Proportional And Derivative Controller Research Articles

Dynamics Modeling and Modal Space Control Strategy of Ship-Borne Stewart Platform for Wave Compensation

Abstract The ship-borne Stewart platform can compensate for the six-degrees-of-freedom (DOFs) motion generated by the ship, which improves the reliability and safety of offshore operations and increases the executable window period. The heavy and off-center load of the gangway significantly influences the high-precision compensation control of the platform. Besides, the gangway assembled on the platform vibrates easily due to its low natural frequency that requires high dynamic performance of the compensating. To deal with the problem mentioned, the modal space control strategy is introduced to fully consider the inertia characteristics. First, based on Kane's method, the complete dynamic model considering the ship's motion and actuator inertia is established. Then, the modal space proportional and derivative (PD) controller (MSPDC) and the modal space sliding mode controller (MSSMC) are designed based on the modal theory. Finally, simulations are carried out to show the advantages of the proposed model and the advantages of proposed controllers in compensation accuracy and anti-interference ability. Furthermore, the significant compensation rate (SCR) is proposed to evaluate the six-DOFs compensation accuracy. Compared with the PD controller with gravity compensation (PDCGC), the position SCR of MSSMC is increased from 95.37% to 99.28%, and the angle SCR increased from 85.57% to 99.65%.

A novel vibration measurement and active control method for a hinged flexible two-connected piezoelectric plate

Abstract A novel non-contact vibration measurement method using binocular vision sensors is proposed for piezoelectric flexible hinged plate. Decoupling methods of the bending and torsional low frequency vibration on measurement and driving control are investigated, using binocular vision sensors and piezoelectric actuators. A radial basis function neural network controller (RBFNNC) is designed to suppress both the larger and the smaller amplitude vibrations. To verify the non-contact measurement method and the designed controller, an experimental setup of the flexible hinged plate with binocular vision is constructed. Experiments on vibration measurement and control are conducted by using binocular vision sensors and the designed RBFNNC controllers, compared with the classical proportional and derivative (PD) control algorithm. The experimental measurement results demonstrate that the binocular vision sensors can detect the low-frequency bending and torsional vibration effectively. Furthermore, the designed RBF can suppress the bending vibration more quickly than the designed PD controller owing to the adjustment of the RBF control, especially for the small amplitude residual vibrations.

RBF neural network-based sliding mode vibration control of a flexible cantilever plate using laser displacement measurement

This paper is concerned with active vibration control of a flexible piezoelectric cantilever plate using a nonlinear radial basis neural network sliding mode control (RBFNN-SMC) algorithm and laser displacement measurement. In order to decouple the low-frequency vibration signals of the bending and torsional modes on measurement, two laser displacement sensors are used. The decoupling method is provided. A hyperbolic tangent function is used instead of the sign function, and the chattering phenomenon is alleviated. Also, the RBFNN is utilized to adjust the switching control gain adaptively to balance the chattering phenomenon and the control effect. The controllers for bending and torsional modes are designed independently. Experimental setup of the flexible piezoelectric cantilever plate with two laser displacement sensors is constructed. Experiments on vibration measurement and control are conducted by using the decoupling method and the designed controller, compared with the classical proportional and derivative (PD) control algorithm. The experimental results demonstrate that the proposed method can decouple the low-frequency bending and torsional vibration signals on measurement. Furthermore, the designed nonlinear RBFNN-SMC can suppress both the bending and torsional vibrations more quickly than the traditional linear PD controller, especially for the small amplitude residual vibration.

Model predictive control of gantry/bridge crane with anti-sway algorithm

This paper presents MPC (Model predictive control) controller, which provides fast transfer of cargo with sway reduction. The solution for criterion function of MPC controller was reached through multicriteria optimization. Intuitive adjustment of crane dynamics system is done by means of multicriteria optimization weights. The mathematical model of crane, which MPC controller is using to determine optimum control, is introduced and it takes into account the hoisting dynamics of cargo. Experimentally confirmed is the MPC controller on a bridge crane laboratory scale model and compared with the classical control system, which uses PD (Proportional and derivative) controller to control the position and prevent swaying.

