LQR Controller with Kalman Estimator Applied to UAV Longitudinal Dynamics

The aim of this study is designing an optimal controller with linear quadratic regulator (LQR) method for a small unmanned air vehicle (UAV). To better evaluate the effect of disturbances on the obtained measurements a Kalman filter is also used in the system. For this purpose a small UAV that is normally used as a radio controlled plane is chosen. The linearized equations for a wings level flight condition and the state space matrices are obtained. An optimal controller using LQR method to control the altitude level is then designed. The effect of the disturbances on the measurements are taken into account and the effectiveness of the Kalman filter in obtaining the correct measurements and achieving the desired control level are shown using the controller designed for the system. The small UAV is commanded to the desired altitude using the LQR controller through the control inputs elevator deflection and thrust rate. The LQR effectiveness matrices are chosen to find the gains necessary to build an effective altitude controller. Firstly the controller is tested under the situation where disturbances are absent. Then a Kalman filter is designed and the system under disturbances is tested with the designed controller and the filter. The results reveal the effectiveness of the Kalman filter and the LQR controller.

Using Adaptive Gain Scheduling LQR Method Control of Arm Driven Inverted Pendulum System Based on PIC18F4431

The arm driven inverted pendulum system is a highly nonlinear model, muhivariable and absolutely unstable dynamic system so it is very difficult to obtain exact mathematical model and balance the inverted pendulum with variable position of the ann. To solve this problem, this paper presents a mathematical model for arm driven inverted pendulum in mid-position configuration and an adaptive gain scheduling linear quadratic regulator control method for the stabilizing the inverted pendulum. The proposed controllers for arm driven inverted pendulum are simulated using MATLAB-SIMULINK and implemented on an experiment system using PIC 18F4431 mieroeontroller. The result of experiment system shows the control performance to be very good in a wide range stabilization of the arm position.

基于LQR对直线倒立摆的稳摆控制研究及实现

针对倒立摆的稳摆控制问题,研究设计了一个LQR控制器。首先,考虑摆杆摆动的阻力矩,采用牛顿力学分析方法推导出直线倒立摆的数学模型,建立了其线性状态空间模型,并分析了系统的稳定性、能控性与能观性。通过采用仿真试凑确定加权矩阵Q、R,得到状态反馈增益矩阵K,完成LQR控制器的设计。之后,搭建了以开放式运动控制器为核心的倒立摆实验平台,在计算机上开发了实时人机交互程序,在运动控制器里编写了倒立摆控制算法。最后,进行了仿真与实测实验,验证了所设计的LQR控制器的有效性和可行性。

Vibration Control of FGM Piezoelectric Plate Based on LQR Genetic Search

Active vibration control of functionally graded material (FGM) plate with integrated piezoelectric layers is studied. In this regard, a finite element model based on the classical plate theory is adopted and extended to the case of FGM plate to obtain a space state equation. Rectangular four node and eight node elements are used for the analysis purpose. The material proprieties of FG plate are assumed to be graded along the thickness direction. In order to control the vibration of the plate, an LQR controller has been designed and developed. The weighing factors are obtained by using genetic algorithm. The proposed results of finite element modeling are verified with the results obtained using ANSYS. Also the validation of methodology is done with comparing the results with that of available in literature and found in well agreement. Further analysis is performed for three sets of power law exponent n = 0, 1 and 100 which gives benchmark results for vibration control of FGM piezoelectric plate.

轮毂电机电动汽车空气悬架阻尼GA-LQR控制研究

针对轮毂电机驱动电动汽车因电机内部不平衡电磁力引起的负面振动加剧等问题,提出一种基于遗传算法的线性二次型调节器(GA-LQR)的空气悬架阻尼控制方法。建立包含轮毂电机和空气悬架系统的轮毂电机驱动电动汽车8自由度半车动力学模型,并进行实车试验验证模型;仿真分析路面激励和不平衡电磁力两者对电动汽车垂向振动的影响;根据最优控制理论提出LQR控制策略,并通过遗传算法对LQR控制中的加权矩阵Q和R进行全局搜索优化,构建了GA-LQR阻尼控制器。仿真结果表明:相较于被动悬架和LQR控制的空气悬架,基于GA-LQR控制的空气悬架对电动汽车各评价指标的改善效果明显,可有效抑制轮毂电机因偏心引起的不良振动,极大地提高车辆的乘坐舒适性。

基于LQR控制的两轮自平衡小车设计

采用LQR控制算法,实现一种两轮自平衡小车的系统设计.搭建了以STM32F103RCT6为主控制器、MPU6050模块为姿态数据采集、N10激光雷达模块为测距的硬件系统.根据两轮自平衡小车的数学模型,利用LQR控制算法实现小车系统的平衡控制,使用Matlab/Simulink进行系统仿真及分析,并在硬件平台上进行实际测试.实验结果表明:小车功能多样、系统运行平稳、抗干扰能力强、调节速度快,具有应用推广价值.

