Modeling, Simulation and Control Issues for a Robot ARM; Education and Research (III).

Transcription

1 I.J. Intelligent Sytem and Application, 2014, 04, Publihed Online March 2014 in MECS ( DOI: /ijia Modeling, Simulation and Control Iue for a Robot ARM; Education and Reearch (III). Farhan A. Salem 1,2 1 Mechatronic ec., Dept. of Mechanical Engineering, College of Engineering, Taif Univerity, 888, Taif, Saudi Arabia; 2 Alpha Center for Engineering Studie and Technology Reearche, Amman, Jordan alem_farh@yahoo.com Abtract Thi paper extend writer' previou work and propoe deign, modeling and control iue of a imple robot arm deign. Mathematical, Simulink model and MATLAB program are developed to return maximum numerical viual and graphical data to elect, deign, control and analyze arm ytem. Teting the propoed model and program for different input value, when different control trategie are applied, how the accuracy and applicability of derived model. The propoed are intended for education and reearch purpoe. Index Term Robot ARM, DC Machine, Modeling/ Simulation I. Introduction The accurate control of motion i a fundamental concern in Mechatronic application, where placing an object in the exact deired location with the exact poible amount of force and torque at the correct exact time i eential for efficient ytem operation [1]. Thi paper extend writer' previou work [1,2], the ultimate goal of thi work addree deign, Modeling, imulation and control iue for robotic arm, Particularly, to deign a robot arm, elect and apply different control trategie, o that an applied input voltage with a range of 0-12 volt correpond linearly to an output arm angle of 0 to 180, The deigned ytem hould repond to the applied input with an overhoot le than 5%, a ettling time le 2 econd and a zero teady tate error, a well a, to implify and accelerate the proce of robot and control deign and analyi, two uggeted MATLAB function block model with it function block parameter for robot arm deign, control election and analyi purpoe to be propoed. Having both electrical and mechanical parameter, a ingle joint robot arm i an application example of a Mechatronic electromechanical ytem ued in indutrial automation. Each degree of freedom (DOF) i a joint on Robot arm, where arm can rotate or tranlate, each DOF require an actuator, A ingle joint Robot arm i a ytem with one DOF that i one actuator, when deigning and building a robot arm it i required to have a few degree of freedom allowed for given application. A hown in Figure1, PMDC motor i, widely, ued a an electric actuator to drive a robot arm horizontally. The motor ytem input ignal ued to provide the control voltage and current to the PMDC motor i a voltage ignal. In part I [1] to implify and accelerate the proce of DC motor izing, election and dynamic analyi for different application, uing different approache, different refined mathematical model in term of output poition, peed, current, acceleration and torque, a well a correponding Simulink model, upporting MATLAB m.file and function block model are introduced for comparion and analyi purpoe were introduced. In part II [2] addree a comprehenive tudy and analyi of mot ued control trategie of a given DC motor for comparion and analyi purpoe, to elect the bet and mot uitable control trategy for pecific motion application, e.g. to control the output angular poition, θ and peed of a given DC motor, ued in Mechatronic motion application. Thee work are intended for reearch purpoe, a well a for the application in educational proce. In [3] to implify and accelerate Mechatronic motion control deign proce including; performance analyi and verification of a given electric DC ytem, proper controller election and verification for deired output peed or angle, a new, imple and uer friendly MATLAB built-in function, mathematical and Simulink model are introduced II. Sytem Modeling, Simulation, Characteritic And Analyi In modeling proce, to implify the analyi and deign procee, linear approximation are ued a long a the reult yield a good approximation to reality [3]. A hown in Figure 1, Single joint robot arm ytem conit of three main part; arm, connected to actuator through gear train with gear ratio, n [4]. Becaue of the eae with which they can be controlled, ytem of DC machine have been frequently ued in many application requiring a wide range of motor peed and a precie output motor control [5-6]. The robot arm ytem to be deigned, ha the following nominal value; arm ma, M= 8 Kg, arm length, L=0.4 m, and vicou damping contant, b = 0.09 N.ec/m. The following nominal value for the variou

