Adaptive Nonlinear PD Controller of Two-Wheeled Self-Balancing Robot with External Force

This paper proposes an adaptive nonlinear proportional-derivative(ANPD)controller for a two-wheeled self-balancing robot(TWSB)modeled by the Lagrange equation with external forces.The proposed control scheme is designed based on the combination of a nonlinear proportional-derivative(NPD)controller and a genetic algorithm,in which the proportional-derivative(PD)parameters are updated online based on the tracking error and the preset error threshold.In addition,the genetic algorithm is employed to adaptively select initial controller parameters,contributing to system stability and improved control accuracy.The proposed controller is basic in design yet simple to implement.The ANPD controller has the advantage of being computationally lightweight and providing high robustness against external forces.The stability of the closed-loop system is rigorously analyzed and verified using Lyapunov theory,providing theoretical assurance of its robustness.Simulations and experimental results show that the TWSB robot with the proposed ANPD controller achieves quick balance and tracks target values with very small errors,demonstrating the effectiveness and performance of the proposed controller.The proposed ANPD controller demonstrates significant improvements in balancing and tracking performance for two-wheeled self-balancing robots,which has great applicability in the field of robot control systems.This represents a promising solution for applications requiring precise and stable motion control under varying external conditions.

Repetitive PD control strategy with inverse transfer function compensation for CVCF inverter

A novel repetitive control strategy for the output waveform of single-phase CVCF inverters is presented. In this scheme, the inverse transfer function of inverter is used as a compensator to obtain stable and satisfy harmonic rejection. Besides, PD controller is adopted to improve transient performance. Simulation and experimental results, which are gotten from a DSP-based 400Hz, 5.5KW inverter, indicate that the proposed control scheme can achieve not only low THD during steady-state operation but also fast transient response during load step change.

Decentralized PD Control for Non-uniform Motion of a Hamiltonian Hybrid System

In this paper, a decentralized proportional-derivative （PD） controller design for non-uniform motion of a Hamiltonian hybrid system is considered. A Hamiltonian hybrid system with the capability of producing a non-uniform motion is developed. The structural properties of the system are investigated by means of the theory of Hamiltonian systems. A relationship between the parameters of the system and the parameters of the proposed decentralized PD controller is shown to ensure local stability and tracking performance. Simulation results are included to show the obtained non-uniform motion.

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.

On the Comparisons of PID and GI-PD Control

In conjunction with a second order uncertain nonlinear system, this paper makes some comparisons between PID control and general-integral-proportional-derivative (GI-PD) control;that is, by Routh’s stability criterion, we demonstrate that the system matrix under GI-PD control can be stabilized more easily;by linear system theory and Lyapunov method, we demonstrate that GI-PD control can deal with the uncertain nonlinearity more effectively;by analyzing and comparing the integral control action, we demonstrate that GI-PD control has the better control performance. Design example and simulation results verify the justification of our conclusions again. All these mean that GI-PD control has the stronger robustness and higher control performance than PID control. Consequently, GI-PD control has broader application prospects than PID control.

A Parameter Varying PD Control for Fuzzy Servo Mechanism

This paper presents the formulation of novel implementation method based on parameter varying PD controller for fuzzy servo controllers. This formulation uses the approximation of fuzzy nonlinear function including error and error derivation in operation point. Obtained fuzzy control law has been employed to control angular position of servo using digital control technique applied to a typical microcontroller like AVR. The performance and robustness of modified fuzzy controller in comparison with PID controller evaluated in no load, applied external disturbance with different magnitude conditions has been studied. The simulation results showed that the proposed fuzzy controller has a considerable advantage in rise time, settling time and overshoot respect to PID controller when the servo system encounters with nonlinear features like saturation and friction.

