DSpace at VNU: Online tuning gain scheduling MIMO neural PID control of the 2-axes pneumatic artificial muscle (PAM) robot arm

Expert Systems with Applications 37 (2010) 6547–6560 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa Online tuning gain scheduling MIMO neural PID control of the 2-axes pneumatic artificial muscle (PAM) robot arm Ho Pham Huy Anh * Faculty of Electrical and Electronic Engineering, Ho Chi Minh City University of Technology, Ho Chi Minh City, Viet Nam a r t i c l e i n f o Keywords: Pneumatic artificial muscle (PAM) Highly nonlinear PAM robot arm Proposed online tuning gain scheduling MIMO dynamic neural PID controller (MIMO DNN-PID) Real-time joint angle position control Fast online tuning back propagation (BP) algorithm a b s t r a c t This paper presents a detailed study to investigate the possibility of applying the online tuning gain scheduling MIMO neural dynamic DNN-PID control architecture to a nonlinear 2-axes pneumatic artificial muscle (PAM) robot arm so as to improve its joint angle position output performance The proposed controller was implemented as a subsystem to control the real-time 2-axes PAM robot-arm system so as to control precisely the joint angle position of the 2-axes PAM robot arm when subjected to system internal interactions and load variations The results of the experiment have demonstrated the feasibility and benefits of the novel proposed control approach in comparison with the traditional PID control strategy The proposed gain scheduling neural MIMO DNN-PID control scheme forced both joint angle outputs of 2-axes PAM robot arm to track those of the reference simultaneously under changes of the load and system coupled internal interactions The performance of this novel proposed controller was found to be outperforming in comparison with conventional PID These results can be applied to control other highly nonlinear systems Ó 2010 Elsevier Ltd All rights reserved Introduction The development of compliant manipulator aimed to replace monotonous and dangerous tasks, which has motivated lots of researchers to develop more and more sophisticated and intelligent controllers for human-friendly industrial manipulators Due to uncertainties, it is difficult to obtain an accurate mathematical model for robot manipulators Thus, conventional control methodologies find it difficult or impossible to handle un-modeled dynamics of a robot manipulator Furthermore, most of conventional control methods, for example PID controllers, are based on mathematical and statistical procedures for modeling the system and estimation of optimal controller parameters In practice, such manipulator to be controlled is often highly nonlinear and a mathematical model may be difficult to derive Consequently, to accommodate system uncertainties and variations, learning methods and adaptive intelligent techniques must be incorporated Furthermore, the orientation of industrial robotics toward applications needing greater proximity between the robot and the human operator has recently led researchers to develop novel actuator sharing some analogous features with natural skeletal muscle The PAM actuator now has been achieving increased popularity by providing advantages such as high power/weight ratio, full of hygiene, easiness in preservation and especially the capacity * Tel.: +84 08 39490415 E-mail address: hphanh@hcmut.edu.vn 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd All rights reserved doi:10.1016/j.eswa.2010.02.131 of human compliance which is the most important requirement in medical and human welfare field Thus, PAM actuator has been regarded during the recent years as an interesting alternative to hydraulic and electric actuators However, the air compressibility and the lack of damping ability of the PAM manipulator bring the dynamic disturbance of the pressure response and cause the oscillatory motion Therefore, it is not easy to realize the performance of transient response with high speed and with respect to various external inertia loads in order to realize a human-friendly therapy robot Numerous intelligent control methods have been devised to solve complicated problems of industrial manipulators in general and of PAM manipulators in particular Neo and Er (1996) and Lilly, Chan, Repperger, and Berlin (2003) improved fuzzy controllers to PAM manipulators A Kohonen-type neural network for the position control of robot arm is applied in Hesselroth, Sarkar, Patrick van der Smagt, and Schulten (1994) Forwardly, the authors have developed a feed-forward neural network controller (Patrick van der Smagt, Groen, & Schulten, 1996) Caldwell et al applied an adaptive controller and the error is better than ±0.5° (Caldwell, Bowler, & Medrano-Cerda, 1996) Carbonell et al applied successfully sliding mode to control PAM actuator (Carbonell, Jiang, & Repperger, 2001) Applied fuzzy and PID control to PAM system (Balasubramanian & Rattan, 2003a) Forwardly, authors improved fuzzy feed-forward control to PAM system (Balasubramanian & Rattan, 2003b) Ahn et al developed Hinfinity control to a 6-DOF manipulator (Ahn, Lee, & Yang, 2003) Gini, Folgheraiter, Perkowski, and Pivtoraiko (2003) proposed an 6548 H.P.H Anh / Expert Systems with Applications 37 (2010) 6547–6560 adaptive controller based on the neural network applied to the artificial hand, which is composed of the PAM Nil et al developed a hybrid fuzzy neural network to control a 3-DOF robot manipulator (Nil, Yuzgec, & Kakir, 2006) Recently, in Ahn and Thanh (2006), Ahn et al have applied magneto-rheological (MR) brake combining LVQNN to control the 1-link PAM manipulator Forwardly, Ahn and Anh have successfully identified the highly nonlinear PAM manipulator using neural NARX model (Ahn & Anh, 2007) and GA-based fuzzy NARX model (Ahn & Anh, 2009) for improving the control performance of the 1-link PAM manipulator Though these control systems were partially successful in obtaining smooth actuator motion in response to input signals, the manipulator must be controlled slowly in order to get stable and accurate position control Furthermore, the external inertia load was also assumed to be constant or slowly varying It is because PAM manipulators are multivariable nonlinear coupled systems and frequently subjected to structured and/or unstructured uncertainties even in a well-structured setting for industrial use or human-friendly applications as well Assuming that PAM manipulator is applied as an elbow and wrist rehabilitation robot in future, which is the final purpose of our study, it is necessary to realize fast response, even if the external inertia load changes severely At the same time, the external inertia loads can always be varied and not be known exactly Therefore, it is necessary to propose a new control algorithm, which is applicable to a highly nonlinear PAM system with various loads To overcome these drawbacks, the proposed online tuning MIMO DNN-PID algorithm in this paper is a newly developed algorithm that has the following good features such as highly simple and dynamic self-organizing structure, fast learning speed, good generalization and flexibility in learning The proposed online tuning MIMO DNN-PID controller is employed to compensate for environmental variations such as payload mass and time-varying parameters during the operation process By virtue of online training by BP learning algorithm and then auto-tuned gain scheduling K and PID weighting values Kp, Ki and Kd, it is able to learn the 2axes PAM robot-arm dynamics and make control decisions simultaneously In effect, it offers an exciting online estimation scheme of the plant The outline of this paper composes Section for introducing related works in PAM robot-arm control Section presents procedure of design an online tuning gain scheduling MIMO DNN-PID controller for the 2-axes PAM robot arm Section presents and analyses experiment studies and results Finally, the conclusion is given in Section Control system 2.1 Controller design Many efforts have been made to compensate the coupled effect and nonlinear features of n-DOF PAM actuators Since the simplicity and efficiency of the feedback PID controller in closed-loop system is a commonly used technique and has been proven to be more stable, this scheme is used in this paper In the feedback PID controller system design, the proposed online tuning gain scheduling MIMO DNN-PID of the 2-axes PAM robot arm is updated online to learn as close as possible the dynamic features of nonlinear 2axes PAM robot arm This online tuning gain scheduling MIMO DNN-PID controller is to increase the accuracy for the two-joint position control of the 2-axes PAM robot arm The block diagram of the proposed controller is shown in Fig The structure of the newly proposed online tuning MIMO DNNPID control algorithm using MLFNN is shown in Fig This control algorithm is a new one and has the characteristics such as simple + - eP (k) Neural ΔT z −1 + YREF1 (k) eI (k) - 1− z ΔT −1 ed (k) PID Online Tuning Controller Gain Joint Scheduling 2-Axes PAM Manipulator MLFNN Network + U1 (k) U2 (k) - eP (k) Neural ΔT z −1 + YREF2 (k) eI (k) - − z −1 ΔT ed (k) PID Online Tuning Controller Gain Joint Scheduling MLFNN Network Fig Block diagram of proposed online tuning gain scheduling MIMO DNN-PID position control system Y1 (k) Y2 (k) 6549 H.P.H Anh / Expert Systems with Applications 37 (2010) 6547–6560 structure, little computation time and more robust control, compared with the previous neural network controller (Thanh & Ahn, 2006) From Figs and 2, a control input u applied to the two-joints of the 2-axes PAM manipulator can be obtained from the following equation u ¼ Kf xị ỵ Bh 1ị where x is input of hyperbolic tangent function f(Á) which is presented in Eq (2), K and Bh are the bias weighting values of input layer and hidden layer, respectively The hyperbolic tangent function f(Á) has a nonlinear relationship as explained in the following equation f xị ẳ ex ị ỵ ex ị ð2Þ The block diagram of proposed online tuning gain scheduling