主动悬架的遗传算法优化LQR控制策略研究

为了提高车辆的行驶平顺性和操纵稳定性,本文提出了一种基于遗传算法的线性二次型调节器(linear quadratic regulator,LQR)控制,求解最佳权重矩阵参数的方法。此控制算法克服了传统的LQR控制方法中,由经验主观性确定的权重矩阵Q和R的缺点,使其达到最优的控制效果。本文首先建立了1/4车辆主动悬架模型和道路输入模型,并将遗传算法优化的LQR控制器应用于主动悬架系统中。以主动悬架作为被控对象,车身垂向加速度、悬架弹簧动挠度以及轮胎动位移作为评价指标,通过仿真分析,相比被动控制和LQR控制的主动悬架系统,此优化算法可以显著减小车身垂向加速度与悬架弹簧动挠度,而轮胎动位移的影响不大,从而验证了控制策略的有效性。

基于模糊LQR的Spar型海上浮式风力机载荷抑制

针对复杂环境变化易引起海上浮式风力机不稳定的问题,提出一种基于模糊LQR、模糊PI相结合且易于工程应用的桨距控制新方案,实现维持浮式风力发电机组输出功率稳定、抑制浮台运动、减少叶根及塔基疲劳载荷的目的。模糊PI根据发电机转子转速误差变化动态选择期望的PI增益,模糊LQR基于模糊规则自适应调整闭环反馈增益,在保证风力机输出功率和浮台稳定的基础上,进一步减小叶根和塔基疲劳载荷。基于FAST与Matlab/Simulink在不同环境条件下进行联合仿真,验证所提方案的有效性和优越性;通过时域、频域分析表明,与PI控制相比,所提方案在减少叶根处平面外载荷和塔基横向载荷方面有明显改善效果。

基于前馈+预测LQR的智能车循迹控制器设计

为提升智能车辆循迹性能,基于线性二次调节器(linear quadratic regulator,LQR)理论和滑模理论,提出了一种兼顾横纵向跟踪精度与转向稳定性的横纵向控制器。首先,构建了基于二自由度横向动力学模型的前馈LQR控制器。针对模型线性化后前馈LQR控制器转向稳定性降低的问题,结合恒定转弯率和速度(constant turn rate and velocity,CTRV)模型设计预测控制器,建立了基于实时车速-曲率模糊自适应预测时间的前馈LQR控制器。此外为提升纵向车速跟踪稳定性和跟踪精度,提出了一种基于滑模控制理论的纵向跟踪方法。并进行了联合仿真和硬件在环实验验证。结果表明:文中提出的横纵向控制器有效解决了跟踪精度与稳定性两者难以兼顾的问题,提升了智能车辆循迹性能。

Genetic algorithm based LQR vibration wireless control of laminated plate using photostrictive actuators

A photostrictive type of opto-electromechanical actuator activated by high-energy lights can introduce actuation and control effects without hard-wired connections. This paper addresses the controllability aspect in wireless vibration control of plate structures via photostrictive actuators. A modal force index, which has taken into account the mode number, the spatial distribution, and the dimension of the actuator, is chosen as an objective function to determine the optimal locations of photostrictive actuators. A linear methodology is proposed in this paper and the vibration equation is written in the standard state-space form. A binary-coded GA based combined optimal placement and LQR （linear quadratic regulator） control scheme has been incorporated, which maximizes the modal force index, the closed loop damping and minimizes input light intensity to the actuators. In the present method only three weighting factors have been used to search optimal Q and R matrices using GA, which reduces chromosome length and hence minimizes computational time. Numerical results demonstrate that the use of strategically positioned actuator patches can effectively control the fundamental modes that dominate the structural vibration.