Stability Improvement of Power System by Using PI ＆ PD Controller

This paper presents the model of a SVC （Static VAR Compensator） which is controlled externally by a PI （Proportional Integral） ＆ PD （Proportional Differential） controllers for the improvements of voltage stability and damping effect of an on line power system. Both controller parameters has been optimized by using Ziegler-Nichols close loop tuning method. Both single phase and three phase （L-L） faults have been considered in the research. In this paper, a power system network is considered which is simulated in the phasor simulation method ＆ the network is simulated in four steps; without SVC, With SVC but no externally controlled, SVC with PI controller ＆ SVC with PD controller. Simulation result shows that without SVC, the system parameters become unstable during faults. When SVC is imposed in the network, then system parameters become stable. Again, when SVC is controlled externally by PI ＆ PD controllers, then system parameters becomes stable in faster way then without controller. It has been observed that the SVC ratings are only 50 MVA with controllers and 200 MVA without controllers. So, SVC with PI ＆ PD controllers are more effective to enhance the voltage stability and increases power transmission capacity of a power system. The power system oscillations are also reduced with controllers in compared to that of without controllers. So with both controllers the system performance is greatly enhanced.

Stability and bifurcation control of a neuron system under a novel fractional-order PD controller

In this paper, we address the problem of bifurcation control for a delayed neuron system. By introducing a new fractional-order Proportional-Derivative(PD) feedback controller, this paper aims to control the stability and Hopf bifurcation through adjusting the control gain parameters. The order chosen in PD controller is different with that of the integer-order neuron system. Sufficient conditions for guaranteeing the stability and generating Hopf bifurcation are constructed for the controlled neuron system. Finally,numerical simulation results are illustrated to verify our theoretical derivations and the relationships between the onset of the Hopf bifurcation and the gain parameters are obtained.

N-PD cross-coupling synchronization control based on adjacent coupling error analysis

In order to improve the trajectory tracking precision and reduce the synchronization error of a 6-DOF lightweight robot, nonlinear proportion-deviation （N-PD） cross-coupling synchronization control strategy based on adjacent coupling error analysis is presented. The mathematical models of the robot, including kinematic model, dynamic model and spline trajectory planing, are established and verified. Since it is difficult to describe the real-time contour error of the robot for complex trajectory, the adjacent coupling error is analyzed to solve the problem. Combined with nonlinear control and coupling performance of the robot, N-PD cross-coupling synchronization controller is designed and validated by simulation analysis. A servo control experimental system which mainly consists of laser tracking system, the robot mechanical system and EtherCAT based servo control system is constructed. The synchronization error is significantly decreased and the maximum trajectory error is reduced from 0.33 mm to 0.1 mm. The effectiveness of the control algorithm is validated by the experimental results, thus the control strategy can improve the robot＇s trajectory tracking precision significantly.

A Three-axis PD Control Model for Bumblebee Hovering Stabilization

Flight stabilization in insects is normally achieved through a closed-loop system integrating the intemal dynamics and feedback control. Recent studies have reported that flight instability may exist in most flying insects but how insects achieve the flight stabilization still remains poorly understood. Here we propose a control model specified for bumblebee hovering stabilization by applying a three-axis PD （proportional-derivative）-controller to a free-flying bumblebee computational model with six Degrees of Freedom （DoFs）. Morphological and kinematic models of a realistic bumblebee in hovering are built up based on measurements whereas a versatile bio-inspired dynamic flight simulator is employed in simulations. A simplified flight dynamic model is further developed as a fast model for control parameter tuning. Our results demonstrate that the stabilizing control model is capable of achieving the hovering stabilization with small perturbations in terms of 6-DoF, implying that the simplified linear algorithms can still work reasonably for bumblebee hovering. A further sensitivity analysis of the control parameters reveals that yaw control via manipulating pitch angle of the wing is mostly sensitive, implicating that bumblebee may utilize alternative yaw control strategies.

