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毕 业 设 计（论 文） 外 文 参 考 资 料 及 译 文 译文题目： Adaptive Real-time Predictive Compensation Control for 6-DOF Serial Arc Welding Manipulator 自适应 实时预测补偿 控制 的 六 自由度 串联 电弧焊接 机械手 学生姓名： 符 金冬 学 号： 1404501023 专 业： 电气工程及其 自动化 所在学院： 机电工程 学院 指导教师： 李国利 职 称： 副教授 2016 年 02 月 25 日Adaptive Real-time Predictive Compensation Control for 6-DOF Serial Arc Welding Manipulator WANG Xuanyin ,DING Yuanming CHINESE JOURNAL OF MECHANICAL ENGINEERING,2010(3):361-366. Abstract Because of long driving chain and great system load inertia, the serial manipulator has a serious time delay problem which leads to significant real-time tracking control errors and damages the welding quality finally. In order to solve the time delay problem and enhance the welding quality, an adaptive real-time predictive compensation control(ARTPCC) is presented in this paper. The ARTPCC technique combines offline identification and online compensation. Based on the neural network system identification technique, the ARTPCC technique identifies the dynamic joint model of the 6-DOF serial arc welding manipulator offline. With the identified dynamic joint model, the ARTPCC technique predicts and compensates the tracking error online using the adaptive friction compensation technique. The ARTPCC technique is proposed in detail in this paper and applied in the real-time tracking control experiment of the 6-DOF serial arc welding manipulator. The tracking control experiment results of the end-effector reference point of the manipulator show that the presented control technique reduces the tracking error, enhances the system response and tracking accuracy efficiently. Meanwhile, the welding experiment results show that the welding seam turns more continuous, uniform and smooth after using the ARTPCC technique. With the ARTPCC technique, the welding quality of the 6-DOF serial arc welding manipulator is highly improved. Key words: adaptive friction compensation, neural network, system identification 1. Introduction With the progress of the world industrial technology, welding robots are more widely used in industrial manufacturing. Due to the characteristics of simple structure, wide workspace and high dexterity, the serial structure becomes the preferred structure of welding robots. However, serial robots have a long driving chain, because of greater system load inertia, when the running speed changes, greater joint driving torques will be needed. Because of the impact of friction and structural strain, it leads to time delay and significant accumulative error problems. The factors which cause the system time delay lagging response can be classified into two categories: one is system dynamic factors, such as gravity, inertia moment, viscous friction, disturbance and coupled moment; the other one is system static factors, such as coulomb friction and other non-identified inertia force, etc. Among all these non-linear factors, friction always gains scholars concern, which makes the friction compensation a research hotspot of motion control. Many friction compensation methods have been presented, such as a modified Southwards method1, the Lugre friction model2, the decomposition-based friction estimation3, and adaptive compensation methods45, which all depend on the non-linear dynamic model of the controlled object. Moreover, a friction compensation method based on joint-torque sensory feedback is studied by AGHILI, et al6, which does not need the dynamic models, but expensive joint-torque sensors are still needed. Neural network predictive control7, fuzzy control8, fuzzy adaptive predictive control9, and linear quadratic state-feedback control10 are also used for time delay systems. Although the concept of online learning is popular, one must pay attention to the instability caused by the drift of learning parameters. Adaptive friction compensation1112 first tunes proportional-integral-derivative(PID) control as well as possible. According to the time delay lagging properties of serial arc welding manipulators, an adaptive real-time predictive compensation control(ARTPCC) technique is presented in this paper, which is based on the neural network system identification technique and the adaptive friction compensation technique. This presented control technique includes two parts, the adaptive compensation part presented in section 2 and the system identification part presented in section 3. The ARTPCC works in the following way, firstly, joint model of the manipulator is established offline based on the neural network system identification technique, then joint tracking errors is predicted using the joint models and weight coefficients of the joint adaptive compensation control is modified online according to these errors to compensate the joint lagging response. In section 4, real-time tracking control experiments on a 6-DOF serial arc welding manipulator with and without the ARTPCC are presented to show the control performance of the proposed technique. Section 5 concludes the paper. 