Theoretical Study of Double Cost Function Linear Quadratic Regulator(LQR)

Double cost function linear quadratic regulator (DLQR) is developed from LQR theory to solve an optimal control problem with a general nonlinear cost function. In addition to the traditional LQ cost function, another free form cost function was introduced to express the physical need plainly and optimize weights of LQ cost function using the search algorithms. As an instance, DLQR was applied in determining the control input in the front steering angle compensation control (FSAC) model for heavy duty vehicles. The brief simulations show that DLQR is powerful enough to specify the engineering requirements correctly and balance many factors effectively. The concept and applicable field of LQR are expanded by DLQR to optimize the system with a free form cost function.

Adaptive Linear Quadratic Regulator for Continuous-Time Systems With Uncertain Dynamics

In this paper, adaptive linear quadratic regulator(LQR) is proposed for continuous-time systems with uncertain dynamics. The dynamic state-feedback controller uses inputoutput data along the system trajectory to continuously adapt and converge to the optimal controller. The result differs from previous results in that the adaptive optimal controller is designed without the knowledge of the system dynamics and an initial stabilizing policy. Further, the controller is updated continuously using input-output data, as opposed to the commonly used switched/intermittent updates which can potentially lead to stability issues. An online state derivative estimator facilitates the design of a model-free controller. Gradient-based update laws are developed for online estimation of the optimal gain. Uniform exponential stability of the closed-loop system is established using the Lyapunov-based analysis, and a simulation example is provided to validate the theoretical contribution.

Kalman Filter and H_(∞)Filter Based Linear Quadratic Regulator for Furuta Pendulum

This paper deals with Furuta Pendulum(FP)or Rotary Inverted Pendulum(RIP),which is an under-actuated non-minimum unstable non-linear process.The process considered along with uncertainties which are unmodelled and analyses the performance of Linear Quadratic Regulator(LQR)with Kalman filter and H∞filter as two filter configurations.The LQR is a technique for developing practical feedback,in addition the desired x shows the vector of desirable states and is used as the external input to the closed-loop system.The effectiveness of the two filters in FP or RIP are measured and contrasted with rise time,peak time,settling time and maximum peak overshoot for time domain performance.The filters are also tested with gain margin,phase margin,disk stability margins for frequency domain performance and worst case stability margins for performance due to uncertainties.The H-infinity filter reduces the estimate error to a minimum,making it resilient in the worst case than the standard Kalman filter.Further,when theβrestriction value lowers,the H∞filter becomes more robust.The worst case gain performance is also focused for the two filter configurations and tested where H∞filter is found to outperform towards robust stability and performance.Also the switchover between the two filters is dependent upon a user-specified co-efficient that gives the flexibility in the design of non-linear systems.The non-linear process is tested for set point tracking,disturbance rejection,un-modelled noise dynamics and uncertainties,which records robust performance towards stability.

Reduction of data amount in data-driven design of linear quadratic regulators

This paper discusses the data-driven design of linear quadratic regulators,i.e.,to obtain the regulators directly from experimental data without using the models of plants.In particular,we aim to improve an existing design method by reducing the amount of the required experimental data.Reducing the data amount leads to the cost reduction of experiments and computation for the data-driven design.We present a simplified version of the existing method,where parameters yielding the gain of the regulator are estimated from only part of the data required in the existing method.We then show that the data amount required in the presented method is less than half of that in the existing method under certain conditions.In addition,assuming the presence of measurement noise,we analyze the relations between the expectations and variances of the estimated parameters and the noise.As a result,it is shown that using a larger amount of the experimental data might mitigate the effects of the noise on the estimated parameters.These results are verified by numerical examples.