MIMO DNN-PID control based on Multi-Layer Feed-Forward Neural Network (MLFNN) composed of three-layers is shown in Fig In this figure, K, Kp, Ki and Kd, are scheduling, proportional, integral and derivative gain while ep, ei and ed are system error between desired set-point output and output of joint of the PAM manipulator, integral of the system error and the difference of the system error, respectively MLFNN is trained online by the fast learning back propagation (FLBP) algorithm as to minimize the system error between desired set-point output and output of joint of the PAM manipulator From Fig 2, the input signal of the hyperbolic tangent function f(Á) becomes xðkÞ ẳ K p kịep kị ỵ K i kịei kị ỵ K d kịed kị ỵ Bi kị Okị ẳ f xkịị 3ị @Ekị @K @Ekị K p k ỵ 1ị ẳ K p kị gp @K p @Ekị K i k ỵ 1ị ẳ K i kị gi @K i @Ekị K d k ỵ 1ị ẳ K d kị gd @K d Kk ỵ 1ị ¼ KðkÞ À g and the bias weighting values Bi(k) and Bh(k) are updated as follows: @EðkÞ @Bi @EðkÞ Bh k ỵ 1ị ẳ Bh kị gBh @Bh Bi k ỵ 1ị ẳ Bi kị gBi with ep kị ẳ yREF kị ykị ei kị ẳ ep ðkÞ Á DT ð4Þ ep ðkÞð1 À zÀ1 Þ ed kị ẳ DT where DT is the sampling time, z is the operator of Z-transform, k is the discrete sequence, yREF(k) and y(k) are the desired set-point output and output of joint of the PAM manipulator, respectively Furthermore, Bi, Kp, Ki and Kd are weighting values of input layer, and Bh and K are weighting values of hidden layer These weighting values will be tuned online by fast learning back propagation (FLBP) algorithm As to online tuning the gain scheduling K and PID parameters Kp, Ki and Kd, the gradient descent method used in BP learning algorithm using the following equations were applied eD (k) Kd eI (k) Ki eP (k) Kp Ekị ẳ y kị ykịị2 REF ð7Þ Appling the chain rule with Eqs (5) and (6), it leads to @Ekị @Ekị ẳ @K @y @Ekị @Ekị ẳ @K p @y @Ekị @Ekị ẳ @K i @y @Ekị @Ekị ẳ @K d @y @ykị @u @yðkÞ @u @yðkÞ @u @yðkÞ @u @uðkÞ @K @uðkÞ @OðkÞ @xðkÞ @O @x @K p @uðkÞ @OðkÞ @xðkÞ @O @x @K i @uðkÞ @OðkÞ @xðkÞ @O @x @K d ð8Þ @yðkÞ @u @yðkÞ @u @uðkÞ @OðkÞ @xðkÞ @O @x @Bi @uðkÞ @Bh ð9Þ and From Eqs (1), (3), and (6), the following equations can be derived: @Ekị ẳ yREF kị ykịị ẳ ep kị @y @ykị Dy ykị yk 1ịị % ẳD ẳ @u Du ukị uk 1ịị @ukị ẳK @O @Okị ẳ f xkịị @x @xkị @xkị @xkị ẳ 1; ẳ ep kị; ¼ ei ðkÞ; @Bi @K p @K i @uðkÞ @uðkÞ ¼1 ¼ OðkÞ; @K @Bh MLFNN Network Σ x(k) Bi ð6Þ where g, gp, gi, gd, gBi and gBh are learning rate values determining the convergence speed of updated weighting values; E(k) is the error defined by the gradient descent method as follows: @Ekị @Ekị ẳ @Bi @y @Ekị @Ekị ẳ @Bh @y ukị ẳ KkịOkị ỵ Bh kị ð5Þ f f(x) K O(x) Σ Bh Fig Structure of MLFNN network system used in proposed online tuning MIMO DNN-PID controller u(k) 10ị @xkị ẳ ed kị @K d 6550 H.P.H Anh / Expert Systems with Applications 37 (2010) 6547–6560 Fig Working principle of the 2-axes PAM robot arm Fig Experimental set-up configuration of the 2-axes PAM robot arm and @Ekị @Ekị @ykị @ukị @Okị @xkị ẳ @Bi @y @u @O @x @Bi 0 ¼ Àep kịDKf xkịị1 ẳ DKf xịep kị 12ị @Ekị @Ekị @ykị @ukị ẳ ẳ ep kịD1 ẳ Dep kị @Bh @y @u @Bh and with f xị ẳ Fig Photograph of the experimental 2-axes PAM robot arm From Eqs (8)–(10), the following resulting equations can be derived: @Ekị @Ekị ẳ @K @y @Ekị @Ekị ẳ @K p @y @ykị @u @ykị @u @ukị ẳ ep kịDOkị @K @ukị @Okị @xkị ẳ ep kịDKf xkịịep kị @O @x @K p ẳ DKf xịe2p kị @Ekị @Ekị @ykị @ukị @Okị @xkị ẳ ẳ ep kịDKf xkịịei ðkÞ @K i @y @u @O @x @K i ¼ ÀDKf ðxÞep ðkÞei ðkÞ @EðkÞ @EðkÞ @yðkÞ @uðkÞ @OðkÞ @xkị ẳ ẳ ep kịDKf xkịịed kị @K d @y @u @O @x @K d ẳ DKf xịep kịed kị 11ị ex 13ị ỵ ex ị2 From Eqs (5) and (6), the final equations for online tuning gain scheduling K and PID parameters Kp, Ki and Kd are expressed as follows: Kk ỵ 1ị ẳ Kkị ỵ g ep kịD Okị K p k ỵ 1ị ẳ K p kị ỵ gp e2p kịDK 2ex ỵ ex ị2 2ex K i k ỵ 1ị ẳ K i kị ỵ gi ep kịei kịDK ỵ ex ị2 2ex K d k ỵ 1ị ẳ K d kị ỵ gd ep kịei kịDK ỵ ex ị2 14ị and the bias weighting values Bi(k) and Bh(k) are updated as follows: Bi k ỵ 1ị ẳ Bi kị ỵ gBi ep kịDK Bh k ỵ 1ị ẳ Bh kị ỵ gBh ep kịD 2ex ỵ ex ị2 15ị 6551 H.P.H Anh / Expert Systems with Applications 37 (2010) 6547–6560 Table Lists of the experimental hardware set-up No Name Model name Company Proportional valve (2) Pneumatic artificial muscle (4) D/A board Counter board Rotary encoder (2) MPYE-5-1/8HF-710 B MAS-10-N-220-AA-MCFK PCI 1720 PCI QUAD-4 H40-8-3600ZO FESTO FESTO ADVANTECH COMPUTING MEASUREMENT METRONIX REF1 1/z [REF1] To Workspace Unit Delay3 1/z [REF2] Unit Delay8 Goto5 Goto3 U2 REF2 To Workspace19 To Workspace15 du/dt U1 Ucontrol2 To Workspace16 To Workspace6 Derivative1 1/s Integrator1 Analog Output DYNAMIC_NEURAL_PID Wpid2 To Workspace3 z Unit Delay2 z Sine Wave1 Unit Delay1 du/dt DNN-PID2 [Wpid2] Derivative [Ucontrol2] Integrator Constant1 z Unit Delay5 DYNAMIC_NEURAL_PID [error2] Ucontrol2 Ucontrol1 [Ucontrol1] To Workspace13 Goto2 Analog Output Wpid1 z From10 [error1] Analog Output1 Advantech PCI-1720 [auto] Goto1 Goto9 1/s Sine Wave2 TRAPEZOID Reference1 Saturation To Workspace7 Unit Delay4 DNN-PID1 Analog Output2 Advantech