliding mode tracking controller and the parameter update law is detailed.FindingsComparative tests are also conducted to verify the effectiveness of the proposed controller, which show that the proposed controller achieves significantly better dynamic trajectory tracking performances as compared with conventional proportional derivative controller and sliding mode controller under the same conditions.Originality/valueThis is a new innovation for industrial assembly robot to improve assembly automation.

A Fast Learning Control Strategy for Unmanned Aerial Manipulators

We present an artificial intelligence-based control approach, the fusion of artificial neural networks and type-2 fuzzy logic controllers, namely type-2 fuzzy-neural networks, for the outer adaptive position controller of unmanned aerial manipulators. The performance comparison of proportional-derivative (PD) controller working alone and the proposed intelligent control structures working in parallel with a PD controller is presented. The simulation and real-time results show that the proposed online adaptation laws eliminate the need for precise tuning of conventional controllers by learning system dynamics and disturbances online. The proposed approach is also computationally inexpensive due to the implementation of the fast sliding mode control theory-based learning algorithm which does not require matrix inversions or partial derivatives. Both simulation and experimental results have shown that the proposed artificial intelligence-based learning controller is capable of reducing the root-mean-square error by around 50% over conventional PD and PID controllers.

Enhanced Robust Motion Tracking Control for 6 Degree-of-freedom Industrial Assembly Robot with Disturbance Adaption

Industrial assembly robots are designed to enable accurate and repeatable tracking of the positions and orientations of the robot’s end-effector and are hence often required to perform complex tasks within uncertain environments. Therefore, trajectory tracking control is vital to the wide range of applications of industrial robotic systems. This paper presents an enhanced robust motion tracking controller with disturbance adaption for trajectory tracking control of industrial assembly robot. The dynamics of the industrial assembly robotic system is formulated in the working space of the end-effector and the tracking control problem is then formulated. The enhanced robust motion tracking control is synthesized by using disturbance adaption and modified iterative control terms, which is a refined version of conventional robust adaptive control with only disturbance rejection. The capability and effectiveness of the enhanced robust motion tracking control have been evaluated based on an industrial robotic platform. The comparative results clearly show that the proposed control can be used to better minimize the trajectory tracking errors in finite time as compared with conventional proportional derivative control.