Classical Proportional Derivative Research Articles

Altitude control of a quadcopter using interval type-2 fuzzy controller with dynamic footprint of uncertainty

Footprint of uncertainty (FOU) characteristics of interval type-2 membership functions (IT2-MFs) play an important role in the performance and robustness of interval type-2 fuzzy controllers (IT2-FCs). In literature, fixed FOU structures are used in almost all IT2-FC designs. In this study, an IT2-FC with dynamic FOU is proposed to provide high performance and robustness in the altitude control of a quadcopter. A proportional–derivative (PD) type FC with Takagi–Sugeno rule structure is used in the design procedure of the proposed controller. Additionally, input variables (error and derivative of error) are defined by using triangular IT2-MFs. To provide a dynamic FOU structure, the height of the lower MF (LMF) of each interval type-2 fuzzy set is defined as a function of the system error. In this way, FOU levels of IT2-MFs are adjusted dynamically since the height value of the LMF directly determines the FOU level of the IT2-MF. To evaluate the effectiveness of the proposed controller, comparison studies are performed under different conditions, including unmodeled measurement noises, an external disturbance, and a system parameter uncertainty. A classical PD, a type-1 fuzzy PD, and an interval type-2 fuzzy PD with fixed FOU controllers are used in the comparisons. The comparison results demonstrate that the proposed interval type-2 fuzzy PD controller with dynamic FOU exhibits better performance and more robustness than the other controllers.

Reference Spreading: Tracking Performance for Impact Trajectories of a 1DoF Setup

In this brief, trajectory tracking control for nonperiodic motions with impacts is analyzed by means of physical experiments. This brief aims at demonstrating the effectiveness and robustness of the control method called reference spreading (RS) on a physical setup. An actuated rebounding pendulum, a one-degree-of-freedom system specifically designed for performing trajectories with partially elastic impacts, acts as a test bench. RS control is compared to both classic proportional derivative (PD) feedback control and distance function-based control, showing superior performance. Evidence of RS’s robustness to delayed impact detection, deteriorated velocity estimation accuracy, and model inaccuracies is moreover reported.

Active Queue Management Supporting TCP Flows Using Disturbance Observer and Smith Predictor

Active queue management (AQM) is a technique to avoid serious congestion of the transmission control protocol (TCP) flows at a router. AQM based on control theory, which utilizes congestion controllers such as proportional-derivative (PD) controller or proportional-integral-derivative (PID) controller, has been previously proposed. In addition, disturbance observer (DOB) has been utilized to compensate for modeling error of a TCP/AQM congestion control system. However, the DOB-based controllers cannot cope with a large time delay in TCP/AQM networks. Although one of the effective time delay compensators is Smith predictor (SP), the implementation of the DOB and SP in an integrated manner has not been accomplished, because of saturation due to the input limit of packet drop probability. In this paper, a novel TCP/AQM congestion control system with the DOB and SP considering the saturation function is proposed to compensate for the modeling error and time delay simultaneously. Simulation results show that the proposed controller provides better throughput and goodput than conventional controllers. One of the simulations assume that the propagation delay and bottleneck link capacity are set to 100 ms and 100 Mbps, respectively. Under this assumption, it is confirmed that the proposed controller achieves a goodput of 99.55 Mbps whereas the classical PID controller and PD controller with DOB achieve 99.23 Mbps and 99.24 Mbps, respectively.

Position controller design and implementation of ball and beam system with SMC and PD control methods

Today, several methods are proposed and tested for controlling many nonlinear and unstable systems. This study employed the sliding mode control (SMC) and proportional-derivative (PD), which are used to control the position and modeling of ball and beam system that is a fundamental system used to test the control methods. Such systems are nonlinear and unstable due to their nature. Therefore, these systems are affected by external disturbances and this leads to a decrease in the control quality. The study tested the system by utilizing the classical PD and SMC methods, and the results were assessed by employing the Integral-Square-Error (ISE) performance criterion. The system results were provided as graphics and tables. Besides, the results were compared and analyzed.