PCI-1720 [auto] Constant2 [Wpid1] From5 Saturation1 Goto10 TRAPEZOID Reference2 Y1 error1 Ucontrol1 To Workspace1 XY Graph1 To Workspace4 TRIANGLE Reference2 Encoder Input Encoder Input1 -0.025 error1 Gain1 [error1] [Y1] Measurement Computing PCI-QUAD04 [auto] Goto7 Goto4 [Y1] From4 error2 Y2 RECTANGLE Reference1 To Workspace5 To Workspace2 error2 Encoder Input RECTANGLE Reference2 0.025 Encoder Input2 Gain3 XY Graph [REF1] Y1 TRIANGLE Reference1 [Y2] [error2] Goto8 [Y2] From [REF2] [error1] From8 From2 From9 [Wpid2] From11 Goto6 Measurement Computing PCI-QUAD04 [auto] From6 [error2] From3 [Ucontrol1] [Ucontrol2] From7 [Wpid1] Results From1 Fig 6a Experiment SIMULINK model of PAM robot-arm position control using proposed MIMO DNN-PID control 2.2 Experimental set-up A general configuration of the investigated 2-axes PAM manipulator shown through the schematic diagram of the 2-axes PAM robot arm and the photograph of the experimental apparatus presented in Figs and 4, respectively Fig presents the block diagram for joint angle position control of the both joints of the 2-axes PAM robot arm using proposed online tuning gain scheduling neural MIMO DNN-PID control scheme The hardware includes an IBM compatible PC (Pentium 1.7 GHz) which sends the voltage signals u1(t) and u2(t) to control the two proportional valves (FESTO, MPYE-5-1/8HF-710B), through a D/A board (ADVANTECH, PCI 1720 card) which changes digital signals from PC to analog voltage u1(t) and u2(t), respectively The rotating torque is generated by the pneumatic pressure difference supplied from air-compressor between the antagonistic artificial muscles Consequently, both joints of the 2-axes PAM robot arm will be rotated to follow the desired joint angle references (YREF1(k) and YREF2(k)), respectively The joint angles, h1 (°) and h2 (°), are detected by two rotary encoders (METRONIX, H40-8-3600ZO) and fed back to the computer through a 32-bit counter board (COMPUTING MEASUREMENT, PCI QUAD-4 card) which changes digital pulse signals to joint angle values y1(t) and y2(t) The pneumatic line is conducted under the pressure of bar and the software control algorithm of the closed-loop system is coded in C-mex program code run in Real-Time Windows Target of MATLAB-SIMULINK environment Table presents the configuration of the hardware set-up installed from Fig Experimental results The performance of proposed online tuning gain scheduling MIMO DNN-PID control scheme is verified on joint angle position control of the both joints of the 2-axes PAM robot arm Figs 3–5 describe the working diagram of this control scheme Fig 6a presents the real-time SIMULINK diagram of proposed online tuning gain scheduling neural MIMO DNN-PID control algorithm which run in Real-time Windows Target In this novel control scheme, DYNAMIC_NEURAL_PID1 and DYNAMIC_NEURAL_PID2 are two subsystems programmed in C then compiled and run in real-time C-mex code Three initial PID parameters Kp, Ki, Kd and gain scheduling K value are chosen by trial-and-error method and determined as K = 0.6, Kp = 0.089, Ki = 0.09, Kd = 0.07 for Joint and K = 0.6, Kp = 0.089, Ki = 0.09, Kd = 0.05 for Joint 6552 H.P.H Anh / Expert Systems with Applications 37 (2010) 6547–6560 REF1 1/z [REF1] To Workspace Unit Delay3 Goto3 1/z [REF2] UcontrolPID2 Upid2 Unit Delay8 Goto5 To Workspace6 To Workspace15 Analog Output REF2 To Workspace19 RECTANGLE Reference1 Sine Wave1 Saturation [Ucontrol2] Advantech PCI-1720 [auto] z Unit Delay2 Analog Output1 Goto1 Constant1 RECTANGLE Reference2 Sine Wave2 z Unit Delay5 PID TRAPEZOID Reference1 Ucontrol2 UcontrolPID1 [Ucontrol1] To Workspace13 Goto2 Analog Output Saturation1 PID Gain2 Analog Output2 Advantech PCI-1720 [auto] Upid1 Constant2 To Workspace16 TRAPEZOID Reference2 Ypid1 errorPID1 Ucontrol1 To Workspace1 XY Graph1 To Workspace4 TRIANGLE Reference1 Encoder Input Encoder Input1 -0.025 error1 Gain1 [error1] [Y1] Measurement Computing PCI-QUAD04 [auto] Goto7 Goto4 [REF1] Y1 TRIANGLE Reference2 [Y1] PID 0.6 From4 PID Gain4 errorPID2 Ypid2 To Workspace5 To Workspace2 error2 Encoder Input 0.025 Encoder Input2 Gain3 [Y2] Goto6 [error2] [Y2] From9 XY Graph From [REF2] [error1] From2 From8 From6 [error2] From3 [Ucontrol1] [Ucontrol2] Goto8 From7 Results Measurement Computing PCI-QUAD04 [auto] Fig 6b Experiment SIMULINK model of 2-axes PAM robot-arm position control using conventional PID control Fig 6b presents the experiment SIMULINK diagram of 2-axes PAM robot-arm position control using conventional PID controller in order to compare as to demonstrate the superiority of proposed control system Three PID parameters Kp, Ki, Kd and gain scheduling K value of each PID controller are chosen by trial-and-error method and determined as K = 0.6, Kp = 0.089, Ki = 0.09, Kd = 0.07 for Joint and K = 0.6, Kp = 0.089, Ki = 0.09, Kd = 0.05 for Joint Fig shows that the parameter configuration of DYNAMIC_ NEURAL_PID subsystem composes seven parameters The first vector parameter contains number of inputs and outputs of neural DYNAMIC_NEURAL_PID