Proportional And Derivative Research Articles

Dynamics modeling and attitude-vibration hybrid control of a large flexible space structure

The challenges in the dynamic modeling and control of large flexible space structures (LFSSs) include the high number of degrees of freedom in the model, the geometric nonlinearities in the flexible components, and the nonlinear coupling effects between overall motions and vibrations of the structure. In this study, we propose a systematic method to solve the mentioned problems in the research of LFSSs. We use the referenced nodal coordinate formulation (RNCF) to build the dynamic model. The modeling method is general and the model can better describe the large deformations of flexible structures compared with the modal-based dynamic model. The key feature of our work is that we use a hybrid control strategy for the attitude and vibration control directly performing on the full-scale dynamic model. Specifically, the control strategy combines a proportional and derivative (PD) control algorithm based on SO(3) for the attitude control and an analytical linear-quadratic (LQ) vibration control method for the vibration control. The simulation results are presented to demonstrate the effectiveness of the proposed hybrid control strategy both in the three-axis attitude maneuver task and on-orbit pointing scenario.

SIMPLIFIED EXPONENTIAL REACHING LAW BASED SLIDING MODE CONTROL OF TWO-LINK PLANAR ROBOT

Robotics has gained attention for its ability to perform industrial tasks like welding, machining, position con- trol, and other essential medical operations. Controllers are continuously being improved in design for simplicity, robustness, and performance accuracy. High-accuracy trajectory tracking is a challenging area in robot control due to nonlinearities and input couplings. To achieve high accuracy and precision, robots need accurate, and fast- processing controllers. This research focuses on applying the exponential reaching law (ERL) to control a two-link planar robot. The Euler-Lagrange approach was used for dynamic modeling, and the MATLAB/Simulink toolbox was used for the simulation. The result was obtained in terms of RMS error for the links, with and without the fric- tional disturbance, in the case of the proportional and derivative (PD) controller, reaching law based sliding mode controller (RSMC), and the simplified exponential reaching law based sliding mode controller (SSMC). RMSE with disturbance for SSMC (0.0753 rad, 0.0817 rad for link 1 and link 2 respectively), RSMC (0.0828 rad, 0.0852 rad) and PD (0.2784 rad, 0.1062 rad), and RMSE values without disturbance for SSMC (0.0743rad, 0.0811rad for link 1 and link 2 respectively), RSMC (0.0752 rad, 0.0815 rad) and PD (0.2579 rad, 0.1021 rad). Based on the result obtained, SSMC was found to be more accurate and robust as a result of having the minimum tracking error minimum change in RMSE respectively, as compared to the other controllers. It is evident that SSMC control scheme has proven to have an improved performance with simplicity and robustness.

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%.

"CONTROL OF SHIP FIN STABILIZERS BY A PID CONTROLLER: A NUMERICAL ANALYSIS "

The reduction of ship roll motion is important in order to prevent damage to cargo, to allow the crew to work efficiently and to provide comfort for the passengers. There are passive devices like bilge keels or anti – roll tanks and active devices like gyrostabilizer and stabilizing fins which are commonly used to generate an opposed moment to the wave and wind excitation roll moments in response to the command of a control system. The paper presents numerical results of using a Proportional - Integral – Derivative (PID) controller for damping the roll motion of a fishing boat equipped with a fin stabilizer system and sailing in regular waves. The nonlinear roll equation, which includes B1 type damping and quantic restoring, besides the wave excitation moment and moment generated by fins, was linearized for relative small roll angles. The role of PID controller was to generate the corrective roll moment through the controlled fins in order to stabilize the roll motion. The thresholds for the controller’s gains were determined using the Laplace transform and Routh – Hurwitz criterion. A simple but precise iterative scheme was used for the rapid integration of the system equations of motion in three cases: only proportional (P) component, proportional and derivative (PD) components and full PID controller. The numerical simulations have showed that all the analysed variants achieved roll reduction satisfactorily.