采用转角补偿LQR的自动驾驶集卡路径跟踪控制

为了解决自动驾驶集卡中半挂车在行驶过程中的路径偏移问题,提出了一种引入铰接角偏差和转角补偿的线性二次调节器(LQR)控制方法。基于集卡三自由度动力学模型建立了考虑铰接角偏差的路径跟踪误差模型;通过采用比例-积分-微分(PID)算法进行转角补偿设计了LQR路径跟踪控制器;通过MATLAB/Simulink和TruckSim搭建联合仿真平台,在不同工况下进行仿真分析验证。结果表明:通过采用提出的路径跟踪算法,引入PID转角补偿,牵引车平均距离偏差降低62%以上,半挂车平均距离偏差降低31%以上,航向偏差和铰接角偏差也均有所改善。因此,该文提出的控制算法具有较好的路径跟踪性能,提高了对期望路径跟踪的精度和稳定性。

Computing of LQR Technique for Nonlinear System Using Local Approximation

The main idea behind the present research is to design a state-feedback controller for an underactuated nonlinear rotary inverted pendulum module by employing the linear quadratic regulator(LQR)technique using local approximation.The LQR is an excellent method for developing a controller for nonlinear systems.It provides optimal feedback to make the closed-loop system robust and stable,rejecting external disturbances.Model-based optimal controller for a nonlinear system such as a rotatory inverted pendulum has not been designed and implemented using Newton-Euler,Lagrange method,and local approximation.Therefore,implementing LQR to an underactuated nonlinear system was vital to design a stable controller.A mathematical model has been developed for the controller design by utilizing the Newton-Euler,Lagrange method.The nonlinear model has been linearized around an equilibrium point.Linear and nonlinear models have been compared to find the range in which linear and nonlinear models’behaviour is similar.MATLAB LQR function and system dynamics have been used to estimate the controller parameters.For the performance evaluation of the designed controller,Simulink has been used.Linear and nonlinear models have been simulated along with the designed controller.Simulations have been performed for the designed controller over the linear and nonlinear system under different conditions through varying system variables.The results show that the system is stable and robust enough to act against external disturbances.The controller maintains the rotary inverted pendulum in an upright position and rejects disruptions like falling under gravitational force or any external disturbance by adjusting the rotation of the horizontal link in both linear and nonlinear environments in a specific range.The controller has been practically designed and implemented.It is vivid from the results that the controller is robust enough to reject the disturbances in milliseconds and keeps the pendulum arm deflection angle to zero degrees.

基于LQR的三有源桥变换器控制

针对三有源桥变换器解耦控制中工况远离稳态点解耦矩阵变化时控制性能较差的问题,提出一种基于线性二次型调节器(LQR)的三有源桥变换器控制方法。通过电路等效变换和端口功率传输方程建立状态空间模型,进一步设计基于状态反馈的LQR控制方法,在实现功率潮流控制的同时保持端口电压的稳定,通过仿真控制验证所提出方法的控制性能,对比传统PI解耦控制,在工况变化时,该控制方法具有更好的动态性能。

考虑模型失配的波浪发电系统功率优化LQR控制

为降低复杂海况对波浪发电系统的影响,改良目标价值函数,设计线性二次型最优控制器,约束系统运动状态同时提升波能捕获能力。通过调整权重矩阵求取最优反馈增益,获得理想q轴电流并采用空间矢量控制策略跟踪控制之,平衡系统物理约束与功率捕获关系;模型失配时根据理想模型与实际装置位移差值,基于HJI理论设计RBF鲁棒控制器,补偿系统失配运动状态与功率。仿真结果表明:在不规则激励力下,所提控制策略动态性能好、鲁棒性强,在满足系统物理约束的同时可有效提高波能捕获能力,补偿系统因失配减少的功率。

基于GA-PSO的智能汽车横向LQR控制器优化设计

针对线性二次型调节器(LQR)在智能汽车横向控制中,系数矩阵Q和R选取困难导致的控制精度低和参数整定效率低的问题,提出了一种遗传粒子混合优化(GA-PSO)方法。基于车辆二自由度模型设计了横向LQR控制器和前馈控制器,以该模型下控制器自身能量损失函数作为代价函数对系数矩阵进行优化,并对比了GA-PSO和粒子群优化(PSO)算法的优化效果。CarSim/Simulink联合仿真结果表明,经GA-PSO算法优化后的控制器跟踪精度和计算效率分别提高了47.06%和63.54%,且优化后的控制器具有较强的鲁棒性。