subsystem; the second relates to the number of neurons of hidden layer used; the third declares the step size used in real-time operation of PAM system; the fourth declares the learning rate value used in real-time operation of PAM manipulator; the fifth parameter contains logic value as to choose the sigmoid function (1) or the hyperbolic tangent function (0); the sixth parameter contains logic value as to choose the linear function (0) or the sigmoid/hyperbolic tangent function (1) of output layer; and the seventh vector parameter contains the offline-training K, Kp, Ki, Kd weighting values and two initial bias weighting values Bi and Bh The final purpose of the PAM manipulator is to be used as an elbow and wrist rehabilitation robot Thus, the experiments were carried out with respect to three different waveforms as reference input (triangular, trapezoidal and sinusoidal reference) with two different end-point payloads (Load 0.5 kg and Load kg) as to demonstrate the performance of novel proposed controller Furthermore, the comparisons of control performance between the conventional PID controller and the proposed online tuning gain scheduling MIMO DNN-PID controller were performed The gain scheduling value K and PID controller parameters Kp, Ki and Kd were set to be K = 0.6, Kp = 0.089, Ki = 0.09, Kd = 0.07 for Joint and K = 0.6, Kp = 0.089, Ki = 0.09, Kd = 0.05 for Joint These parameters of both PID controllers were obtained by trial-and-error through experiments The proposed neural DNN-PID control of the 2-axes PAM manipulator is investigated with initial parameter configuration as follows: both of DYNAMIC_NEURAL_PID1 and DYNAMIC_NEU- Fig Parameter configuration of DYNAMIC_NEURAL_PID subsystem used in proposed online tuning DNN-PID control RAL_PID2 subsystems possessed a three-layer MLFNN structure composes one neurons in hidden layer, three inputs, one output with its structure is shown in Fig 2; the sampling time 0.01 s; the learning rate value k is chosen equal 0.0005; the hyperbolic tangent function is chosen as activated function of hidden layer; the linear function is chosen as activated function of output layer; the initial weighting values are chosen with the same value as K, Kp, Ki and Kd of corresponding PID controller and forwardly, the two initial bias weighting values Bi and Bh are chosen equal 0; finally error back propagation (BP) method is chosen as fast learning algorithm First, the experiments were carried out to verify the effectiveness of the proposed online tuning MIMO DNN-PID controller using neural network with triangular reference input Fig 8a and b shows the experimental results between the conventional PID controller and the proposed nonlinear DNN-PID controller with respect to Joints and in two cases of Load 0.5 kg and Load kg, respectively The online updating of each control parameter ( K, 6553 H.P.H Anh / Expert Systems with Applications 37 (2010) 6547–6560 JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg 25 Reference PID control proposed DNN-PID control JOINT ANGLE [deg] Reference PID control proposed DNN-PID control 20 -2 15 -4 10 -6 -8 -10 0 10 20 30 40 50 60 10 20 30 40 50 60 PID control proposed DNN-PID control ERROR [deg] 1.5 PID control proposed DNN-PID control 1 0.5 0 -1 -0.5 -1 -2 -1.5 10 20 30 40 50 60 10 20 t [sec] 30 40 50 60 t [sec] Fig 8a Triangular response of both joints of the 2-axes PAM robot arm – Load 0.5 kg JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] 25 Reference PID control proposed DNN-PID control JOINT ANGLE [deg] 20 -2 15 -4 10 -6 -8 -10 0 10 20 30 ERROR [deg] Reference PID control proposed DNN-PID control 40 50 60 PID control proposed DNN-PID control 10 20 30 40 50 60 PID control proposed DNN-PID control 1 0 -1 -1 -2 10 20 30 40 50 60 t [sec] 10 20 30 40 50 60 t [sec] Fig 8b Triangular response of both joints of the 2-axes PAM robot arm – Load kg Kp, Ki and Kd) with respect to Joints and in two cases of Load 0.5 kg and Load kg was shown in Fig 8c In the experiment of the proposed online tuning MIMO DNN-PID controller, the initial values of K, Kp, Ki and Kd are set to be the same as that of conventional PID controller Due to the sophisticated online tuning of K, Kp, Ki and Kd, the error between desired reference yREF and actual 6554 H.P.H Anh / Expert Systems with Applications 37 (2010) 6547–6560 JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] 0.8 PID PARAMETER 0.8 0.6 0.6 Kp Ki Kd Kgain 0.4 Kp Ki Kd Kgain 0.4 0.2 0.2 0 10 20 30 40 50 60 0 JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] 20 30 40 50 60 JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] 0.7 0.7 Kp Ki Kd Kgain 0.6 PID PARAMETER 10 0.5 0.6 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 Kp Ki Kd Kgain 0 10 20 30 40 50 60 10 20 t [sec] 30 40 50 60 t [sec] Fig 8c The online tuning convergence of proposed MIMO DNN-PID controller parameters with triangular reference JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] 0.2 U control [V] PID control proposed DNN-PID control PID