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## 基于LQR-QPSO的地下铲运机控制参数优化研究

1.中南大学资源与安全工程学院，湖南 长沙 410083

2.中南大学数字矿山研究中心，湖南 长沙 410083

## Optimization of Control Parameters for Underground Load-Haul-Dump Machine Based on LQR-QPSO

LIU Yongchun,1,2, WANG Liguan,1,2, WU Jiaxi1,2

1.School of Resources and Safety Engineering，Central South University，Changsha 410083，Hunan，China

2.Digital Mine Research Center，Central South University，Changsha 410083，Hunan，China

 基金资助: 国家重点研发计划项目“深部集约化开采生产过程智能管控技术”.  2017YFC0602905“井下人机定位和作业环境感知分析技术与系统”.  2018SK2053

Received: 2020-09-17   Revised: 2020-10-26   Online: 2021-03-22

Abstract

With the increase of mining depth，the mining operation environment is worse and worse.It is of great significance to realize the underground unmanned load-haul-dump（LHD） machine to ensure the safe and efficient production of mine enterprises.In underground operation，the long，low articulated body of under-ground LHD machine has the characteristics of high mass，high inertia and high steering delay，which makes the precise tracking of the scraper path a difficult point for its realization of unmanned driving.As an important technique of path tracing control，the control algorithm based on optimization principle often has the problem of parameter selection and adjustment.In industrial applications，manual trial-and-error methods are commonly used for parameter selection.This method not only consumes a lot of human and time costs，but also makes it difficult to ensure the accuracy because of the lack of relevant experience of the operator.In this paper，the method of parameter optimization for linear quadratic regulator（LQR） state feedback controller by quantum-behaved particle swarm optimization（QPSO） algorithm was proposed.The LQR state feedback controller was cons-tructed based on error dynamics model.After parameter optimization，the maximum lateral error of path tracking is not more than 0.23 m.In a large number of repeated experiments，it is found that the standard particle swarm optimization（PSO） algorithm is difficult to find the proper parameter that can make the controller cross deviation lower than 0.5 m in 100 iterations.The QPSO algorithm has found the optimal parameter which meets the condition in the 10 repeated experiments.In 100 iterations，the fitness of the PSO algorithm tends to converge at 21 iterations，while that of the QPSO algorithm converges to a lower level than that of the PSO in the seventh iteration.The maximal lateral position deviation of the path tracking controller is reduced by 53.4%.It can be seen that the parameter optimization ability of the QPSO algorithm is obviously stronger than that of the PSO algorithm.The QPSO algorithm has faster optimization speed and higher success rate than the PSO algorithm.The control parameters of the LQR state feedback controller are automated by the QPSO algorithm.The design and parameter tuning process of the entire path tracking controller has important reference significance for realizing the unmanned driving of underground LHD machine.

Keywords： underground load-haul-dump machine ; path tracking control ; optimization of control parameters ; particle swarm optimization ; quantum particle swarm optimization ; linear quadratic regulator

LIU Yongchun, WANG Liguan, WU Jiaxi. Optimization of Control Parameters for Underground Load-Haul-Dump Machine Based on LQR-QPSO[J]. Gold Science and Technology, 2021, 29(1): 25-34 doi:10.11872/j.issn.1005-2518.2021.01.167

### 图1

$x˙y˙θ˙fγ˙=cosθfsinθfsinγLfcosγ+Lr0vf+00LrLfcosγ+Lr1γ˙$

### 图2

Fig.2   Schematic diagram of movement track of underground load-haul-dump unit

### 图3

Fig.3   Schematic diagram of error dynamic model of underground load-haul-dump unit

$ε˙dε˙θε˙c=0v000v000εdεθεc+001Lγ˙+00LrvLγ¨$

$ε˙dε˙θε˙c=0v000v000εdεθεc+0LrL1Lγ˙$

### 2.1 LQR控制器

LQR理论是现代控制理论中率先提出、发展较完善的一种状态空间设计方法。LQR的控制系统基于状态空间方程建立，将控制系统的状态变量和输入的控制变量的二次型函数作为性能指标函数，可以在系统失稳时，使得系统状态的多个分量在接近平衡状态的同时，不消耗过多的控制能量（李国勇，2008）。由于地下铲运机车身自由度高，地下矿山无人驾驶场景复杂，环境噪声信号较高，选择 LQR用于地下铲运机路径跟踪过程中对铰接转向角的控制具有突出优势。