Reinforcement learning vibration control of a multi-flexible beam coupling system

An active vibration control algorithm based on reinforcement learning (RL) is applied to suppress the coupling vibration of a multi-flexible beam coupling system. The experimental setup of four-flexible beam coupling system is constructed. Piezoelectric sensors/actuators are used to detect vibration signals and suppress vibration. The finite element method (FEM) is used to establish the system dynamics model, and the model is modified by identifying parameters using the experimental data to obtain an accurate system model. The identified model is used as the simulation environment of RL algorithm. The multi-agent twin delayed deep deterministic policy gradient (MATD3) algorithm is designed to train the RL vibration controller through interaction with the simulation environment. The trained RL vibration controller is used to suppress the vibration of the four-flexible beam coupling system in simulation and experimental environment. Simulation and experimental results show that compared with proportional and derivative (PD) controller, the RL controller trained by the MATD3 algorithm has better control effect, especially for small amplitude vibration.

Improved Third Order PID Sliding Mode Controller for Electrohydraulic Actuator Tracking Control

An electrohydraulic actuator (EHA) system is a combination of hydraulic systems and electrical systems which can produce a rapid response, high power-to-weight ratio, and large stiffness. Nevertheless, the EHA system has nonlinear behaviors and modeling uncertainties such as frictions, internal and external leakages, and parametric uncertainties, which lead to significant challenges in controller design for trajectory tracking. Therefore, this paper presents the design of an intelligent adaptive sliding mode proportional integral and derivative (SMCPID) controller, which is the main contribution toward the development of effective control on a third-order model of a double-acting EHA system for trajectory tracking, which significantly reduces chattering under noise disturbance. The sliding mode controller (SMC) is created by utilizing the exponential rule and the Lyapunov theorem to ensure closed-loop stability. The chattering in the SMC controller has been significantly decreased by substituting the modified sigmoid function for the signum function. Particle swarm optimization (PSO) was used to lower the total of absolute errors to adjust the controller. In order to demonstrate the efficacy of the SMCPID controller, the results for trajectory tracking and noise disturbance rejection were compared to those obtained using the proportional integral and derivative (PID), the proportional and derivative (PD), and the sliding mode proportional and derivative (SMCPD) controllers, respectively. In conclusion, the results of the extensive research given have indicated that the SMCPID controller outperforms the PD, PID, and SMCPD controllers in terms of overall performance.

Establishing and Maintaining a Reliable Optical Wireless Communication in Underwater Environment

This paper proposes the trajectory tracking problem between an autonomous underwater vehicle (AUV) and a mobile surface ship, both equipped with optical communication transceivers. The challenging issue is to maintain stable connectivity between the two autonomous vehicles within an optical communication range. We define a directed optical line-of-sight (LoS) link between the two vehicle systems. The transmitter is mounted on the AUV, while the surface ship is equipped with an optical receiver. However, this optical communication channel needs to preserve a stable transmitter-receiver position to reinforce service quality, which typically includes a bit rate and bit error rates. A cone-shaped beam region of the optical receiver is approximated based on the channel model; then, a minimum bit rate is ensured if the AUV transmitter remains inside of this region. Additionally, we design two control algorithms for the transmitter to drive the AUV to the angle of the maximum achievable data rate and maintain it in the cone-shaped beam region and under an uncertain oceanic environment. Lyapunov function-based analysis that ensures asymptotic stability of the resulting closed-loop tracking error is used to design the proposed Non-linear Proportional and Derivative (NLPD) controller. Numerical simulations are performed using MATLAB/Simulink to show the controllers’ ability to achieve favorable tracking in the presence of the solar background noise within competitive times. Finally, results demonstrate the proposed NLPD controller improves the tracking error performance more than 70% under nominal conditions and 35% with model uncertainties and disturbances compared to the original Proportional and Derivative (PD) strategy.

Delay Consensus Margin of First-Order Multiagent Systems With Undirected Graphs and PD Protocols

In this article, we study robust consensus problems for continuous-time first-order multiagent systems (MASs) with time delays. We assume that the agents input is subject to an uncertain constant delay, which may arise due to interagent communication or additionally, also by self-delay in the agent dynamics. We consider dynamic feedback control protocol in the form of proportional and derivative (PD) control, and seek to determine the delay consensus margin (DCM) achievable by PD feedback protocols, whereas the DCM is a robustness measure that defines the maximal range of delay within which robust consensus can be achieved despite the uncertainty in the delay. With an undirected graph, we show that the DCM can be determined exactly by solving a unimodal concave optimization problem, which is one of univariate convex optimization and can be solved using convex optimization or gradient-based numerical methods. The results show how unstable agent dynamics and graph connectivity may limit the range of delay tolerable, so that consensus can or cannot be maintained in the presence of delay variations.