基于WOA- LQR的无人水翼航行器横航向控制

针对一种新型的无人水翼航行器在航行过程中受到不规则海浪干扰时的横向姿态与航向控制问题,首先建立无人水翼航行器横向四自由度运动的非线性数学模型,并对数学模型进行线性化处理;然后针对普通线性二次型调节器(linear quadratic regulator, LQR)控制算法手动调试参数效率较低且控制效果难以达到最优的问题,使用鲸鱼优化算法(whale optimization algorithm, WOA)对LQR控制器的参数进行寻优以增强控制效果;最后在不同强度的随机海浪干扰下对航行器的横向姿态与航向控制进行仿真,验证了鲸鱼算法优化LQR的有效性。

改进的LQR横向路径跟踪控制器

路径跟踪在自动驾驶中起着至关重要的作用。为了保证控制器的实时性并提高路径跟踪控制器的稳定性和自适应性,提出了一种基于改进的LQR算法的横向路径控制策略。首先将汽车的动力学模型拆解为横向误差动力学模型,并以此模型设计了前馈+反馈的离散LQR控制器。然后采用模糊控制方法实时根据车辆状态调整LQR的权重系数。此外,为了降低控制器的计算量,设计了基于余弦相似度的更新机制。最后,通过Simulink-Carsim平台对改进的LQR控制器进行双移线路况测试。结果表明,该控制算法在跟踪精度和计算效率方面得到了较大的改善。

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。

基于LQR的新能源虚拟惯量自适应控制策略

为提升基于直流电容能量虚拟惯量控制的新能源并网变流器对电力系统的惯量支撑能力,提出了一种基于线性二次调节器(LQR)的自适应虚拟惯量控制方法。在分析虚拟同步机(VSG)动力学特性的基础上,获得惯量参数和系统频率响应特性的数学关系,并建立了基于LQR的自适应惯量控制模型,通过LQR代价函数寻找最优反馈矩阵,使状态变量快速趋近于零且以最少的输入能量来满足控制需求。仿真结果表明,该方法能够使得新能源并网变流器根据系统频率波动情况对有限直流电容能量进行优化分配,快速阻尼频率变化,改善了系统频率响应特性,提升了新能源并网变流器对电力系统的惯量支撑能力,保障了电力系统的稳定性。

基于非线性补偿LQR的全驱动碟式水下机器人控制

本文提出了一种仅使用6个推进器实现全自由度可控的圆碟式水下机器人结构,在静水环境下对其进行动力学建模.随后,基于此模型提出一种带非线性补偿环节的线性二次型调节器(LQR)反馈控制方法,可通过双向水下推进器实现对水下机器人6个自由度的全驱动控制并抑制由重力矩导致的扰动.最后,经仿真试验表明本文设计的非线性补偿算法对重力矩扰动具有很强的抑制作用,控制器能稳定实现水下机器人六自由度状态跟踪,本文中设计的推进器布局也对全驱动水下机器人的设计具有一定的指导意义.

适应道路曲率多变的前馈-预测LQR横向控制

针对传统LQR(linear quadratic regulator)横向控制的不足,提出了一种前馈-预测LQR反馈控制,实现了曲率多变道路的跟踪控制。在传统动力学模型的基础上建立了误差模型,以误差模型为研究对象分别求解了反馈控制量和前馈控制量。为提高LQR对道路多变的适应性,根据航向和横向位置误差建立了模糊规则实时调节Q、R矩阵。同时利用道路曲率信息,设计了预测模块,实时更新预测点和预测时间,解决了传统LQR响应迟滞问题。在给定规划路径的基础上进行了硬件在环实验,测试了单、双移线多车速工况下传统LQR和前馈-预测LQR的路径跟踪效果,结果表明本文中设计的前馈-预测LQR的控制效果优于传统LQR,单移线工况下轨迹跟踪误差最大可减少4.5%,双移线工况下轨迹跟踪误差最大可减少9.5%。

