Position Control of Manipulator s Links Using Artificial Neural Network with Backpropagation Training Algorithm

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1 Poition Control of Manipulator Link Uing Artificial Neural Network with Backpropagation Training Algorith Thiang, Handry Khowanto, Tan Hendra Sutanto Electrical Engineering Departent, Petra Chritian Univerity Siwalankerto Surabaya, Indoneia e-ail: Abtract Thi paper decribe about application of artificial neural network for controlling the poition of anipulator link. In thi cae, the anipulator ha three degree of freedo and the anipulator i ipleented for drilling a printed circuit board. In thi application, artificial neutral network wa ued a the control yte ethod therefore it act a the controller. The artificial neural network architecture ued a the controller i a ultilayer perceptron network with backpropagation training algorith. The artificial neural network ha two input of control ignal and one output of control ignal and varie in nuber of hidden layer. The input of network are error ignal and delta error ignal. The output of network i peed of the DC otor. The experient were done in variation of nuber of hidden layer, neuron per layer and learning rate. Experiental reult how that architecture of the network that give the bet repone i 1 hidden layer with 20 neuron per layer for the firt link and 2 hidden layer with 40 neuron per layer for the econd link. Thi paper decribe another application of ANN which i a further work of previou work [2][3]. In thi cae, ANN wa applied to control the poition of anipulator link. The anipulator ha three degree of freedo, which conit of two revolute oint and one priatic oint. Fig. 1 how the odel of anipulator that wa controlled by ANN. Becaue the anipulator wa ipleented for drilling proce, there are only two link that are controlled by ANN. Therefore, there are two parallel ANN ued in thi yte in order to control the two link of the anipulator. The training data are created fro the knowledge of the expert. ANN learn the training data in order to odel the training data autoatically. The reulted odel i in for of architecture of ANN including the weight and bia connection of the network. Keyword- artificial neural network; anipulator; control yte; intelligent control; backpropagation I. INTRODUCTION Artificial neural network (ANN) are iplified odel of the central nervou yte. It i believed by any reearche in the field that neural network odel offer the ot proiing unified approach to build truly intelligent coputer yte. ANN have been hown to be effective a coputational proceor for variou tak including pattern recognition, aociative recall, claification, data copreion, odeling and forecating, adaptive control and noie filtering[1]. Reference [2] decribe one of application of ANN in control yte. ANN i applied for controlling one ar robot. In thi application, ANN i ued to odel the econd order controller o that ANN can act a the controller. Architecture of ANN ued in thi yte i fully connected ultilayer perceptron with backpropagation training algorith. The reult how that ANN can control one ar robot uccefully. Reference [3] decribe about another application of ANN in control yte. ANN i applied to control the peed of DC otor. In thi application, ANN alo act a the controller and the reult how that ANN can control the peed of DC otor well. Felix Paila and friend have uccefully applied ANN cobined with Fuzzy Logic for electrical load forecating application [4][5][6]. Figure 1. The anipulator with three degree of freedo II. METHODS A. Deign of Artidficial Neural Network Architecture Block diagra of the control yte applied in thi reearch i hown at Figure 2. Figure 2. Block diagra of control yte uing artificial neural network 290 Dept. of EE and IT, GMU Yogyakarta, 2-3 March 2010