Performance Study of PID Controller and LQR Technique for Inverted Pendulum

The inverted pendulum is a classic problem in dynamics and control theory and is widely used as a benchmark for testing control algorithms. It is unstable without control. The process is non linear and unstable with one input signal and several output signals. It is hence obvious that feedback of the state of the pendulum is needed to stabilize the pendulum. The aim of the study is to stabilize the pendulum such that the position of the carriage on the track is controlled quickly and accurately. The problem involves an arm, able to move horizontally in angular motion, and a pendulum, hinged to the arm at the bottom of its length such that the pendulum can move in the same plane as the arm. The conventional PID controller can be used for virtually any process condition. This makes elimination the offset of the proportional mode possible and still provides fast response. In this paper, we have modelled the system and studied conventional controller and LQR controller. It is observed that the LQR method works better compared to conventional controller.

基于前馈补偿LQR与PID的矿井无轨胶轮车横纵向控制研究

无人驾驶技术是实现无轨胶轮车井下安全、智能、高效运输的重要方案之一,为了提高无人驾驶过程中的轨迹跟踪精度,提出了基于前馈补偿的横向线性二次型调节器(Linear Quadratic Regulator,LQR)与纵向比例积分微分(Proportion Integration Derivative,PID)位移速度调节器相结合的控制策略,实现车辆的横纵向协调控制。通过建立考虑轮胎侧偏特性的2自由度无轨胶轮车动力学模型和跟踪误差模型,并采用井下无轨胶轮车实车参数建立其电机模型,得到车辆的驱动制动输出。利用Carsim和Matlab/Simulink搭建联合仿真环境,分别在井下双车道工况、单车道工况与颠簸路面工况下进行了轨迹跟踪仿真验证。结果表明:在3种工况下车辆轨迹跟踪过程中的最大横向误差仅为5 cm,最大纵向误差仅为10 cm,速度误差控制在1 m/s以内,航向误差范围为±0.1 rad,前轮偏转角变化平稳未出现抖动现象。为验证控制器在井下实际环境下的跟踪性能,使用实验室小车于陕西某井下巷道进行了现场试验验证,结果表明:井下实际巷道下试验结果误差仍在合理范围内,解决了车辆运行过程中的速度和路径的时变问题,反映出该控制器具有较高的精度和较好的稳定性。

无人驾驶农机装备的模糊PI-LQR转向控制算法

无人驾驶农机装备转向系统处于小流量、小角度控制时会出现非线性和时滞,这会导致转向控制超调或者控制时滞,进而导致无法快速准确地跟踪到路径预瞄点。针对这个问题,本文提出了一种模糊比例积分-线性二次型调节器(PI-LQR)数据融合的内外环控制算法。该算法以模糊PI控制为内环,基于转角误差和转角误差变化率,通过模糊逻辑运算自适应调节PI参数,进行转向角度的闭环控制。以LQR控制为外环,基于农机装备XY-横摆角控制,融合内环的转角误差,进一步提升无人驾驶农机装备转向的精准控制。Carsim和Matlab/Simulink联合仿真表明:通过100 m长的双移线路径下,最大横向误差为0.18 m,最大横向摆角误差为0.067 rad。实车测试表明:通过100 m长的双移线路径下,最大横向误差0.26 m,相较于PID纯跟踪控制算法,最大横向误差减少了0.19 m。

Non-probabilistic reliability method and reliability-based optimal LQR design for vibration control of structures with uncertain-but-bounded parameters

Uncertainty is inherent and unavoidable in almost all engineering systems. It is of essential significance to deal with uncertainties by means of reliability approach and to achieve a reasonable balance between reliability against uncertainties and system performance in the control design of uncertain systems. Nevertheless, reliability methods which can be used directly for analysis and synthesis of active control of structures in the presence of uncertainties remain to be developed, especially in non-probabilistic uncertainty situations. In the present paper, the issue of vibration con- trol of uncertain structures using linear quadratic regulator （LQR） approach is studied from the viewpoint of reliabil- ity. An efficient non-probabilistic robust reliability method for LQR-based static output feedback robust control of un- certain structures is presented by treating bounded uncertain parameters as interval variables. The optimal vibration con- troller design for uncertain structures is carried out by solv- ing a robust reliability-based optimization problem with the objective to minimize the quadratic performance index. The controller obtained may possess optimum performance un- der the condition that the controlled structure is robustly re- liable with respect to admissible uncertainties. The proposed method provides an essential basis for achieving a balance between robustness and performance in controller design ot uncertain structures. The presented formulations are in the framework of linear matrix inequality and can be carried out conveniently. Two numerical examples are provided to illustrate the effectiveness and feasibility of the present method.