半挂汽车列车挂车转向PSO-LQR控制器设计

针对低速转向时挂车跟踪牵引车轨迹性能较差的问题,设计了一种基于粒子群优化(particle swarm optimization, PSO)的挂车主动转向LQR控制器,探讨了不同权重矩阵获取方式对挂车转向控制效果的影响。验证了构建的挂车转向半挂汽车列车运动学模型的可靠性;设计了挂车的低速轨迹跟踪LQR控制器,利用PSO算法优化了LQR控制器的权重矩阵;研究了不同权重矩阵获取方式下的控制器性能。研究结果表明:经PSO算法优化后的LQR控制器能使挂车更快地进入稳定跟踪状态;当权重矩阵R分别取作0.1和1时,相比于由人为整定得到的权重矩阵Q对应的挂车跟踪误差,全局最优权重矩阵对应的挂车跟踪误差在单U形路径下分别减小26.1%和19.4%,在匝道螺旋路径下分别减小了40.9%和43.4%。

基于改进灰狼算法的LQR优化控制方法研究

针对二级倒立摆在使用LQR(线性二次调节器)进行优化控制过程中,由经验选取的加权矩阵Q和R参数存在着较大的随机性和不稳定性问题,提出了改进灰狼算法优化控制器加权矩阵Q和R的方法。为灰狼算法设计了基于二次余弦规律的自适应收敛因子a和增强α狼适应度值fα的比例权重方法。增强了算法迭代前期的全局搜索能力和后期的收敛速度,通过MATLAB/Simulink仿真,并与传统灰狼算法相比较,得出改进算法能够有效降低倒立摆回归平衡状态时的超调量,更快达到稳定状态,使控制效果更加理想。

Reduced-Order Observer-Based LQR Controller Design for Rotary Inverted Pendulum

The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Despite the implementation of various control strategies to maintain equilibrium,optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive.Existing methods frequently rely on extensive experimental data or the designer’s expertise,presenting a notable drawback.This paper proposes a novel tracking control approach for RIP,utilizing a Linear Quadratic Regulator(LQR)in combination with a reduced-order observer.Initially,the RIP system is mathematically modeled using the Newton-Euler-Lagrange method.Subsequently,a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states.This approach enhances the controller’s robustness by eliminating differential terms from the observer,thereby attenuating unknown disturbances.Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below50Hz and achieve precise tracking below1.4 rad,validating the effectiveness of the proposed control scheme.

Predictive active control of building structures using LQR and artificial intelligence

This study presents a neural network-based model for predicting linear quadratic regulator(LQR)weighting matrices for achieving a target response reduction.Based on the expected weighting matrices,the LQR algorithm is used to determine the various responses of the structure.The responses are determined by numerically analyzing the governing equation of motion using the state-space approach.For training a neural network,four input parameters are considered:the time history of the ground motion,the percentage reduction in lateral displacement,lateral velocity,and lateral acceleration,Output parameters are LQR weighting matrices.To study the effectiveness of an LQR-based neural network(LQRNN),the actual percentage reduction in the responses obtained from using LQRNN is compared with the target percentage reductions.Furthermore,to investigate the efficacy of an active control system using LQRNN,the controlled responses of a system are compared to the corresponding uncontrolled responses.The trained neural network effectively predicts weighting parameters that can provide a percentage reduction in displacement,velocity,and acceleration close to the target percentage reduction.Based on the simulation study,it can be concluded that significant response reductions are observed in the active-controlled system using LQRNN.Moreover,the LQRNN algorithm can replace conventional LQR control with the use of an active control system.

基于改进PID-LQR的导弹稳定控制方法研究

导弹稳定控制系统是提高导弹制导性能的关键技术之一,一直以来都是研究的热点和重点。以导弹纵向平面为例,建立了导弹稳定控制的状态空间模型,推导了LQR控制算法,在传统LQR方法的基础上,结合PID算法提出了一种改进的PID-LQR导弹稳定控制方法。通过仿真分析,比较了所提方法和传统LQR方法、改进LQR方法、模糊PID-LQR方法的控制性能,并对建立的导弹模型参数进行了拉偏试验,仿真结果表明所提出的方法优于其他3种方法,具有良好的控制性能和鲁棒性。