Hybrid Reinforcement Learning Control for a Micro Quadrotor Flight

This letter presents a combination of reinforcement learning (RL) and deterministic controllers to learn a quadrotor control. Learning the quadrotor flight in a standard RL approach requires many iterations of trial and error, which may bring about risky exploration and battery consumption. In this letter, we integrate a classical controller such as PD (proportional and derivative) or LQR (linear quadratic regulator) with a RL policy using their linear combination. The proposed method is not only simple to use, but also fast in learning convergence. When the algorithm is evaluated for a quadrotor trajectory tracking by means of a velocity control for both simulation and experiment, it demonstrates the faster convergence rate and better control performance in comparison with an existing rapid model-based RL method.

Optimizing the Execution of Dynamic Robot Movements With Learning Control

High-speed robotics typically involves fast dynamic trajectories with large accelerations. Kinematic optimization using compact representations can lead to an efficient online computation of these dynamic movements, however successful execution requires accurate models or aggressive tracking with high-gain feedback. Learning to track such references in a safe and reliable way, whenever accurate models are not available, is an open problem. Stability issues surrounding the learning performance, in the iteration domain, can prevent the successful implementation of model-based learning approaches. To this end, in this paper we propose a new adaptive and cautious iterative learning control (ILC) algorithm where the stability of the control updates is analyzed probabilistically: the covariance estimates of the adapted local linear models are used to increase the probability of update monotonicity, exercising caution during learning. The resulting learning controller can be implemented efficiently using a recursive approach. We evaluate it extensively in simulations as well as in our robot table tennis setup for tracking dynamic hitting movements. Testing with two seven degree of freedom anthropomorphic robot arms, we show improved and more stable tracking performance over high-gain proportional and derivative (PD) control, model-free ILC (simple PD feedback type) and model-based ILC without cautious adaptation.

Fractional PD-IλDμ Error Manifolds for Robust Tracking Control of Robotic Manipulators

Linear proportional-integral-derivative (PID) controller stands for the most widespread technique in industrial applications due to its simple structure and easy tuning rules. Recently, considering fractional orders λ and μ, there has been studied the fractional-order PIλDμ (FPID) controller to provide salient advantages in comparison to the conventional integer-order PID, such as, a more flexible structure and a preciser performance. In addition, proportional and derivative (PD) and PID error manifolds have been classically proposed; however, there remains the question on how FPID-like error manifolds perform for the control of nonlinear plants, such as robots. In this paper, this problem is addressed by proposing a PD-IλDμ error manifold for novel vector saturated control. The stability analysis shows convergence into a small vicinity of the origin, wherein, such hybrid combination of integer- and fractional-order error manifolds provides further insights into the closed-loop response of the nonlinear plant. Simulations studies are carried out to illustrate the feasibility of the proposed scheme.

Multi-Input–Multi-Output Control of a Utility-Scale, Shaftless Energy Storage Flywheel With a Five-Degrees-of-Freedom Combination Magnetic Bearing

The modeling and control of a recently developed utility-scale, shaftless, hubless, high strength steel energy storage flywheel system (SHFES) are presented. The novel flywheel is designed with an energy/power capability of 100 kWh/100 kW and has the potential of a doubled energy density when compared to conventional technologies. In addition, it includes a unique combination magnetic bearing (CAMB) capable of providing five-degrees-of-freedom (5DOF) magnetic levitation. Initial test results show that the CAMB, which weighs 544 kg, can provide a stable lift-up and levitation control for the 5543 kg flywheel. The object of this paper is to formulate and synthesize a detailed model as well as to design and simulate a closed-loop control system for the proposed flywheel system. To this end, the CAMB supporting structures are considered flexible and modeled by finite element modeling. The magnetic bearing is characterized experimentally by static and frequency-dependent coefficients, the latter of which are caused by eddy current effects and presents a challenge to the levitation control. Sensor-runout disturbances are also measured and included. System nonlinearities in power amplifiers and the controller are considered as well. Even though the flywheel has a large ratio of the primary-to-transversal moment of inertias, multi-input–multi-output (MIMO) feedback control demonstrates its effectiveness in canceling gyroscopic toques at the designed operational spinning speed. Various stages of proportional and derivative (PD) controllers, lead/lag compensators, and notch filters are implemented to suppress the high-frequency sensor disturbances, structural vibrations, and rotor imbalance effects.

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.

