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.

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.

无人驾驶车辆路径跟踪混合控制策略研究

针对单一控制算法无法同时满足无人驾驶车辆对路径跟踪精度和控制器求解速度需求的问题,提出一种基于线性二次型调节器(LQR)和模型预测控制(MPC)的混合控制策略。该策略在低速工况下使用线性二次型调节器、在高速工况下使用模型预测控制算法进行路径跟踪控制,在此基础上设计基于有限状态机(FSM)的控制算法切换机制,并通过遗传算法(GA)对控制参数进行优化,基于CarSim和MATLAB/Simulink仿真平台对混合控制策略进行仿真验证,并进一步完成了实车试验。试验结果表明,所设计的混合控制策略能够在提高跟踪精度的基础上缩短计算时间,与单一控制算法相比,平均横向误差和平均航向误差分别减小了26.3%和39.6%,平均计算时间缩短了10.9%。

履带车辆主动悬挂多点布置优化

为实现履带车辆主动悬挂减振性能和能耗达到综合最优,基于正交试验方法开展履带车辆主动悬挂多点布置优化设计。首先,建立了履带车辆悬挂系统动力学模型,并通过道路模拟试验验证了该模型的合理性;其次,开展了履带车辆悬挂系统正交试验,分析了4种典型路面下各子悬挂对悬挂系统减振性能影响的敏感性;最后,设计了主动悬挂作动器的6个布置方案,通过建立基于线性二次最优(linear quadratic regulator,简称LQR)控制的履带车辆主动悬挂动力学模型,分析了典型路面下各布置方案对悬挂系统减振性能的影响规律及能耗变化规律。结果表明,通过对履带车辆主动悬挂作动器的布置优化,可以实现悬挂减振性能和能耗之间的平衡。

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。

基于改进势场法的智能车超车动态路径规划

为了改进人工势场法(artificial potential field,APF)在智能车高速超车状态下规划出的轨迹规范性差、安全性得不到保障、以及路径不平滑的问题。设计用于指引智能车换道的换道引力势场,以保证换道轨迹的规范性;构建异向分布结构的障碍车斥力势场提高换道的安全性;并建立带有转向缺口的道路中心线斥力势场和设计平滑代价函数优化规划出的轨迹点,使规划出的路径更加平滑。基于线性二次型调节器(linear quadratic regulator,LQR)设计路径跟踪控制器跟踪规划出的路径。通过Simulink与Carsim联合仿真,结果表明:所改进的APF算法能规划出更加合理的路径,设计的LQR路径跟踪控制器跟踪误差趋近于零,能够较好地控制车辆完成超车换道。

基于模型预测控制的车辆路径跟踪控制技术研究

以车辆三自由度动力学模型为研究对象,对自动驾驶车辆模型预测控制算法进行研究。结合魔术轮胎模型线性区域和小角度假设理论对车辆动力学模型进行简化处理,设计基于模型预测控制算法的路径跟踪控制器。使用MATLAB/CarSim联合仿真平台,选用多组工况进行仿真试验。设定车辆的速度分别为低速、中速、高速3种状态,并且使用线性二次型最优控制器进行换道工况路径跟踪,与模型预测控制器进行控制效果对比与分析,结果表明,模型预测控制算法路径跟踪控制效果更加优秀。

An iterative linear quadratic regulator based trajectory tracking controller for wheeled mobile robot

We present an iterative linear quadratic regulator(ILQR) method for trajectory tracking control of a wheeled mobile robot system.The proposed scheme involves a kinematic model linearization technique,a global trajectory generation algorithm,and trajectory tracking controller design.A lattice planner,which searches over a 3D(x,y,θ) configuration space,is adopted to generate the global trajectory.The ILQR method is used to design a local trajectory tracking controller.The effectiveness of the proposed method is demonstrated in simulation and experiment with a significantly asymmetric differential drive robot.The performance of the local controller is analyzed and compared with that of the existing linear quadratic regulator(LQR) method.According to the experiments,the new controller improves the control sequences(v,ω) iteratively and produces slightly better results.Specifically,two trajectories,'S' and '8' courses,are followed with sufficient accuracy using the proposed controller.