control proposed DNN-PID control 0.4 0.3 0.2 -0.2 0.1 -0.4 10 20 30 40 50 60 -0.1 20 30 40 50 60 JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] 0.2 0.5 PID control proposed DNN-PID control U control [V] 10 PID control proposed DNN-PID control 0.4 0.3 0.2 -0.2 0.1 -0.4 10 20 30 40 50 t [sec] 60 -0.1 10 20 30 40 50 60 t [sec] Fig 8d The voltage control applied to both joints of the 2-axes PAM robot arm with triangular reference joint angle response y continually decreased Consequently, the error decreases only in the range ±0.7° with Joint and ±0.6° with Joint in case of Load 0.5 kg The same good result is obtained with the error only in the range ±0.8° with Joint and ±0.6° with Joint in case of Load kg These results are really optimistic in comparison with the bad and unchanged error of conventional PID controller (±1.7° with Joint and ±1.8° with Joint in both case of Load) Fig 8d shows the refined shape of voltage control U1 and U2 applied to Joint and Joint 2, which are generated by the proposed online tuning MIMO DNN-PID controller as to improve the performance and the accuracy of both joints of the 2-axes PAM robotarm response Forwardly, the experiments were carried out to verify the superiority of the proposed online tuning DNN-PID controller with trapezoidal reference input Fig 9a and b shows the experi- 6555 H.P.H Anh / Expert Systems with Applications 37 (2010) 6547–6560 JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] Reference PID control proposed DNN-PID control JOINT ANGLE [deg] 20 -2 15 -4 10 -6 -8 -10 0 10 20 30 40 50 60 10 20 30 40 PID control proposed DNN-PID control 70 1.5 ERROR [deg] Reference PID control proposed DNN-PID control 25 50 60 70 PID control proposed DNN-PID control 0.5 0 -1 -0.5 -1 -2 10 20 30 40 50 60 70 10 20 30 t [sec] 40 50 60 70 t [sec] Fig 9a Trapezoidal response of both joints of the 2-axes PAM robot arm – Load 0.5 kg JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] 25 Reference PID control proposed DNN-PID control JOINT ANGLE [deg] 20 -2 15 -4 10 -6 -8 -10 0 10 20 30 40 50 60 70 PID control proposed DNN-PID control 1.5 ERROR [deg] Reference PID control proposed DNN-PID control 10 20 30 40 60 70 PID control proposed DNN-PID control 50 0.5 0 -1 -0.5 -2 -1 10 20 30 40 50 60 t [sec] 70 10 20 30 40 50 60 70 t [sec] Fig 9b Trapezoidal response of both joints of the 2-axes PAM robot arm – Load kg mental results of the conventional PID controller and the proposed neural MIMO DNN-PID controller with respect to Joints and in cases of Load 0.5 kg and Load kg, respectively The online tuning of four DNN-PID controller parameters (K, Kp, Ki and Kd) with respect to Joints and in two cases of Load 0.5 kg and Load kg was shown in Fig 9c In the experiment of the proposed 6556 H.P.H Anh / Expert Systems with Applications 37 (2010) 6547–6560 JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] PID PARAMETER 0.6 0.6 0.5 0.5 Kp Ki Kd Kgain 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 10 Kp Ki Kd Kgain 0.4 20 30 40 50 60 70 30 40 50 60 70 0.6 0.6 PID PARAMETER 20 JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] 0.5 0.5 Kp Ki Kd Kgain 0.4 0.3 0.3 0.2 0.1 0.1 10 Kp Ki Kd Kgain 0.4 0.2 10 20 30 40 50 60 70 0 10 20 30 t [sec] 40 50 60 70 t [sec] Fig 9c The online tuning convergence of proposed MIMO DNN-PID controller parameters with trapezoidal reference JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] 0.2 U control [V] PID control proposed DNN-PID control PID control proposed DNN-PID control 0.4 0.3 0.2 0.1 -0.2 -0.4 -0.1 10 20 30 40 50 60 70 10 20 30 40 50 60 70 JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] 0.5 0.2 PID control proposed DNN-PID control U control [V] PID control proposed DNN-PID control 0.4 0.3 0.2 0.1 -0.2 -0.1 -0.4 10 20 30 40 50 60 t [sec] 70 10 20 30 40 50 60 70 t [sec] Fig 9d The voltage control applied to both joints of the 2-axes PAM robot arm with trapezoidal reference online tuning DNN-PID controller, the initial values of K, Kp, Ki and Kd are set to be the same as that of conventional PID controller These figures show that due to the refined online tuning of K, Kp, Ki and Kd, the error between desired reference yREF and actual joint angle response y continually minimized Consequently, the optimized error decreases only in the range ±0.7° with Joint and ±0.5° with Joint in case of Load 0.5 kg The same good result is obtained with the minimized error in the range ±0.7° with Joint and ±0.6° with Joint in case of Load kg These results are really outperforming in comparison with the bad and unchanged error of conventional PID controller (±1° with Joint and ±1.8° with Joint in both case of Load) Furthermore, in case of Load kg, Fig 9b shows that PID controller caused 2-axes PAM robot-arm response begun to be oscillatory and unstable Other- 6557 H.P.H Anh / Expert Systems with Applications 37 (2010) 6547–6560 JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] Reference PID control proposed DNN-PID control 15 JOINT ANGLE [deg] 10 -5 -10 -5 -15 -10 -20 10 