非线性递减权值PSO优化下的LQR轨迹跟踪研究

针对二次线性调节器(LQR)权重矩阵选取困难导致的自动驾驶车辆控制精度低、系统适应度欠佳等问题,设计了一种非线性递减权值粒子群算法(NLDW-PSO)。基于二自由度车辆动力学模型,构建了横向跟踪误差模型,设计了前馈控制消除了LQR稳态误差;并设计以横向偏差、航向偏差和前轮转向角为评价函数,将系统输出误差状态量反馈至NLDW-PSO算法,所设计的非线性递减惯性权重因子通过提升粒子群体寻优性能,从而自适应调整LQR权重系数更新策略,形成闭环优化控制,最终求解得到系统目标函数极值。将所设计控制器的跟踪效果进行了对比,Carsim/Smulink联合仿真结果表明所提出NLDW-PSO优化LQR算法的跟踪控制效果最优,横向距离偏差最大值为0.076 m,横向距离偏差均值相较于固定权重系数LQR降低了69.74%,显著提高了车辆跟踪控制精度和自适应能力,且对速度变化具有较强鲁棒性。

遥控武器站伺服系统的模糊LQR控制方法

针对遥控武器站伺服控制系统中存在负载力矩变化大、跟踪精度要求高等特点,提出一种模糊LQR控制策略,运用于武器站转速控制,以解决PI控制器存在快速性和稳态精度之间的矛盾,以及鲁棒性较差的问题。基于永磁同步电机转速跟踪模型设计了LQR控制器;针对LQR控制器权重系数固定、调参困难,且电机在不同转速和负载条件下运行时参数适应性较差的问题,提出了一种基于转速跟踪误差的LQR权重系数模糊调整策略,并以此设计模糊LQR控制器。通过仿真与实物试验,验证了控制器的控制性能。结果表明,设计的模糊LQR控制器在不同转速下均具有较高的跟踪精度与稳定性,同时对负载扰动和系统参数摄动具有较强的鲁棒性。

基于PSO的LQR车辆横纵向跟踪控制研究

为了解决LQR控制器在固定权重下对复杂道路的跟踪精度和稳定性较差的问题,该文提出一种基于PSO算法优化的预测前馈转角补偿横纵向系统控制方法。横向控制采用PSO优化的LQR控制器,纵向控制采用位置PID和速度PID的双PID控制器进行路径跟踪,位置误差通过PID控制器对前轮转角进行补偿,来解决车辆转向不足的问题。通过MATLAB/Simulink和Carsim进行联合仿真,结果表明,在侧方泊车实验中,最大横向误差降低了约51%;在避障换道超车实验中,最大横向误差减少了约49%。

风力发电机叶片MRD模糊LQR减振控制研究

针对在载荷作用下风力机叶片面内外振动控制问题,基于磁流变阻尼器MRD(Magnetorheological Damper)开展风力机叶片减振控制研究,采用模糊控制和LQR(Linear Quadratic Regulator)控制算法相结合的策略对MRD的阻尼力进行最优控制设计,以实现风力机叶片最优减振控制。首先,介绍MRD的原理和力学模型;其次,以NREL-5MW风力发电机组为数值仿真对象,建立风机叶片MRD动力学模型;最后,设计相应的模糊LQR半主动控制算法,跟踪识别风力机叶片在载荷作用下的动力响应。结果表明:与MRD叶片响应相比,模糊控制及模糊LQR控制策略均具有良好的减振效果,均使叶片面内外响应明显减小。此外,对比分析发现模糊LQR控制效果相比模糊控制效果更好,且叶片减振效果接近LQR主动控制下的位移响应,同时也充分表明该控制方法的合理性和优越性。

基于LQR的倾转旋翼机过渡段控制律设计

倾转旋翼机具有直升机模态、过渡段模态和定翼机模态,既有直升机的悬停和垂直起降性能,又有定翼机的高速巡航飞行能力,在过渡段模态,气动干扰严重且稳定性较差,因此,设计过渡段的控制律具有一定意义。以XV-15倾转旋翼机作为原型,首先用MATLAB建立飞机的气动模型,然后基于LQR最优控制算法对过渡段的纵垂向飞行姿态进行控制律的设计,最后进行模拟仿真。结果表明,LQR控制器对倾转旋翼机的飞行姿态具有较好的控制效果。