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1. 哈尔滨工程大学 自动化学院, 黑龙江 哈尔滨 150001;
2. 哈尔滨船舶锅炉涡轮机研究所, 黑龙江 哈尔滨 150036

Fuzzy PID control of pitching robots
ZHAO Xinhua1 , WANG Pu1, CHEN Xiaohong2
1. College of Automation, Harbin Engineering University, Harbin 150001, China;
2. Harbin Marine Boiler and Turbine Research Institute, Harbin 150036, China
Abstract:The PID and fuzzy PID controls were exploited to improve the control performance of the system for solving the problems of the slow response and low accuracy in the trajectory tracking of the pitching robot. Kinematics modeling of a dual-arm pitching robot was built. The dynamic model of the robotic arm was established and the constraint matrix equation was obtained by simultaneous equations. The PID and fuzzy PID controls were selected to control the trajectory of the dual-arm pitching robot. The mathematical model of the system was simulated using SimMechanics and the comparison of the two kinds of control schemes was completed using MATLAB. The numerical simulation results showed that the fuzzy PID control has a better effect.
Key words: robot     pitching robot     PID     fuzzy PID     dynamics model     constraint matrix     trajectory tracking

1 二连杆投球机器人的运动学建模 1.1 二连杆机械臂

 图 1 二连杆机械臂结构 Fig. 1 Dual-arm mechanical structure

Rpl相应于xy的坐标方程为

1.2 机械臂动力学方程

 图 2 第1根连杆受力分析 Fig. 2 The first arm force analysis

 图 3 第2根连杆受力分析 Fig. 3 The second arm force analysis

 图 4 负载受力分析 Fig. 4 Load force analysis

2 二连杆投球机器人的控制方法

2.1 PID控制

PID控制策略其结构简单、稳定性好、可靠性高[12]。式(20)为PID控制标准公式,其中U(t)为PID控制器输出，Kp为比例放大系数，Ti为积分常数,Td为微分放大系数，e为偏差信号。

PID参数设置：首先确定比例增益Kp，而后确定积分时间常数Ti，最后确定微分时间常数Td，通常为0即可。

2.2 模糊PID控制 2.2.1 模糊控制基本原理

 图 5 模糊控制器基本结构 Fig. 5 The basic structure of the fuzzy controller

2.2.2 输入量的模糊化

 图 6 隶属函数曲线 Fig. 6 Membership functions curve
2.2.2 输入量的模糊化

 e u ec=NB ec=NM ec=NS ec=ZO ec=PS ec=PM ec=PB NB PB PB PB PB PM 0 0 NM PB PB PB PB PM 0 0 NS PM PM PM PM 0 NS NS ZO PM PM PS 0 NS NM NM PS PS PS 0 NM NM NM NM PM 0 0 NM NB NB NB NB PB 0 0 NM NB NB NB NB
3 系统仿真 3.1 动力学仿真

 参数 取值 M1/kg 2.5 M2/kg 2.8 Mpl/kg 0.05 l1/m 1.0 l2/m 0.5 r1/m 0.8 r2/m 0.1 J1/(kg·m2) 0.15 J2/(kg·m2) 0.05

 图 7 两连杆机器人的Simuarm仿真模型 Fig. 7 Simuarm simulation model of dual-arm robot

 图 8 关节转角θ1和θ2的变化曲线 Fig. 8 Curve of joint angle θ1 and θ2
3.2 PID控制仿真

3.2.1 控制模型

 图 9 二连杆机器人仿真框图 Fig. 9 Simulation block of dual-arm robot
3.2.2 PID控制仿真

 图 10 AB杆模型参数 Fig. 10 Model parameters of AB arm

 图 11 两连杆机械臂旋转角度 Fig. 11 Rotation angle of dual-arm
3.3 模糊PID控制仿真

 图 12 第1、2根杆模糊PID模块 Fig. 12 Fuzzy PID block of the first and second arm

 图 13 第1根杆旋转角度完整图 Fig. 13 The complete graph of the first arm rotation angle

 图 14 第1根杆旋转角度局部放大图 Fig. 14 Partial enlarged drawing of the first arm rotation angle

 图 15 第2根杆旋转角度完整图 Fig. 15 The complete graph of the second arm rotation angle

 图 16 第2根杆旋转角度局部放大图 Fig. 16 Partial enlarged drawing of the second arm rotation angle
4 结束语

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DOI: 10.3969/j.issn.1673-4785.201404041

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#### 文章信息

ZHAO Xinhua, WANG Pu, CHEN Xiaohong

Fuzzy PID control of pitching robots

CAAI Transactions on Intelligent Systems, 2015, 10(03): 399-406.
DOI: 10.3969/j.issn.1673-4785.201404041