2 Proceeding of ICGC-RCICT 2010 Technical Paper ISSN: A hown at Fig. 2, ANN i applied a the control yte ethod. ANN run a the controller in order to control the plant. In thi reearch, the plant i a anipulator with three degree of freedo. The deigned ANN ha two input and one output. The input are error ignal (ERR) and delta error ignal (DERR). ERR and DERR are deterined by uing the following equation: ERR = SP PV (1) DERR = ERR(n) ERR(n-1) (2) where SP = Setting point PV = Proce variable ERR(n) = Current error ERR(n-1) = Previou error The output i peed of the DC otor that i ued a the actuator for oving the link of anipulator. The ANN wa deigned by uing fully connected ultilayer perceptron architecture. Fig. 3 how the architecture of ANN ued a the controller in order to control the link of anipulator. Backpropagation algorith i ued a the training ethod of the deigned artificial neural network. The backpropagation algorith include the following tep: 1. Initialize weight and biae to all rando nuber. 2. Preent a training data to neural network and calculate the output by propagating the input forward through the network uing (3). 3. Propagate the enitivitie backward through the network: M 2F M M ( n )( t a) 1 T F ( n )( W ) 1 where f ( n1 ) 0 0 f ( n2 ) F ( n ) f n 0 0 f f ( ) ( n ) n 4. Calculate weight and bia update, for M 1,..., 2,1 0 0 ( n ) (5) (6) (7) (8) h 1 h 2 h 10 W b ( k) k 1 ) T ( ) ( a Where i learning rate. 5. Update the weight and biae W ( k 1) W ( k) W ( k) b ( k 1) b ( k) b ( k) (9) (10) (11) (12) n 50 n 50 n 50 Figure 3. Architecture of ANN ued a controller Nuber of hidden layer varie fro 1 to 10 layer. Nuber of neuron per hidden layer varie fro 1 to 50 neuron. If the ANN ha layer and receive input of vector p, then the output of the network can be calculated by uing the following equation: (3) 6. Repeat tep 2 5 until error i zero or le than a liit value. B. Ipleentation of Artificial Neural Network a Controller Ipleentation of ANN a the control yte ethod conit of two tep. Firt tep i the deigned ANN were trained to create odel of the controller o that atify training data. The training data are created fro the knowledge of the expert. Training data are alo created by conidering the tep repone of general autoatic control yte, which i hown at Fig. 4. where f i log-igoid tranfer function of the th layer of the network that can be defined a following equation: f n 1 1 e n (4) W i weight of the th layer of the network, and b i bia of the th layer of the network. Equation (3) i known a the feed forward calculation. Becaue there are two link that are controlled by ANN, the yte run two ANN yte, one for each link. Both ANN have the ae architecture. Figure 4. Step repone of general autoatic control yte For exaple, at the point a in Fig. 4, the input error and delta error can be deterined. The value of error i poitive and big value and the value of delta error i zero. Yogyakarta, 2-3 March 2010 Dept. of EE and IT, GMU 291

3 Thu, by conidering the expert knowledge, output peed of DC otor can be deterined. It wa done ae a creating the rule of fuzzy logic controller. Other training data were created with the ae procedure uing other point. ANN learn the training data autoatically in order to odel the controller equation. The reulted odel i in for of architecture of ANN including the weight and bia connection of the network. There are 600 data ued to train the ANN. The econd tep i ipleentation of the trained ANN for controlling the link poition of anipulator. The ANN yte wa ipleented on a Peronal Coputer (PC), which i connected to the anipulator. III. EXPERIMENTAL RESULTS For teting the perforance of ANN to create odel of controller equation and to control link poition of anipulator, everal experient were done in variation of ANN architecture and training paraeter, i.e. variation of hidden layer nuber, variation of neuron nuber per layer and variation of learning rate. The perforance of artificial neural network i indicated by the MSE value. A. Experiental Reult of Modeling the Controller Thi experient wa done in variation of nuber of hidden layer, nuber of neuron per layer, learning rate value. Thi experient wa done for teting how well ANN can odel the controller equation. Nuber of hidden layer variation, ued for thi experient are 1 hidden layer, 2 hidden layer, and 3 hidden layer. Nuber of neuron varie fro 1 neuron, 20 neuron, and 40 neuron. Learning rate ued for thi experient are 0.1, 0.5, and 0.9. The experient wa done for both link, which were controlled by ANN. Table I how the uary of experiental reult for the firt link and Table II how the experiental reult uary for the econd link. TABLE I. EXPERIMENTAL RESULT SUMMARY OF MSE VALUE FOR FIRST LINK Nuber of hidden Layer/Neuron per layer 1 Hidden Layer 2 Hidden 3 Hidden Learning Rate Neuron Neuron Neuron Neuron Neuron Neuron TABLE II. EXPERIMENTAL RESULT SUMMARY OF MSE VALUE FOR SECOND LINK Nuber of hidden Layer/Neuron per layer 1 Hidden Layer 2 Hidden 3 Hidden Learning Rate Neuron Neuron Neuron Neuron Neuron Neuron For the firt link, the bet architecture of ANN that can odel the controller equation by learning the training data i ANN with two hidden layer and each layer ha 20 neuron. It could achieve MSE value of Increaing the nuber of hidden layer doe not alway give better value of MSE. In cae of firt link, the bet reult i achieved by ANN with 2 hidden layer although the difference of MSE value aong 1, 2, and 3 hidden layer architecture are all epecially at 20 and 40 neuron per layer. Table I alo how that increaing nuber of neuron per layer give a ignificant iproveent of MSE value until it reache a pecific nuber. When the nuber i greater than that pecific nuber, there i no ignificant iproveent of MSE value. For the econd link, the bet architecture of ANN that can odel the controller equation by learning the training data i ANN with three hidden layer and each layer ha 40 neuron. It could achieve MSE value of Sae a the firt link, increaing the nuber of hidden layer doe not give better MSE value. Moreover, it tend giving wore reult. Table II alo how that increaing nuber of neuron per layer give a ignificant iproveent of MSE value until it reache a pecific nuber. When the nuber i greater than that pecific nuber, there i no ignificant iproveent of MSE value. B. Experiental Reult of Poition Control Perforance Thi experient wa done uing the bet architecture of ANN that wa reulted fro previou experient. There are three architecture of ANN ued in thi experient. The firt i the bet architecture of ANN uing 1 hidden layer, the econd i the bet architecture of ANN uing 2 hidden layer and the third i the bet architecture of ANN uing 3 hidden layer. The purpoe of thi experient i to tet perforance of the controller in order to control the link poition of anipulator. Thi experient wa done in variation of etting point (SP) value. The paraeter ued to ee perforance of control yte i rie tie (t r ), ettling tie (t ), and axiu overhoot (M o ). 292 Dept. of EE and IT, GMU Yogyakarta, 2-3 March 2010