Indoor Multi-Camera-Based Testbed for 3-D Tracking and Control of UAVs

Flight testbeds with multiple unmanned aerial vehicles (UAVs) are especially important to support research on multi-vehicle-related algorithms. The existing platforms usually lack a generic and complete solution allowing for software and hardware design. For such a purpose, this paper presents the design and implementation of a comprehensive multi-camera-based testbed for 3-D tracking and control of UAVs. First, the testbed software consists of a multi-camera system and a ground control system, which performs image processing, camera calibration, 3-D reconstruction, pose estimation, and motion control. In the multi-camera system, the positions and orientations of UAVs are first reconstructed by using epipolar geometric constraints and triangulation methods and then filtered by an extended Kalman filter (EKF). In the ground control system, a classical proportional–derivative (PD) controller is designed to receive the navigation data from the multi-camera system and then generates control commands to the target vehicles. Then, the testbed hardware employs smart cameras with field-programmable gate array (FPGA) modules to allow for real-time computation at a frame rate of 100 Hz. Lightweight quadcopter Parrot Bebop drones are chosen as the target UAVs, which does not require any modification to the hardware. Artificial infrared reflective markers are asymmetrically mounted on target vehicles and observed by multiple infrared cameras located around the flight region. Finally, extensive experiments are performed to demonstrate that the proposed testbed is a comprehensive and complete platform with good scalability applicable for research on a variety of advanced guidance, navigation, and control algorithms.

Adaptive output control of a mobile manipulator hanging from a quadcopter unmanned vehicle

This article summarizes the comprehensive design of an adaptive control that solves the trajectory tracking of a four-rotor unmanned aerial vehicle supplied by an own-designed grasping device. The controller design uses the regular proportional–derivative (PD) structure which is common to solve regulation, as well as tracking problems for robotic systems. The PD structure needs the estimation of the time-derivative to be exerted on-line. The super-twisting algorithm served to operate as a decentralized estimator of the derivatives for the tracking errors. The controller gains were adjusted by the differential laws aimed to track attainable reference trajectories. The adaptive strategy adjusts the controller gains enforcing the convergence of both the estimation and the tracking errors. A numerical example showed the observer/controller performance. A comparison with a classic non-adaptive PD controller confirms the effectiveness on the tracking task by the proposed design. In addition, a set of virtual numerical evaluations using the parameters of a real quadcopter system confirmed the performance benefits of the adaptive controller based on the PD structure aided with the estimation of the velocity obtained by the observer.

Proportional Retarded Control of Robot Manipulators

In the present contribution, a methodology to solve the tracking control problem of robot manipulators through the use of a Proportional Retarded plus Gravity (PR+G) compensation scheme is presented. The main advantage of the proposal is to avoid the necessity of velocity measurements or their estimation, which is commonly used in most control schemes, such as the proportional derivative-type controllers or the computed torque control. The design of the PR+G controller is addressed via σ-stability analysis and its performance is tested in an experimental platform that consists of 2 degrees of the freedom robot manipulator. The proposed controller is compared with a classic proportional derivative plus gravity compensation scheme. The results are analyzed from a frequency perspective and measured by a quadratic error index.

An Expanded Two-Dimensional Proportional–Derivative Command to Line-of-Sight Guidance Law

This paper deals with an expanded two-dimensional (2D) proportional-derivative (PD) command to line-of-sight (CLOS) guidance law which fights the spiral type trajectory of an anti-tank guided missile (ATGM) in the plane perpendicular to the line-of-sight (LOS) or the so called picture plane, in order to improve the transition process performance while putting the missile onto the LOS. The guidance law acts as a classical PD control law within a small predetermined area around the LOS while at missile deviations pointing a position outside this area the control law includes additional nonlinear components connected with the derivatives of the missile position vector in the plane perpendicular to the LOS. The global asymptotic stability of the guidance loop is established by a specific positive definite Lyapunov function. The effectiveness of the proposed approach is illustrated by simulation results. The guidance law enables to decrease the near-field boundary of the missile operational range.