Distributed optimal energy scheduling based on a novel PD pricing strategy in smart grid

Pricing function plays an important role in optimal energy scheduling problem in smart grid systems. The authors propose a novel real-time pricing (RTP) strategy named proportional and derivative (PD) pricing . Different from conventional RTP strategies, which only depend on the current total energy consumption, their proposed pricing strategy also takes the historical energy consumption into consideration, which aims to further fill the valley load and shave the peak load. An optimal energy scheduling problem is then formulated to minimise the total social cost of the overall power system. Two different distributed optimisation algorithms with different communication strategies are proposed to solve the problem. Several case studies implemented on a heating ventilation and air conditioning system are tested and discussed to show the effectiveness of both the proposed pricing function and distributed optimisation algorithms.

Power grid enhanced resilience using proportional and derivative control with delayed feedback

This paper investigates the resilience of an elementary electricity system (machine-generator) under proportional and derivative (PD) control when subject to large perturbations. A particular attention is paid to small power grids, representative of power grid structure in some developing countries. The considered elementary electricity system consists of a consumer (machine), a power plant (generator) and a transmission line. Both Runge-Kutta and Newton methods are used to solve the dynamical equations and the characteristic equations for stability. It is found that the controller increases the resilience of the system. We also show that time delays associated to the feedback loop of the controller have a negative impact on the performance. It is also shown that the asymmetry due to energy demand of different consumers to power plant increases the stability of the system.

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.

Time-Delayed Vibration Control of a Rotating Flexible Manipulator Based on Model Output Prediction Feedback

AbstractThis paper is concerned with vibration control of a single-link flexible beam structure. The proposed beam is controlled by a servo motor through a harmonic gear reducer. After obtaining the models by system identification, a time-delayed optimal controller based on model output prediction and optimal control theory was designed to compensate the unknown time delay in the controlled system. Then, experiments on the proposed control scheme were conducted in a set-point vibration control process. The experimental results demonstrate that the performance of vibration suppression can be improved substantially when applying the proposed method in the presence of time delay compensation, as compared to the traditional proportional and derivative (PD) controller. The accuracy of models was validated according to experimental results, and the factors that influence the output prediction accuracy are analyzed in this paper.

Vibration control of a pneumatic driven piezoelectric flexible manipulator using self-organizing map based multiple models

A kind of hybrid pneumatic-piezoelectric flexible manipulator system has been presented in the paper. A hybrid driving scheme is achieved by combining of a pneumatic proportional valve based pneumatic drive and a piezoelectric actuator bonded to the flexible beam. The system dynamics models are obtained based on system identification approaches, using the established experimental system. For system identification of the flexible piezoelectric manipulator subsystem, parametric estimation methods are utilized. For the pneumatic driven system, a single global linear model is not accurate enough to describe its dynamics, due to the high nonlinearity of the pneumatic driven system. Therefore, a self-organizing map (SOM) based multi-model system identification approach is used to get multiple local linear models. Then, a SOM based multi-model inverse controller and a variable damping pole-placement controller are applied to the pneumatic drive and piezoelectric actuator, respectively. Experiments on pneumatic driven vibration control, piezoelectric vibration control and hybrid vibration control are conducted, utilized proportional and derivative (PD) control, SOM based multi-model inverse controller, and the variable damping pole-placement controller. Experimental results demonstrate that the investigated control algorithms can improve the vibration control performance of the pneumatic driven flexible piezoelectric manipulator system.

Robust Motion Control of an Oscillatory-Base Manipulator in a Global Coordinate System

This paper presents a control design method for motion control in a global coordinate system of an oscillatory-base manipulator, which can be regarded as a model system of mechanical systems installed on vessels or oceanic structures. This paper proposes a control design method for such systems exploiting $\cal{H}_{\infty}$ control and proportional and derivative (PD) control. In order to evaluate the proposed method, tracking control simulations and experiments were conducted for both attitude control and position control with practical constraints such as sensor error and actuator saturation. Furthermore, the proposed controller was compared with a conventional proportional, integral, and derivative (PID) controller. The results demonstrate that the proposed controller is successfully effective and is superior to the PID controller. Moreover, robust control experiments and robust stability analyses using our proposed machinery show that the proposed controller has strong robustness against physical parametric perturbations. Our developed robust stability analysis machinery is based on the state-dependent coefficient form and applicable to a wider class of systems than the previous one.

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.