자율주행 이동로봇의 실시간 장애물 회피 및 안드로이드 인터페이스 구현

In this paper we present an real-time obstacle avoidance technique of autonomous mobile robot with steering system and implementation of user interface for mobile devices with Android platform. The direction of autonomous robot is determined by virtual force field concept, which is based on the distance information acquired from 5 ultrasonic sensors. It is converted to virtual repulsive force around the autonomous robot which is inversely proportional to the distance. The steering system with PD(proportional and derivative) controller moves the mobile robot to the determined target direction. We also use PSD(position sensitive detector) sensors to supplement ultrasonic sensors around dead angle area. The mobile robot communicates with Android mobile device and PC via Ethernet. The video information from CMOS camera mounted on the mobile robot is transmitted to Android mobile device and PC. And the user can control the mobile robot manually by transmitting commands on the user interface to it via Ethernet.

Balancing of an Inverted Pendulum Using PD Controller

Balancing of an inverted pendulum robot by moving a cart along a horizontal track is a classical problem in the field of Control Theory and Engineering, for the beginners to understand its dynamics. Several physical models can also be simplified as elastic inverted pendulums like rockets and walking robots. Many researchers have been applying different control algorithm and design techniques such as PID Controller, State Space, Neural Network, Genetic Algorithm (GA) even Particle Swam Optimization (PSO), in both digital and analog domain using various sensors. However, this can also be done by using a single potentiometer as a sensor and Proportional Derivative Controller (PD) controller as the design algorithm. The comparison or difference between the reference and the potentiometer generates control signal to drive the system. In this case, it consists of a thin vertical rod attached at the bottom, referred to as pivot point mounted on a mobile toy car. The car, depending upon the direction of the deflection of the pendulum moves horizontally in order to bring the pendulum to absolute rest. The main idea behind this control process is the use of PD (Proportional and Derivative) controller to generate signal to control the speed and direction of the motor. The only sensor used in this project was a potentiometer (pot) which was attached with the pendulum rod. The variation in its resistance causes change in voltage and afterward, it was compared with the reference voltage to generate the appropriate control signal. PROTEUS software was used for circuit simulation, frequency responses of the system were analyzed in MATLAB with different values of KP and KD. Finally, to represent the system stability, root locus diagram was drawn using MATLAB.DOI: http://dx.doi.org/10.3329/dujs.v60i1.10348 Dhaka Univ. J. Sci. 60(1): 115-120 2012 (January)

Electrostatic Torsional Micromirror With Enhanced Tilting Angle Using Active Control Methods

Electrostatic microelectromechanical systems (MEMS)-based torsional micromirrors are a fundamental building block for many optical network applications, such as optical wavelength-selective switches, configurable optical add-drop multiplexers and optical cross-connects. Although the device architecture, materials and fabrication processes determine the micromirrors' functioning space, one major technical challenge to achieving their full performance potentials is the controllability and stability of the tilting angle. In this paper, an electrostatic micromirror is designed and fabricated using a standard MEMS silicon-on-insulator (SOI) process. Active control approaches including gain scheduling and nonlinear proportional and derivative (PD) control are proposed. Both approaches can improve the performance of the mirror tilting and enhance the robustness of the structures to any stochastic perturbations. Furthermore, the nonlinear PD control can eliminate the micromirror “pull-in” phenomenon, hence significantly expanding the mirror tilt range, and as a result achieving enhanced device performance and functionality. The nonlinear PD control method is experimentally implemented and the results demonstrate the effectiveness of the approach.

Fuzzy Self-Tuning Precompensation PD Control with Gravity Compensation of 3 DOF Planar Robot Manipulators

Industrial robot control covers nonlinearity, uncertainty and external perturbation considered in control laws design. Proportional and Derivative (PD) with gravity compensation control is well-known control used in manipulators to ensure global asymptotic stability for fixed symmetrical positive definite gain matrices. To enhance PD with gravity compensation controller performance, in this paper, we propose hybrid fuzzy PD control precompensation with gravity compensation, consisting of a fuzzy logic-based precompensator followed by hybrid fuzzy PD with gravity compensation controller. Hybrid fuzzy control is done by a Supervisory Hierarchical Fuzzy Controller (SHFC) for tuning conventional controller Proportional and Derivative gains based on actual tracking location and velocity error. Hierarchical hybrid fuzzy control consists of an intelligent upper supervisory fuzzy controller and a lower direct conventional PD controller. Numerical simulations using the dynamic model of a three DOF planar rigid robot manipulator with uncertainty show the effectiveness of the approach in trajectory tracking problems. Our results show that the proposal controller has performance superior to a conventional controller.