20 30 40 50 60 70 80 1.5 10 20 30 40 50 60 70 80 1.5 PID control proposed DNN-PID control ERROR [deg] Reference PID control proposed DNN-PID control PID control proposed DNN-PID control 0.5 0.5 0 -0.5 -0.5 -1 -1 10 20 30 40 t [sec] 50 60 70 80 10 20 30 40 t [sec] 50 60 70 80 Fig 10a Sinusoidal response of both joints of the 2-axes PAM robot arm – Load 0.5 kg JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] 15 JOINT ANGLE [deg] Reference PID control proposed DNN-PID control Reference PID control proposed DNN-PID control 10 -5 -10 -5 -15 -10 -20 10 20 30 40 50 60 70 80 ERROR [deg] 1.5 10 20 30 40 1.5 PID control proposed DNN-PID control 0.5 0 -0.5 -0.5 60 70 80 PID control proposed DNN-PID control 0.5 50 -1 -1 10 20 30 40 50 60 70 t [sec] 80 10 20 30 40 50 60 70 80 t [sec] Fig 10b Sinusoidal response of both joints of the 2-axes PAM robot arm– Load kg wise, proposed online tuning MIMO DNN-PID controller continues to assert robust control to keep 2-axes PAM robot-arm response stable and accurate tracking Fig 9d shows the refined shape of voltage control U1 and U2 applied to Joint and Joint 2, which are generated by the proposed online tuning MIMO DNN-PID controller as to assure the perfor- mance and the accuracy of both joints of the 2-axes PAM robotarm trapezoidal response Next, the experiments were carried out with sinusoidal reference input Fig 10a and b shows the experimental results of the conventional PID controller and the proposed nonlinear MIMO DNN-PID controller with respect to Joints and in two cases of 6558 H.P.H Anh / Expert Systems with Applications 37 (2010) 6547–6560 PID PARAMETER JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] 0.7 0.7 0.6 0.6 0.5 0.5 Kp Ki Kd Kgain 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 10 Kp Ki Kd Kgain 0.4 20 30 40 50 60 70 80 20 30 40 50 60 70 80 JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] PID PARAMETER 10 0.6 0.6 0.5 0.5 Kp Ki Kd Kgain 0.4 0.3 Kp Ki Kd Kgain 0.4 0.3 0.2 0.2 0.1 0.1 0 10 20 30 40 50 60 70 80 10 20 30 t [sec] 40 50 60 70 80 t [sec] Fig 10c The online tuning convergence of proposed MIMO DNN-PID controller parameters with sinusoidal reference JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD 0.5 [kg] 0.2 PID control proposed DNN-PID control U control [V] 0.4 PID control proposed DNN-PID control 0.2 0 -0.2 -0.2 -0.4 10 20 30 40 50 60 70 80 -0.4 10 20 30 40 50 60 70 80 JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] JOINT - 2-AXES PAM MANIPULATOR - LOAD [kg] 0.2 PID control proposed DNN-PID control 0.4 PID control proposed DNN-PID control U control [V] 0.3 0.2 0.1 -0.1 -0.2 -0.2 -0.3 -0.4 10 20 30 40 t [sec] 50 60 70 80 -0.4 10 20 30 40 t [sec] 50 60 70 80 Fig 10d The voltage control applied to both joints of the 2-axes PAM robot arm with sinusoidal reference Load 0.5 kg and Load kg, respectively The online tuning of four parameters of MIMO DNN-PID controller (K, Kp, Ki and Kd) with respect to Joints and in two cases of Load 0.5 kg and Load kg is shown in Fig 10c These figures show that thanks to the refined online tuning of K, Kp, Ki and Kd, the error between desired reference yREF and actual joint angle response y continually minimized Consequently, the optimized error decreases only in the range ±0.4° with Joint and ±0.3° with Joint in case of Load 0.5 kg The same good result is obtained with the minimized error in the range ±0.5° with Joint and ±0.3° with Joint in case of Load kg These results are really outperforming in comparison with the unchanged error of conventional PID controller (±0.8° with Joint and ±0.7° with Joint in both case of Load) Furthermore, in case of Load kg, Fig 10b shows that PID controller caused 2-axes PAM robot-arm response oscillatory and unstable On the contrary, proposed online tuning MIMO DNN-PID controller continues to assert robust control to keep 2-axes PAM robot-arm response stable and accurate tracking Fig 10d shows the resulted control voltage U1 and U2 applied to Joint and Joint 2, which are generated by the proposed online tuning MIMO DNN-PID controller as to improve the performance 6559 H.P.H Anh / Expert Systems with Applications 37 (2010) 6547–6560 LINE TRAJECTORY - LOAD 0.5 [kg] a 18 Y2 [deg] LINE TRAJECTORY - LOAD [kg] b 20 Reference PID control proposed DNN-PID control 20 18 16 16 14 14 12 12 10 10 8 6 4 2 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 Reference PID control proposed DNN-PID control -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 Y2 [deg] Y1 [deg] Fig 11 (a, b) Comparison of line trajectory tracking Y2 [deg] a ELLIPSOIDAL TRAJECTORY - LOAD 0.5 [kg] b Reference PID control proposed DNN-PID control ELLIPSOIDAL TRAJECTORY - LOAD [kg] Reference PID control proposed DNN-PID control 0 -5 -5 -10 -10 -15 -15 -20 -20 -25 -15 -10 -5 10 15 -25 -15 -10 -5 10 15 Y1 [deg] Y1 [deg] Fig 12 (a, b) Comparison of ellipsoidal trajectory tracking and the accuracy of both joints’ sinusoidal response of the 2-axes PAM robot arm This figure shows that PID controller generates an oscillatory and