Fast Ferry Smoothing Motion via Intelligent PD Controller

A novel type of control law was adopted to reduce the vertical acceleration of a fast ferry as well as the motion sickness incidence suffered by the passengers onboard by means of a submerged T-foil. Considering the system changing characteristics under high disturbances, a model-free approach was adopted. In addition, an upgraded proportional-derivative (PD) controller with correction terms resulting from a fast-online estimation of the system dynamics was designed. The overall controller, known as intelligent PD (i-PD) controller, was tested, and the obtained results were compared with those of a classic PD controller. The controllers were also tested in a changing environment and at different operating velocities. The results confirmed the effectiveness of the i-PD controller to smooth the motions with low computational cost control schemes. Furthermore, thanks to ability of the i-PD controller to continually update the estimated dynamics of the system, it showed a better reduction in both vertical motions and the seasickness level of the passengers with the needed robustness under external disturbances and system changing parameters.

A nonlinear controller based on saturation functions with variable parameters to stabilize an AUV

This paper deals with a nonlinear controller based on saturation functions with variable parameters for set-point regulation and trajectory tracking control of an Autonomous Underwater Vehicle (AUV). In many cases, saturation functions with constant parameters are used to limit the input signals generated by a classical PD (Proportional-Derivative) controller to avoid damaging the actuators; however this abrupt bounded harms the performance of the controller. We, therefore, propose to replace the conventional saturation function, with constant parameters, by a saturation function with variable parameters to limit the signals of a PD controller, which is the base of the nonlinear PD with gravitational/buoyancy compensation and the nonlinear PD + controllers that we propose in this paper. Consequently, the mathematical model is obtained, considering the featuring operation of the underwater vehicle LIRMIA 2, to do the stability analysis of the closed-loop system with the proposed nonlinear controllers using the Lyapunov arguments. The experimental results show the performance of an AUV (LIRMIA 2) for the depth control problems in the case of set-point regulation and trajectory tracking control.

TWO DOF ROBOT CONTROL WITH FUZZY BASED NEURAL NETWORKS

In this study, trajectory control of robotic arm which has two degrees of freedom (DOF) is conducted by using the control methods of Proportional-Derivative (PD), Adaptive Neuro Fuzzy System (Anfis), hybrid PD-Anfis and its performance analysis is carried out. In the design of the robot, forward kinematics, inverse kinematics and dynamic equations are used. Firstly, the PD controller is executed, and then the PD controller and Anfis controller are compared applying to a different controller approach with the Anfis of Matlab/Simulink software. The positive and negative sides of the Anfis controller are compared and hybrid PD-Anfis controller method is conducted as a different approach to eliminate the negative sides. While the system constants K p and K v are kept constant by the classical PD control method, the output of PD controller is trained with Anfis in the new method and the output value is adjusted according to the error and the change rate of the error. By this way, outputs which have less error rate and which are able to follow the reference better are obtained.

A Structure Simple Controller for Satellite Attitude Tracking Maneuver

This paper addresses a difficult problem of designing a control approach with simple structure to perform attitude tracking maneuver for rigid satellites. The satellite is subject to external disturbance torque and uncertain inertia parameters. An observer-based estimation law is first proposed to reconstruct the uncertain dynamics. It is shown that such estimation can be achieved with zero estimation error after finite time. A proportional–derivative (PD)-type controller including a classical PD control effort and a compensation control part is then presented. The compensation control is designed based on the estimated information, and applied to completely reject the uncertain dynamics. The closed-loop attitude tracking system is governed to be asymptotically stable. Moreover, the control performance can be achieved by tuning control gains in the theoretical framework of classic PD control theory. Simulation and experimental test are carried out to verify the effectiveness of the developed approach.