Neural-Mechanical Feedback Control Scheme Generates Physiological Ankle Torque Fluctuation During Quiet Stance

We have recently demonstrated in simulations and experiments that a proportional and derivative (PD) feedback controller can regulate the active ankle torque during quiet stance and stabilize the body despite a long sensory-motor time delay. The purpose of the present study was to: 1) model the active and passive ankle torque mechanisms and identify their contributions to the total ankle torque during standing and 2) investigate whether a neural-mechanical control scheme that implements the PD controller as the neural controller can successfully generate the total ankle torque as observed in healthy individuals during quiet stance. Fourteen young subjects were asked to stand still on a force platform to acquire data for model optimization and validation. During two trials of 30 s each, the fluctuation of the body angle, the electromyogram of the right soleus muscle, and the ankle torque were recorded. Using these data, the parameters of: 1) the active and passive torque mechanisms (Model I) and 2) the PD controller within the neural-mechanical control scheme (Model II) were optimized to achieve potential matching between the measured and predicted ankle torque. The performance of the two models was finally validated with a new set of data. Our results indicate that not only the passive, but also the active ankle torque mechanism contributes significantly to the total ankle torque and, hence, to body stabilization during quiet stance. In addition, we conclude that the proposed neural-mechanical control scheme successfully mimics the physiological control strategy during quiet stance and that a PD controller is a legitimate model for the strategy that the central nervous system applies to regulate the active ankle torque in spite of a long sensory-motor time delay.

Stable adaptive compensation with fuzzy CMAC for an overhead crane

In order to control mechanical systems, this paper proposes a novel fast control strategy. The controller includes a normal proportional and derivative (PD) regulator and a fuzzy cerebellar model articulation controller (CMAC). For an overhead crane, this control can realize both position tracking and anti-swing. Using a Lyapunov method and an input-to-state stability technique, the PD control with CMAC compensation is proven to be robustly stable with bounded uncertainties. Real-time experiments are presented comparing this new stable control strategy with regular crane controllers.

Closed-Loop Control of Functional Electrical Stimulation-Assisted Arm-Free Standing in Individuals With Spinal Cord Injury: A Feasibility Study

Objectives. The purpose of the present study was to show that the design of a neuroprosthesis for unsupported (arm-free) standing is feasible. We review findings suggesting that a closed-loop controlled functional electrical stimulation (FES) system should be able to facilitate arm-free quiet standing in individuals with spinal cord injury (SCI). Particularly, this manuscript identifies: 1) a control strategy that accurately mimics the strategy healthy individuals apply to regulate the ankle joint position during quiet standing and 2) the degrees of freedom (DOF) of the redundant, closed-chain dynamic system of bipedal stance that have to be regulated to facilitate stable standing. Methods and Results. First, we utilized a single DOF model of quiet standing (inverted pendulum) to analytically identify a proportional and derivative (PD) feedback controller that regulates the ankle torque in a physiologic manner despite a long sensory-motor time delay. Second, these theoretic results were experimentally validated by implementing the proposed PD controller to stabilize an individual with SCI during quiet standing. Third, a realistic, three-dimensional dynamic model of quiet standing with 12 DOF was used to determine the optimal combination of the minimum number of DOF that need to be regulated with the PD controller to ensure stability during quiet standing. Finally, perturbation simulations confirmed that the kinematics of this system are similar to those of healthy individuals during perturbed standing. Conclusions. The presented results suggest that stable standing can be achieved in individuals with SCI by controlling only six DOF in the lower limbs using FES, and that a PD controller actuating these DOF can stabilize the system despite a long sensory-motor time delay. Our finding that not all DOF in the lower limbs need to be regulated is particularly relevant for individuals with complete SCI, because some of their muscles may be denervated or difficult to access.