Application of the hybrid genetic particle swarm algorithm to design the linear quadratic regulator controller for the accelerator power supply

Purpose The purpose of this paper is to study a new method to improve the performance of the magnet power supply in the experimental ring of HIRFL-CSR.Methods A hybrid genetic particle swarm optimization algorithm is introduced,and the algorithm is applied to the optimal design of the LQR controller of pulse width modulated power supply.The fitness function of hybrid genetic particle swarm optimization is a multi-objective function,which combined the current and voltage,so that the dynamic performance of the closed-loop system can be better.The hybrid genetic particle swarm algorithm is applied to determine LQR controlling matrices Q and R.Results The simulation results show that adoption of this method leads to good transient responses,and the computational time is shorter than in the traditional trial and error methods.Conclusions The results presented in this paper show that the proposed method is robust,efficient and feasible,and the dynamic and static performance of the accelerator PWM power supply has been considerably improved.

单级旋转倒立摆系统辨识与随动稳定控制方法研究

针对单级旋转倒立摆系统参数辨识和随动稳定控制问题,首先建立倒立摆在不受外力控制,摆杆自然下垂的顺摆模型,基于顺摆模型采用快速傅里叶变换方法对系统参数进行辨识;然后推导顺摆模型与倒摆模型之间的关系,进一步得到倒立摆的倒摆模型;根据辨识出的倒摆模型,采用线性二次型控制器对其进行稳定控制,并进行了数值仿真与实物实验验证。研究结果表明,通过辨识得到的系统模型更加精确,对比直接测量参数得到的系统模型,控制效果更好,且能对随动输入指令进行更优的跟随。该方法可以有效避免量测误差,提高模型的准确性,为火炮随动稳定控制提供参考。

无人车换道轨迹与跟踪控制研究

无人车换道是自动驾驶领域的关键技术,针对无人车换道轨迹规划与跟踪控制问题,选择纯电动汽车作为研究对象,设计了一种考虑横纵向协同控制的轨迹跟踪控制器。首先,通过解耦将车辆换道简化为横向运动和纵向运动。根据路径跟踪误差动力学模型设计了线性二次型调节器路径跟踪控制器,并引入前馈控制设计了前馈-反馈LQR横向控制器,以此降低系统稳态误差。随后,考虑位置-速度误差设计了双PID纵向控制器,对车辆速度进行跟踪。选用五次多项式曲线规划换道轨迹。最后,通过Matlab和CarSim搭建联合仿真平台,对所设计的换道轨迹跟踪横纵向协同控制器进行测试研究。结果表明:在双车道换道工况下,该控制器能够较高精度地跟踪换道轨迹,车辆的距离偏差和航向角偏差最大分别为0.01 m和0.007 rad,可见具有良好的精确性和稳定性。

Load shedding scheme for the two-area system with linear quadratic regulator

The power system is prone to many emergency conditions which may lead to emergency state of operation with decay in the system frequency. The dramatic change in the frequency can result in cascaded failure of the system. In order to avoid power system collapse, load shedding （LS） schemes are adopted with the optimal amount of load shed. This paper proposed a methodology in a two-area thermal-thermal system for finding the required amount of load to be shed for setting the frequency of the system within minimum allowable limits. The LS steps have been obtained based on the rate of change of frequency with the increase in load in steps. A systematic study has been conducted for three scenarios： the scheme with a conventional integral controller; the scheme with a linear quadratic regulator （LQR）; and the scheme with an LQR and superconducting magnetic energy storage devices （SMES）. A comparison of the results has been presented on the two-area system.

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。

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。

基于Kent映射的数字集群动态负载均衡算法研究

由于动态负载均衡是保证数字集群系统正常运行中不可缺少的环节,但其在控制过程中存在易受通信故障等因素的干扰问题,为此提出基于Kent映射的数字集群动态负载均衡算法。通过基于云平台的虚拟机系统采集数字集群的节点连接数、响应时间、动态负载等信息,分析数字集群系统的负载情况。其次构建数字集群资源利用率模型,通过基于Kent映射的灰狼算法对模型求解得到数字集群的资源利用率。最后将资源利用率输入LQR(Linear Quadratic Regulator)控制回路器中,通过控制服务器的迁移实现数字集群的动态负载均衡。实验结果表明,所提算法处理后的数字集群响应时间短、适应度值大、容错能力强。

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%。

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。