Fuzzy fast terminal sliding mode vibration control of a two-connected flexible plate using laser sensors

A kind of non-contact vibration measurement method for a two-connected flexible piezoelectric plate using laser sensors is proposed. Decoupling of the bending and torsional vibration on measurement and driving control is carried out via using two laser displacement sensors and piezoelectric actuators. The fuzzy fast terminal sliding mode controller (FFTSMC) is investigated to suppress both the larger and the smaller amplitude vibrations quickly. In order to alleviate the chattering phenomenon and enhance the control effect, the fuzzy logic adaptive algorithm is used to adjust the switching control gain for softening the signum function adaptively. To verify the non-contact measurement method and the designed controller, the experimental setup is built up. Experiments on active vibration control using the designed FFTSMC are conducted, compared with the classical proportional derivative (PD) control algorithm. The experimental identification results demonstrate that the laser displacement sensors can detect the low-frequency bending and torsional vibration effectively, after using the decoupling method. Furthermore, the designed FFTSMC can suppress both bending and torsional vibration more quickly than the designed PD controller owing to the adjustment of the switching control gains and the softening factors, especially for the small amplitude residual vibrations.

Active Vibration Control to Attenuate Hand-arm Vibration from Orbital Sander: A Mathematical Model Approach

Prolonged exposure to the orbital sander with high vibration level can lead to the Hand-arm Vibration Syndrome (HAVs). In order to attenuate the vibration when using the orbital sander, dynamic analysis of the orbital sander is carried out using coupled orbital sander-hand-arm model subjected to the Active Vibration Control (AVC). The orbital sander is modelled as a three-degree-of-freedom system where the values of the dynamic mass, stiffness and damping are derived from the experimental modal analysis and the single-degree-of-freedom of Reynolds and Soedel model is chosen to represent the hand-arm system. Various control schemes are applied in the AVC system including Proportional-Derivative (PD) and Active Force Control (AFC) techniques. Two disturbances are created for the system where the first disturbance is measured from the orbital sander operating condition and the second disturbance is modelled as a sine wave to test the robustness of the control schemes. The simulation result shows that the control scheme with AFC produced a superior result compared to the classical PD controller, even though under the influence of external disturbance with a vibration reduction of 99% and 88%, respectively.

A Microsatellite Reaction Wheel Based on a Fuzzy Logic Controller for the Attitude Control System

Current interest in small satellites lies in the feasibility of achieving specific but limited objectives, by necessity, small satellites technology requires simple control schemes. In this paper, we present a fuzzy logic controller, as an attempt to replace the classical proportional derivative (PD) controller that is widely used in the spacecraft attitude determination control system (ADCS). The fuzzy logic controller is implemented on the Z axis (yaw) closed loop reaction wheel of a low earth orbit microsatellite with a gravity gradient stabilization. The yaw axis is pointed toward earth. We mention here that, when the spacecraft is not in the imaging mode, it starts spinning along the yaw axis to keep it within thermal limits. So that, in this axis the spacecraft is either in the imaging mode (freeze mode) or barbeque mode (BBQ mode).

Proportional derivative fuzzy control supplied with second order sliding mode differentiation

The fuzzy logic controller (FLC) has the ability of handling parametric uncertainties and external perturbations for unknown systems. A regular structure for a FLC is the proportional derivative (PD) form. The proportional derivative fuzzy controller (PDF) could be seen as a variable gain PD controller. Despite this characteristic, the most common drawback for any PD controller, with unknown dynamics or even with unmodeled dynamics is the error signal differentiation. In this manuscript this disadvantage was overtaken implementing the super-twisting algorithm (STA) as a robust exact differentiator (RED). The information provided by the STA was injected into the PDF to enhace its performance. In this study, the stability of the nonlinear system under the fuzzy super twisting PD controller (FSTPD) in closed loop was analyzed using the concept of the second Lyapunov׳s method. Numerical simulations were designed to show the effectiveness and advantages of the proposed FSTPD over the classical PD structure supplied with the STA and a PDF with the derivative part obtained by a linear filter. A first example to stabilize a simple pendulum was developed applying the FSTPD. A second example for solving a tracking control problem was designed for a robot manipulator with six degrees of freedom. In both cases, the FSTPD showed better performance and a significant reduction of the control energy.