$X˙t=AXt+ButYt=CXt+Dut$

LQR需要得到状态反馈控制向量矩阵$K$$Ut=-KX(t)$，使得式（5）性能指标$J$最小化（邹忱忱，2017）：

$J=12∫0∞XtTQXt+utTRutdt$

Table 1  Body geometry parameter of underground load-haul-dump unit

$A=06.920006.92000,B=01.8553.6113.61,C=100010001,D=0$

$rankBABA2B=3rankCCACA2=3$

$J=12∫0∞[εtTQεt+γ˙tTRγ˙t]dt$

$U=-KX(t)=-R-1BTX(t)$

$ATP+PA–PBR-1BTP+Q=0$

### 2.2 粒子群算法优化

$W=wini-wend·Gk-gGk+wend$

Sun et al.（2004）将量子力学的部分概念引入粒子群算法，提出了量子行为粒子群优化算法（QPSO）。在QPSO中，引入粒子的平均历史最优位置$mbest$，表示粒子群内各粒子个体历史最优位置$pbest$的平均值，其表达式为

$mbest=1N∑i=1Npbesti$

### 图4

Fig.4   Flow chart of particle swarm optimization algorithm

$Q=q1000q2000q3$
$R=1$

$fitnessi=∑t=1Tq1εd(t)2+q2εθ(t)2+q3εc(t)2+γ˙(t)2$

### 图5

Fig.5   LQR-QPSO path tracking controller

## 3 仿真试验

### 图6

Fig.6   3D laser point cloud map of test reference laneways

$α=αini-αend·Gk-gGk+αend$

Table 2  Initial parameter setting of the particle swarm optimization algorithm and its improved algorithm

Table 3  Parameter optimization results of the particle swarm optimization algorithm and its improved algorithm

$q1$$q2$$q3$$k1$$k2$$k3$
PSO0.456089.987661.34310.675310.285511.701419.5232
QPSO0.014255.816040.39360.11937.642010.83064.5278

### 图7

Fig.7   Historical optimal fitness

### 图8

Fig.8   Comparison of driving paths with different optimization parameters

### 图9

Fig.9   Control deviation comparison of different optimization parameters

### 图10

Fig.10   Control output comparison of different optimization parameters

## 4 结论

（1）基于误差动力学模型构建了一个LQR路径跟踪控制器，并使用QPSO算法对其进行参数优化，实现了在仿真条件下对地下铲运机精确、稳定的路径跟踪控制，最大横向误差不超过0.24 m。

（2）对比试验结果可知：在对LQR路径跟踪控制器的参数进行优化时，量子行为粒子群优化算法（QPSO）的结果明显优于标准粒子群优化算法（PSO），且成功率更高。这是因为QPSO改善了PSO算法易陷入局部最优的固有缺陷，寻优能力更强，速度更快。

（3）整个控制器设计和参数整定过程对实现地下铲运机的自主行走具有重要的参考意义。该控制器的效果受参数的影响很大，且对于不同的路径需要重新优化参数。地下铲运机的轨迹跟踪控制为马尔可夫过程，未来可以采用强化学习的方法得到能适应不同路径的控制策略。

http://www.goldsci.ac.cn/article/2021/1005-2518/1005-2518-2021-29-1-25.shtml

## 参考文献 原文顺序 文献年度倒序 文中引用次数倒序 被引期刊影响因子

Fang WeiSun JunXie Zhenpingal et2010.

Convergence analysis of quantum-behaved particle swarm optimization algorithm and study on its control parameter

［J］.Journal of Physics，596）：3686-3694.

Guo XinZhan KaiGu Hongshual et2009.

Navigation system research of unmanned scraper

［J］.Nonferrous Metals，614）：143-147.