基于PD-滑模耦合算法的压电智能薄板颤振抑制

针对工件柔性主导的薄壁件铣削颤振问题,提出了一种基于PD–滑模耦合算法的压电智能薄板颤振抑制方法。首先设计了只需位移测量的主动控制算法,基于滑模控制理论处理系统参数不确定性和外部扰动,通过动态补偿器对未知切削状态进行在线近似和补偿;为解决传感误差和系统时滞问题,在滑模控制器中进一步耦合了时空依变PD控制模型,借助ABAQUS仿真拟合控制参数时变函数;最后设计了一套薄壁件主动控制装置,试验结果显示采用主动控制可有效抑制薄壁件铣削颤振,验证了控制方法的可行性。

Optimal PD/PID control of smart base isolated buildings equipped with piezoelectric friction dampers

Long-period pulses in near-field earthquakes lead to large displacements in the base of isolated structures.To dissipate energy in isolated structures using semi-active control,piezoelectric friction dampers（PFD） can be employed.The performance of a PFD is highly dependent on the strategy applied to adjust its contact force.In this paper,the seismic control of a benchmark isolated building equipped with PFD using PD/PID controllers is developed.Using genetic algorithms,these controllers are optimized to create a balance between the performance and robustness of the closed-loop structural system.One advantage of this technique is that the controller forces can easily be estimated.In addition,the structure is equipped with only a single sensor at the base floor to measure the base displacement.Considering seven pairs of earthquakes and nine performance indices,the performance of the closed-loop system is evaluated.Then,the results are compared with those given by two well-known methods：the maximum possive operation of piezoelectric friction dampers and LQG controllers.The simulation results show that the proposed controllers perform better than the others in terms of simultaneous reduction of floor acceleration and maximum displacement of the isolator.Moreover,they are able to reduce the displacement of the isolator systems for different earthquakes without losing the advantages of isolation.

Stochastic averaging technique for SDOF strongly nonlinear systems with delayed feedback fractional-order PD controller

A stochastic averaging technique is proposed to study the randomly excited single-degree-of-freedom(SDOF) strongly nonlinear systems with delayed feedback fractional-order proportional-derivative(PD) controller. The delayed feedback fractional-order PD control force is approximated by an equivalent non-delay feedback control force combining with a quasi-linear elastic force and a quasi-linear damping force. The averaged It? stochastic differential equation for amplitude of the equivalent nonlinear system is derived by the generalized harmonic functions. The analytical stationary probability density function(PDF) is obtained with solving the reduced Fokker-Planck-Kolmogorov(FPK) equation. Two examples of van der Pol oscillator and RayleighDuffing oscillator are studied to illustrate the application and effectiveness of the proposed method. Numerical results display that the proposed method can yield to the high precision, and the time delay could ruin the control effectiveness, but also even amplifies the response of the system more than that of uncontrolled system. Furthermore, the study finds that the parameters of fractional-order α and time delay may cause the stochastic P-bifurcation. It is indicated that the delayed feedback fractional-order PD controller can offer a potentially effective tool for anti-control of stochastic bifurcation

基于分数阶PD控制的分数阶混杂时滞神经网络分岔控制

本文提出了一个具有离散和分布时滞的分数阶神经网络系统,并运用分数阶PD控制器对其进行分岔控制.本文创新之处在于将分数阶引入了一个含离散与分布时滞的双神经元网络系统,并通过在原网络中引入一个虚拟神经元,形成了一个仅涉及离散时滞的新三神经元网络.引入了分数阶PD控制器得到受控系统,采用离散时滞之和作为分岔参数,证明了Hopf分岔的存在性,并通过分数阶PD控制策略实现了对分岔阈值点的控制.研究发现,通过选取合适的控制参数,分数阶PD控制器可以有效地控制系统分岔临界值.此外,各个控制器参数对于系统分岔阈值点的影响效果也被给出.

欠驱动飞行器横侧向通道的自耦PD控制方法

针对欠驱动高超声速飞行器横侧向通道的姿态控制问题,提出一种基于自耦PD(proportional-differential)控制理论的控制方法.该方法将欠驱动飞行器横侧向姿态模型转换为由速度倾斜角与侧滑角两个通道组成的二阶动态模型,并在速度倾斜角通道中引入一个侧滑角虚拟指令,再对速度倾斜角与侧滑角两个通道的内部动态与外部扰动分别定义两个总扰动,从而将非线性欠驱动扰动系统等价映射为虚拟全驱动线性扰动系统.使用最小速度因子及其自适应速度因子来设计外环速度倾斜角的自耦PD控制器,以便获得侧滑角虚拟指令,并根据该虚拟指令来设计内环侧滑角的自耦PD控制器,从而获得副翼偏角的控制力.分析了自耦PD控制系统的鲁棒稳定性和抗扰动鲁棒性.仿真结果表明,本文设计的自耦PD控制器不仅具有良好的抗扰动鲁棒性,而且具有良好的动态品质和稳态性能.