A new attitude control design approach for flexible satellites

This paper presents a new approach for Attitude Control System (ACS) design for flexible satellites. This approach is based on fixed-structure H∞ design weighting the acceleration sensitivity function. This H∞ scheme was previously developed for rigid mechanical system and is reconsidered here for flexible mechanical system taking into account the sub-structure of the model. It allows to obtain a robust controller in the case where the desired bandwidth is very stringent (the desired attitude servo-loop bandwidth is close or beyond the first flexible mode). The proposed approach is illustrated on a telecommunication satellite and compared with classical proportional derivative (PD) control and full order H∞ controller.

Design and implementation of a hybrid fuzzy logic controller for a quadrotor VTOL vehicle

Helicopters have generated considerable interest in both the control community due to their complex dynamics, and in military community because of their advantages over regular aerial vehicles. In this paper, we present the modeling and control of a four rotor vertical take-off and landing (VTOL) unmanned air vehicle known as quadrotor aircraft. This model has been generated using Newton-Euler equations. In order to control the helicopter, classical PD (proportional derivative) and Hybrid Fuzzy PD controllers have been designed. Although fuzzy control of various dynamical systems has been presented in literature, application of this technology to quadrotor helicopter control is quite new. A quadrotor helicopter has nonlinear characteristics where classical control methods are not adequate especially when there are time delays, disturbances and nonlinear vehicle dynamics. On the other hand, Fuzzy control is nonlinear and it is thus suitable for nonlinear system control. Matlab Simulink has been used to test, analyze and compare the performance of the controllers in simulations. For the evaluation of the autonomous flight controllers, some experiments were also performed. For this purpose, an experimental test stand has been designed and manufactured. This study showed that although, both of the classical PD and the Fuzzy PD controllers can control the system properly, the Fuzzy PD controllers performed slightly better than the classical PD controllers, and have benefits such as better disturbance rejection, ease of building the controllers.

Wavelet based artificial neural network applied for energy efficiency enhancement of decoupled HVAC system

Control methodologies could lower energy demand and consumption of heating, ventilating and air conditioning (HVAC) systems and, simultaneously, achieve better comfort conditions. However, the application of classical controllers is unsatisfactory as HVAC systems are non-linear and the control variables such as temperature and relative humidity (RH) inside the thermal zone are coupled. The objective of this study is to develop and simulate a wavelet-based artificial neural network (WNN) for self tuning of a proportional-derivative (PD) controller for a decoupled bi-linear HVAC system with variable air volume and variable water flow responsible for controlling temperature and RH of a thermal zone, where thermal comfort and energy consumption of the system are evaluated. To achieve the objective, a WNN is used in series with an infinite impulse response (IIR) filter for faster and more accurate identification of system dynamics, as needed for on-line use and off-line batch mode training. The WNN-IIR algorithm is used for self-tuning of two PD controllers for temperature and RH. The simulation results show that the WNN-IIR controller performance is superior, as compared with classical PD controller. The enhancement in efficiency of the HVAC system is accomplished due to substantially lower consumption of energy during the transient operation, when the gain coefficients of PD controllers are tuned in an adaptive manner, as the steady state setpoints for temperature and RH are better reached in a shorter period of time. The multi-zone analyses are suggested for future work.

Proportional-derivative energy-based control for manipulator using normalized quasi-velocities

This paper presents a proportional-derivative (PD) controller for rigid manipulators whose dynamics is expressed in terms of the normalized quasi-velocities (NQV) described by Jain and Rodriguez. It is shown that using the NQV it is possible to shape the kinetic energy reduction of the manipulator and at the same time to realize the PD control in its joint space. The energy-based strategy gives an insight into the position control and allows a different method to be used instead of the classical PD controller in order to change the behaviour of the system. The controller uses quasi-velocities arising from a decomposition of the manipulator mass matrix. Its use yields a globally asymptotically stable closed-loop system. The performance of the controller is illustrated via experiment on a two-degree-of-freedom robot arm and in simulation on a three-degree-of-freedom spatial manipulator.