Gupta STripathi R K2014.

Optimal LQR controller in CSC based STATCOM using GA and PSO

［J］.Archives of Electrical Engineering，633）：469-487.

Kang YanSun JunXu Wenbo2007.

Parameter selection of quantum-behaved particle swarm optimization

［J］.Computer Engineering and Applications，4323）：40-42.

Kemmoé Tchomté SGourgand M2009.

Particle swarm optimization：A study of particle displacement for solving continuous and combinatorial optimization problems（Article）

［J］.International Journal of Production Economics，1211）：57-67.

Kennedy JEberhart R1995.

Particle swarm optimization

［C］//International Conference on Neural Networks.PerthIEEE1942-1948.

Li Guoyong2008.

Optimal Control Theory and Application

［M］.Beijing：National Defence Industry Press：246.

Li JianguoZhan KaiShi Fengal et2015.

Auto-driving technology for underground scraper based on optimal trajectory tracking

［J］.Journal of Agricultural Engineering，4612）：323-328.

Liu HongboWang XiukunTan Guozhen2006.

Convergence analysis of particle swarm optimization and its improved algorithm based on Chaos

［J］.Control and Decision，216）：636-640.

Luo WeidongMa BaoquanMeng Yual et2020.

［J］.Journal of China Coal Society，454）：1536-1546.

Meng YuWang JueGu Qingal et2018.

LQR- GA path tracking control of articulated vehicle based on predictive information

［J］.Transactions of the Chinese Society for Agricultural Machinery，496）：375-384.

Nayl TNikolakopoulos GGustafsson T2015.

Effect of kinematic parameters on MPC based on-line motion planning for an articulated vehicle

［J］.Robotics and Autonomous Systems，7016-24.

Ridley PCorke P2003.

Load haul dump vehicle kinematics and control

［J］.Journal of Dynamic Systems. Measurement and Control，1251）：54-59.

Path tracking of an autonomous LHD articulated vehicle

［C］//The 16th IFAC World Congress.PragueIFAC55-60.

Shi YEberhart R1998.

A modified particle swarm optimizer

［C］//IEEE International Conference on Evolutionary Computation.AnchorageIEEE69-73.

Shiroma NIshikawa SInoue Kal et2009.

Nonlinear straight path tracking control for an articulated steering type vehicle

［C］//SICE Annual Conference.FukuokaIEEE2206-2211.

Sun JFeng BXu W2004.

Particle swarm optimization with particles having quantum behavior

［C］//Congress on Evolutionary Computation.PortlandIEEE，（1）：325-331.

Van den Bergh F2001.

An Analysis of Particle Swarm Optimizers

［D］.Pretoria：University of Pretoria.

Wang Yong2000.

Research on Nonlinear PID Control

［D］.Nanjing：Nanjing University of Science and Technology.

Zhang Donglin2002.

Undergound LHD

［M］.Beijing：Metallurgical Industry Press：509.

Zhao XuanYang JueZhang Wenmingal et2015.

Sliding mode control algorithm for path tracking of articulated dump truck

［J］.Journal of Agricultural Engineering，3110）：198-203.

Zheng Weibo2016.

Research on Improvement of Particle Swarm Optimization Algorithm and Its Application

［D］.Qingdao：Qingdao University

Zou Chenchen2017.

Study on the Control of LQR Linear Two-stage Inverted Pendulum Based on Particle Swarm Optimization

［D］.Xi’an：Xi’an University of Science and Technology.

［J］.物理学报，596）：3686-3694.

［J］.有色金属，614）：143-147.

［J］.计算机工程与应用，4323）：40-42.

［M］.北京：国防工业出版社：246.

［J］.农业机械学报，4612）：323-328.

［J］.控制与决策，216）：636-640.

［J］.煤炭学报，454）：1536-1546.

［J］.农业机械学报，496）：375-384.

［D］.南京：南京理工大学.

［M］.北京：冶金工业出版社：509.

［J］.农业工程学报，3110）：198-203.

［D］.青岛：青岛大学.

［D］.西安：西安科技大学.

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