2. ARTPCC Model Typically, the system has a close-loop control as shown in Fig. 1.Where, H(z) is the control system transfer function, G(z) is the controlled object transfer function, u(n) is the control signal, d(n) is the input signal, y(n) is the output signal of the controlled object, e(n) is the system error. Fig. 1. Typical close-loop control model Add an adaptive compensation control into the system as shown in Fig. 2. Fig. 2. Adaptive compensation control model From Fig. 2, the following equations can be obtained: e() = ()() (1) () = ()() (2) b() = ()() (3) () = ()()+() (4) where b(n) is the adaptive compensation control signal, w(n) is the weight coefficient matrix of the adaptive compensation control, w(n)=(w1(n), w2(n),L, wm(n), d(n) is the input signal, d(n)=(d(nm+1), d(nm+2),L, d(n), m is the order of the adaptive compensation control. Let the objective function of the adaptive compensation control be () = ()2 (5) According to the gradient descent algorithm, the modified formula of the weight coefficient can be expressed as ( +1) = () 12 () (6) where is the learning factor. From Eqs. (1), (2) and (5), we yield the following equations: () = 2()() (7) () = ()() +() (8) u(n)w = ()e(n)w （ 9） Combining with Eqs. (3) and (9), Eq. (8) can be rewritten as () =()()1+()() (10) Substituting Eqs. (7) and (10) into Eq. (6), we can rewrite Eq. (6) as ( +1) = ()+()() ()1+()() (11) As shown in Eq. (11), when an adaptive compensation control is added into the system shown in Fig. 1, the controlled object model G(z) has to be known first. If the controlled object is a serious non-linear system such as the serial arc welding manipulator, the compensation algorithm will work badly because of the complicated and large computation. Moreover, due to characters of the system time delay lagging response, e(n) in Eq. (11) will not be the system error which needs to be compensated with current input signal b(n). If the control frequency of the adaptive compensation control is relatively low, the effect of the compensation will not be so good. Therefore, in order to enhance the accuracy of the compensation control, G(z) can be replaced with the identification model (z) of the controlled object. An estimation error e (n) can be got by (z) to replace the error signal e(n). Then the complicated system modeling can be saved and the error signal can be predicted to some extent. With the aforementioned analysis, an ARTPCC model is built as shown in Fig. 3, and the compensation algorithm can be expressed by Eqs. (12)(14): () = ()() (12) () = ()() (13) ( +1) = ()+()() ()1+()() (14) Fig. 3. ARTPCC model 3. Neural Network System Identification Model Neural network system identification is used to get the system model (z), and a BP neural network model is built as shown in Fig. 4. The model has four layers, the input layer i with three nodes, the hidden layer m with nine nodes, the hidden layer j with nine nodes, and the output layer k with one node. The weight coefficients between lays are ， ， ( =1,2,3; = 1,2,9; = 1,2,9; = 1) , respectively. The input signal is () =(1(),2(),3(), and the output signal is yk(n). Fig. 4. BP neural network model Let the input, the output and the threshold of a node be denoted by net, a, , respectively, and () = () = 1 ()1+ () (15) The equations of input and output between layers can be expressed by Eqs. (16)(19): = + = () = 1,2,3; (16) = +3=1 = () m = 1,2,9; (17) = +9=1 = () = 1,2,9; (18) = +9=1 = () = 1 (19) The cost function of the neural network model is = 12( )2=1 (20) In order to get the minimum of Eq. (20), according to the gradient descent algorithm, the modified formulas of the weight coefficient can be expressed as follows: ( +1) = ()+ ( +1) = ()+()(1)( +1) = ()+(1) = (1)( ) = ()()(1)9=1 (21) Where i=1, 2, 3; m=1, 2,L, 9; j=1, 2,L, 9; k=1. Add a saturation term into the modified formulas to enhance the learning efficiency as follows: = ()( 1) (22) and are both learning efficiency factors, changes the gradient searching step size of each layer, determines how much the past weight coefficient changes will affect the current weight coefficient modifications. 4. Real-time Tracking Control Experiments The research object of this paper, a 6-DOF serial arc welding manipulator, is shown in Fig. 5 and its coordinate system of linkages is shown in Fig. 6. As shown in Fig. 6, the bottom rotary joint has the longest driving chain and the biggest load inertia; therefore, this joint will be taken as an example to show the results of the neural network system identification and the ARTPCC experiments. Fig. 5. 6-DOF serial arc welding manipulator Fig. 6. Coordinate system 4.1 Joint velocity step response identification The original control system of the single joint of the manipulator is shown in Fig. 1. A velocity control mode of the joint motor is used, the control signal u(n) 20, 20 V, the corresponding velocity v(n) 150, 150 ()/s. Take 1ms as