Measures Of Postural Stability Are Associated With Gains And Noise In The Control System

Postural stability is reduced with age or neurological disorder and improved with certain types of training (e.g., Tai-chi) as evaluated by various measures using center of pressure (COP) during quiet standing. However, the implications of specific measures with respect to the underlying control mechanisms have remained unclear. PURPOSE: To investigate the influence of variation in the control system on the COP measures during quiet standing, using mathematical simulations. METHODS: A feedback model that represented the human body and the control system during quiet standing was built using an inverted pendulum, a proportional and derivative (PD) controller with a time delay (the neural controller) and another PD controller without a time delay (the mechanical controller). The angle of the pendulum was fed back to the controllers, and the output of the neural controller (corresponding to the motor command) was input into the neuro-muscular torque generator. The sum of the output of the neuro-muscular torque generator and of the mechanical controller represented the ankle torque. A driving noise was added to the motor command to simulate realistic body sway conditions. The gain combinations that robustly stabilized the entire system were used to simulate the COP fluctuations. The gains of the controllers and the noise amount were treated as variables. The statistical relationship between each measure and the controller gains or noise was assessed using the partial correlation analysis. Sixty thousand and five hundred combinations of the variables were tested in total. RESULTS: All gains correlated negatively with the time domain measures (r=-0.372 to-0.659) except the mean velocity, which correlated positively with each gain. The neural derivative gain correlated positively with the frequency domain measures (r =0.964 to 0.973). The proportional gains correlated with Hurst exponent positively for the short term region (r= 0.837 to 0.892) and negatively for the long term region (r=-0.828 to-0.883). The amount of noise correlated positively with time domain measures (r= 0.901 to 0.988) but not with frequency measures. CONCLUSIONS: Each COP measure is associated with the variation in the control system. As such, the COP measures have a potential for investigating or characterizing the control system of balance.

Implementation of a Physiologically Identified PD Feedback Controller for Regulating the Active Ankle Torque During Quiet Stance

Our studies have recently demonstrated that a proportional and derivative (PD) feedback controller, which takes advantage of the body's position and velocity information to regulate balance during quiet standing, can compensate for long neurological time delays and generate a control command that precedes body sway by 100-200 ms. Furthermore, PD gain pairs were identified that ensure a robust system behavior and at the same time generate dynamic responses as observed in quiet standing experiments with able-bodied subjects. The purpose of the present study was to experimentally verify that the PD controller identified in our previous study can: 1) regulate the active ankle torque to stabilize the body during quiet standing in spite of long neurological time delays and 2) generate system dynamics, i.e., a motor command and body sway fluctuation, that successfully mimic those of the physiologic system of quiet standing. Our real-time closed-loop feedback circuit consisted of a center of mass position sensor and a functional electrical stimulator that elicited contractions of the plantar flexors as determined by the aforementioned PD controller. The control system regulated upright stance of a subject who was partially de-afferented and de-efferented due to a neurological disorder called von Hippel-Lindau Syndrome (McCormick Grade III). While the subject was able to generate a motor command for the ankle joints, he could not regulate the resulting torque sufficiently due to a lack of sensory feedback and motor control. It is important to mention that a time delay was included in the closed-loop circuit of the PD controller to mimic the actual neurological time delay observed in able-bodied individuals. The experimental results of this case study suggest that the proposed PD controller in combination with a functional electrical stimulation system can regulate the active ankle torque during quiet stance and generate the same system dynamics as observed in healthy individuals. While these findings do not imply that the CNS actually applies a PD-like control strategy to regulate balance, they suggest that it is at least theoretically possible.

Behaviour rule selection using alpha-level FIS for mobile robot navigation during multiple rule conflicts in complex environments

In this paper, we propose a novel model-free control for overhead crane system. This controller includes position regulation and antiswing control. Since the crane model is unknown, Radial Basis Function (RBF) neural networks are used to compensate friction, gravity and coupling between position and antiswing control. High-gain observer is applied to estimate the joint velocities to realise Proportional and Derivative (PD) control. Real-time experiments are presented to compare our stable antiswing PD control with other normal crane controllers.

An Autonomous Flight Control Strategy Study of a Small-Sized Unmanned Aerial Vehicle

The purpose of this paper is to present a case study of the development, implementation and performance analysis of an autonomous flight control strategy for a 1-meter small-sized unmanned aerial vehicle. Firstly, a learning algorithm based open-loop control is proposed by simulating a skilled human operator's manipulation of the aircraft. This is aimed to generate a set of command data inputs and investigate the multichannel control characteristics with the open-loop control. Stcondly, a feedforward plus a proportional and derivative (PD) feedback control is employed to control the vehicle in following the command data to complete the loitering flight. The PD control gains are tuned automatically according to the attitude of the vehicle using the fuzzy logic theory. Thirdly, autonomous flight experiments conducted on a 1-meter small-sized aerial vehicle demonstrated the effectiveness of the proposed method.