4 Proceeding of ICGC-RCICT 2010 Technical Paper ISSN: TABLE III. EXPERIMENTAL RESULT SUMMARY OF CONTROL SYSTEM RESPONSE FOR FIRST LINK ANN Architecture for Firt Link 1 Hidden layer 20 Neuron 2 Hidden layer 20 Neuron Setting Point tr (econd) t (econd) Mo (%) neuron per layer. Thi architecture reulted rie tie value varie fro 3 to 3.5 econd, ettling tie varie fro 3.5 to 4.5 econd, and axiu overhoot wa 4.4%. Fro table IV, it i hown that the bet repone of controller for econd link i reulted fro ANN architecture with 2 hidden layer, 40 neuron per layer. Thi architecture reulted rie tie value varie fro 3.5 to 4.5 econd, ettling tie varie fro 4 to 5.5 econd, and axiu overhoot wa 4.4%. Fig. 5 and 6 how other experient that were alo done to ee the perforance of the ANN a the control yte ethod. In thi experient, the etting point wa changed every an interval tie in order to ee whether the controller can control both link or not. Fig. 5 how the control yte repone of ANN for controlling the firt link. Fig. 6 how the control yte repone of ANN for controlling the econd link. Fro Fig. 4 and 5, it can be concluded that ANN can control both link poition. The poition of both link can ove according to the changing of etting point value. 3 Hidden layer TABLE IV. EXPERIMENTAL RESULT SUMMARY OF CONTROL SYSTEM RESPONSE FOR SECOND LINK ANN Architecture For Second Link Setting Point tr t Mo (econd) (econd) (%) Hidden layer Figure 5. ANN controller repone yte for firt link Hidden layer Hidden layer Figure 6. ANN controller repone yte for econd link Table III and IV how the experiental reult uary of control yte repone for firt link and econd link repectively. For the firt link, control yte uing ANN ha relatively the ae repone. But, the bet repone wa reulted fro ANN architecture with 1 hidden layer, 20 IV. CONCLUSION Fro experiental reult, it can be concluded that the Artificial Neural Network (ANN) can be ued a the control yte ethod. In thi cae, ANN can odel the controller equation well and ANN can control link poition of the anipulator well. The bet repone control yte wa achieved by ANN architecture with 1 hidden layer, 20 neuron per layer for firt link, and 2 hidden layer, 40 neuron for econd link. In thi cae, the Yogyakarta, 2-3 March 2010 Dept. of EE and IT, GMU 293

5 third link i not controlled by ANN becaue the third link only ove up and down for drilling proce. REFERENCES [1] Dan W. Patteron. Artificial Neural Network, Theory and Application. Singapore: Prentice Hall, [2] Thiang, Rianto Chandra, Iwan Noto Sandaa, One Ar Robot Poition Control Uing Artificial Neural Network, in Proceeding of National Seinar: The Application of Technology Toward Better Life. Yogyakarta, [3] Thiang, Indar Sugiarto, Hendrik Chandra, DC Motor Speed Control Syte Uing Artificial Neural Network, in Proceeding of National Seinar of Coputer Science and Inforation Technology, Jakarta, [4] Felix Paila, Multivariate Input for Electrical Load Forecating on Hybrid Neuro-Fuzzy and Fuzzy C-Mean Forecater, in Proceeding of International Conference on Fuzzy Syte, Hongkong, [5] Felix Paila, Sauta Ronni, Thiang, Lie Hendra Wiaya, Longter Forecating in Financial Stock Market uing Accelerated LMA on Neuro-Fuzzy Structure and Additional Fuzzy C-Mean Clutering for Optiizing the GMF, in Proceeding of International Joint Conference on Neural Network. Hongkong, [6] Felix Paila, Neuro-Fuzzy Forecater for Modeling and Forecating Electrical Load Copetition Uing Multivariate Input on Takagi-Sugeno Network, in Proceeding of International Conference on Soft Coputing, Intelligent Syte, and Inforation Technology. Bali, Dept. of EE and IT, GMU Yogyakarta, 2-3 March 2010