基于自耦PD的四旋翼无人机轨迹跟踪控制

针对输入受限的四旋翼无人机,为了使其能够快速稳定地跟踪期望轨迹,使用了一种基于自耦PD(SCPD)的轨迹跟踪控制方法。该方法将四旋翼无人机系统不确定性和内外扰动等复杂因素定义为总和扰动,进而将非线性不确定系统映射为未知线性系统。根据自耦PID控制理论,为四旋翼无人机位置环和姿态环各控制通道设计了独立的SCPD控制器,并设计了一种基于误差的速度因子模型。以定点悬停、轨迹跟踪等方式,与基于传统PID和滑模控制的飞行控制系统进行了动态响应性能测试和抗干扰性能对比。仿真结果表明:基于SCPD控制的四旋翼飞行控制系统具有较优的动态响应性能和较强的抗干扰能力,验证了SCPD控制旋翼无人机轨迹跟踪的有效性。

基于PD方法T-S模糊奇异系统的H_(∞)控制

研究了一类离散时间T-S模糊奇异系统的H_(∞)控制问题。首先,通过设计比例加差分状态反馈控制器,保证了奇异系统的正则性和无脉冲性,基于李雅普诺夫理论,给出确保系统稳定且具有H_(∞)性能的充分条件;然后,为求出控制器增益,给出严格的线性不等式;最后,通过数值算例证明所提方法的正确性。研究结果可以为T-S模奇异系统的PD控制提供理论支持。

可变形全向移动机器人的自适应鲁棒PD控制研究

针对可变形全向移动机器人两种不同构型的动力学系统中存在的不确定性问题,提出了基于Lyapunov稳定性理论的自适应PD控制律来自逼近系统中的摩擦和外部扰动等不确定项,实现轮椅和轮床两种构型系统的补偿控制。考虑系统的补偿精度和抗干扰性,在控制律中添加了鲁棒项,减小算法的逼近误差。通过Lyapunov稳定性理论证明了提出的自适应鲁棒PD控制律能在可变形全向移动机器人动力学中保证系统的稳定性。以轮椅构型为例,仿真结果显示该算法具有良好的轨迹跟踪性能,验证了该算法的有效性和可行性,进而为移动机器人电机的选型提供了有效参考。

基于推挽拓扑的PWM-PD控制多路输出电路研究

概述现行多路输出电路的控制方法,提出一种基于推挽拓扑的脉冲宽度调制-脉冲延时(PWM-PD)控制的类似于单绕组多路输出的电路结构。相较于传统多路输出技术,可以减小变压器体积,节约开关器件及成本。通过Saber仿真验证其具有良好的动态相应和输出稳定性。

基于压电叠堆的智能风洞尾支杆结构主动抑振PD参数整定

验证飞行器气动性能往往需要进行风洞全模试验,尾支杆支撑结构设计简单、拆装便捷、对试验流场干扰低,因此全尺寸模型普遍采用尾支杆支撑形式。但其支撑刚度低、结构阻尼小,容易引发支杆-模型系统的振动。本文基于压电叠堆设计了集成于尾支杆根部的智能主动抑振结构,应用改进粒子群算法对工程上常用的比例微分(PD)控制方法进行了整定优化,改善了其参数整定所需时间长、整定效率不高的问题。控制仿真及试验结果表明,采用基于改进粒子群算法的PD控制器可降低振动信号振幅最大值为52%,缩短99.48%的调整时间,抑振效果明显,能够为风洞尾支杆主动控制提供理论及实践参考。