unstable control voltage in case of Load kg Otherwise, proposed online tuning MIMO DNN-PID controller continues to robustly control with refined control voltage as to keep 2axes PAM robot-arm response stable and accurate tracking In Fig 11a and b, comparison between conventional PID controller and the proposed online tuning MIMO DNN-PID controller was performed with respect to two-dimensional line trajectory tracking in cases of Load 0.5 kg and Load kg, respectively In Fig 12a and b, comparison between conventional PID controller and the proposed online tuning MIMO DNN-PID controller using neural network was performed with respect to two-dimensional ellipsoidal trajectory tracking in cases of Load 0.5 kg and Load kg From these experimental results, the response of the proposed MIMO DNN-PID controller is always in good agreement with that of reference trajectory tracking in comparison with the response of PID controller In summary, novel proposed online tuning gain scheduling MIMO DNN-PID controller using neural network was proposed in this study It has shown that the proposed method had a good control performance for the highly nonlinear system, such as the 2- axes PAM robot arm The controller had an adaptive control capability and the control PID parameters were optimized via the back propagation learning algorithm The controller designed by this method does not need any training procedure in advance, but it uses only the input and output of the plant for the adaptation of proposed control parameters and can tune these parameters online iteratively From the experiments of the position control of the 2axes PAM robot arm, it was verified that the proposed control algorithm presented in this paper was online control with simple structure and had better dynamic property, strong robustness in comparison with the PID controller Likewise, it was suitable for the control of various plants, including linear and nonlinear process Conclusions An online tuning gain scheduling MIMO DNN-PID controller suitable for real-time human-friendly industrial applications has been designed, developed and implemented for position control the joint angle of the experimental 2-axes PAM robot arm in this paper Simulation and experiment results show that the proposed 6560 H.P.H Anh / Expert Systems with Applications 37 (2010) 6547–6560 online tuning gain scheduling MIMO DNN-PID controller is able to learn the nonlinear and dynamic features of the 2-axes PAM robot arm quickly and thus reduce the tracking error to nearly zero in noload operation The performance of the online tuning gain scheduling DNN-PID controller was found to be very good and robust in the presence of external disturbances Besides, with this proposed online tuning gain scheduling MIMO DNN-PID control algorithm, gain scheduling K and PID parameters Kp, Ki and Kd can be modified in real-time and thus actual trajectories can be monitored as well This facilitates testing under different input conditions and ensures future applications of the 2-axes PAM robot arm as an elbow and wrist rehabilitation device for stroke patients It determines confidently that the proposed online tuning MIMO DNN-PID controller not only proves its superb performance in control the highly nonlinear PAM manipulator but also would be very efficient in control of other real-time industrial and human-friendly applications References Ahn, K K., & Anh, H P H (2007) A new approach of modeling and identification of the pneumatic artificial muscle (PAM) manipulator based on neural network Journal of Systems and Control Engineering (IMECHE), 221(18), 1101–1122 Ahn, K K., & Anh, H P H (2009) Identification of the pneumatic artificial muscle manipulators by MGA-based nonlinear NARX fuzzy model IFAC Journal of Mechatronics, 19(1), 106–133 Ahn, K K., Lee, B R., & Yang, S Y (2003) Design and experimental evaluation of a robust force controller for a 6-link electro-hydraulic manipulator via Ha control theory KSME International Journal, 17(7), 999–1010 Ahn, K K., & Thanh, T D C (2006) Intelligent phase plane switching control of pneumatic artificial muscle manipulators with magneto-rheological brake Mechatronics, 16(2), 85–95 Balasubramanian, K., & Rattan, K S (2003a) Fuzzy logic control of a pneumatic muscle system using a 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artificial muscle manipulator using neural network Mechatronics, 16(9), 577–587  ... features of nonlinear 2axes PAM robot arm This online tuning gain scheduling MIMO DNN -PID controller is to increase the accuracy for the two-joint position control of the 2-axes PAM robot arm The. .. In the feedback PID controller system design, the proposed online tuning gain scheduling MIMO DNN -PID of the 2-axes PAM robot arm is updated online to learn as close as possible the dynamic features... presents the block diagram for joint angle position control of the both joints of the 2-axes PAM robot arm using proposed online tuning gain scheduling neural MIMO DNN -PID control scheme The hardware