A simple hybrid fuzzy PD controller

In many practical applications, the performance of a controlled system highly depends on whether a high quality differential signal can be obtained based on the non-continuous measured position signal only. In this paper, a simple hybrid fuzzy PD (proportional and derivative) controller is developed, by combining two nonlinear tracking differentiators to a conventional fuzzy PD controller. The main improvement of the proposed simple hybrid fuzzy PD controller is that it has high robustness against noise and easy for engineering implementation. Simulation and experimental comparison studies on motion control of a permanent magnet synchronous AC motor validate the effectiveness and efficiency of the proposed controller.

Adaptive SP-D control of a robotic manipulator in the presence of modeling error in a gravity regressor matrix: theory and experiment

Many controllers have been developed for setpoint control of robotic manipulators. An adaptive proportional and derivative (PD) controller is one of the simplest and most effective setpoint controller in the presence of uncertainty in gravitational force. However, an exact model of gravity regressor is required in the adaptive PD control. In this paper, we propose an adaptive setpoint controller with modeling error in the gravity regressor and show that convergence can be guaranteed even when the gravity regressor is uncertain. A new Lyapunov function is presented for the stability analysis of such problem. As a byproduct of the result, we also show that existing setpoint controllers such as an adaptive saturated proportional-derivative (SP-D) and saturated proportional-integral and derivative (SP-ID) in the literature can be analyzed and designed in a unifying way as special cases of the proposed controller.

Active control of the sound field of a constrained panel by an electromagnetic actuator — an experimental study

Reduction of sound power from a vibrating panel was achieved by reducing the panel vibration amplitude. Experimental tests involving a constrained panel and three active control strategies were performed to actively suppress the panel vibration, namely: signal processing techniques involving cross-correlation; feedback control using proportional and derivative (PD) control; and an ideal inverse operational amplifier method. The results show that PD control methods together with the application of a single point force input of an electromagnetic actuator have great potential for use in controlling the low frequency panel vibration, hence reducing the structure-borne noise. Sound power reduction ranged from 3.0 dB to 9.5 dB and was achieved when the actuator was located at the centre of the panel; 1.7 dB to 6.9 dB was achieved with the actuator located at the top left quadrant of the panel. The panel structural modes derived using a finite element method (FEM) show a strong correlation with the sound power radiation pattern from the surface of the panel and could be used to predict sound sources.

Digital high-gain PD control of robot manipulators

For all its simplicity, local proportional and derivative (PD) control remains an effective and popular tool in robot manipulation. The analysis of such a control system has usually been based on the assumption that the PD algorithm is implemented continuously. This article explores the issue of digital high-gain PD control on robot manipulators from the viewpoint of singular perturbation. It is shown that the fast subsystem becomes unstable when the gains are high enough, due to the effect of sample-and-hold. The stability is related to the feedback gains, the length of sampling period, the computation time, and the eigenvalues of the mass matrix. With reasonable approximations, simple and explicit stability criteria are derived. It is also shown that when the gains reach the critical values, chattering in the control signal occurs, similar to what happens in a variable structure system with sliding mode. Since the eigenvalues of the mass matrix vary with robot positions, the system stability and control chattering are also affected by the trajectory that the robot is planned to follow. © 1997 John Wiley & Sons, Inc.

Vibration suppression of a disk-shaped superconductor with PD control

In order to investigate superconducting magnetic bearings (SMBs) using repulsion forces between superconductors and electromagnets, an experimental setup for a thrust SMB able to move in one direction has been made. The experimental setup is composed of a high T c superconductor, permanent magnets, electromagnets and a Hall sensor. The superconductor used in this paper is supported by the permanent magnets in the radial direction. The vibration of the superconductor is suppressed by an analog PD (proportional and derivative) controller. From the experiments, it is found that suppressing the vibration is well performed by the PD controller. Also, it is found that the controller needs more resistance against disturbance caused by the pinning effect.