2 Modeling, Simulation and Control Iue for a Robot ARM; Education and Reearch (III) 27 parameter of eclectic motor ued: V in =12 Volt; J m =0.02 kg m²; b m =0.03;K t =0.023 N-m/A; K b =0.023 θ(t) θ0 V-/rad; R a =1 Ohm; L a =0.23 Henry; T Load, gear ratio, for implicity,n=1. Pinion N1 N2 Ma pur J2, F2 L Load,( arm), torque,t L Load angular poition, θ 2 Gear M*g Motor angular poition, θ 1 Motor torque,t m θi Z Motor J1, F1 Y X (a) (b) Fig. 1(a)(b): Simplified chematic model of a ingle joint (one DOF) robot arm and DC motor ued to drive arm horizontally Baed on the Newton law combined with the Kirchoff law, the mathematical model of PMDC motor in the form of differential equation or tate pace equation, decribing electric and mechanical characteritic of the motor can be derived. In [2-4], baed on different approache, detailed derivation of different refined mathematical model of PMDC motor (e.g. Eq (1-2)) and correponding Simulink model are introduced, a well a an function block with it function block parameter window for open loop DC ytem motor election, verification and performance analyi. Any of thoe propoed model (e.g. Figure 2(a)(b)) can be ued to analyze the performance of open loop robot arm ytem and obtaining angular/linear poition/time, angular/linear peed/time, angular/linear Acceleration/time, Current/time and Torque/time repone curve for tep input voltage, defining deired robot arm ytem parameter and running thi model will reult in repone curve hown in Figure 3.

3 28 Modeling, Simulation and Control Iue for a Robot ARM; Education and Reearch (III) The PMDC motor open loop tranfer function without any load attached relating the input voltage, V in (), to the motor haft output angle, θ m (), and given by: G angle () Kt () V () 3 2 in La Jm ( Ra Jm bm La ( Rabm KtKb) (1) The PMDC motor open loop tranfer function relating the input voltage, V in (), to the motor haft output angular velocity, ω m (), given by: G peed ( ) K t ( ) V ( ) 2 in LaJ m ( RaJ m bm La ) ( Rabm K t K b ) (2) Fig. 2(a) PMDC motor Simulink model baed on Eq. (1) and (2) Fig. 2 (b)

4 Modeling, Simulation and Control Iue for a Robot ARM; Education and Reearch (III) 29 Fig. 2 (c) Fig. 2(b)(c): Subytem and function block model with it function block parameter window for DC motor performance verification and analyi [2] To model, Simulate and analyze the open loop Robot arm ytem,conidering that the end-effector i a part of robot arm, The total equivalent inertia, J equiv and total equivalent damping, b equiv at the armature of the motor are given by: 2 2 N 1 N 1 bequiv bm bload Jequiv J m J Load N 2 N 2 (3) The geometry of the mechanical part determine the moment of inertia and damping,to compute the total inertia, J equiv, we firt conider robot arm a thin rod of ma m, length l, (o that m = ρ*l*), thi rod i rotating around the axi which pae through it center and i perpendicular to the rod. The moment of inertia of the robot arm can be found by computing the following integral: l/2 3 2 x l/2 l/2 x dx 3 l/2 3 m l / ml l 3 12 Calculating and ubtituting value in (14) give: 2 J Load = (8*(0.4) ^2)/12 = kg.m 2 Subtituting, we obtain, J equiv,to be : J equiv = J m + J load * (1/1) J equiv = = kg m² Obtaining the total damping, b total, give: b equiv = b m + b load (1/1) b equiv = = 0.12 N.ec/m In order to obtain total ytem tranfer function, relating input voltage V in and Arm-Load output angular poition θ Load, We Subtitute value into tranfer function given by (12) with gear ratio, n, give:

5 30 Modeling, Simulation and Control Iue for a Robot ARM; Education and Reearch (III) G G G arm _ angle _ open Load ( ) K t * n ( ) V ( ) 3 2 in LaJequiv ( RaJequiv bequiv La ( Rabequiv K t K b ) Load arm _ angle _ open 3 2 Vin ( ) arm _ angle _ open ( ) ( ) Load ( ) ( ) V ( ) in (4) Defining the given DC motor' nominal value, gear ratio and arm parameter, and running any of both model,we can analyze the performance of open loop Robot arm ytem and obtaining the repone curve for tep input voltage (0-12 volt), in term of output Poition/time, peed/time, Acceleration / time, Current/time and Torque/time, hown in Figure 3. Fig. 3: Open loop DC motor ytem; Angular Poition/time, Angular peed/time, Angular Acceleration / time, Current/time and Torque/time repone curve for 12 V input III. Control Sytem Selection, Deign and Analyi A negative cloed loop feedback control ytem with forward controller and correponding Simulink model hown in Figure.4(a)(b) are to be ued [3]. Our deign goal i to deign, model, imulate and analyze a control ytem o that a voltage input in the range of 0 to 12 volt correpond linearly of an Robot arm output angle range of 0 to 180, that i to move the robot arm to the deired output angular poition, θ L, correponding to the applied input voltage, V in, with overhoot le than 5%, a ettling time le than 2 econd and zero teady tate error. The error ignal, e i the difference between the actual output robot arm poition, θ L, and deired output robot arm poition. E= Vin- Vp Input voltage, + Vin - DC motor open loop ytem Output θ 1 Gear ratio, n Output θ 2 Robot arm Robot arm actual output angle, θ Vp = θa * Kp Potentiometer Fig. 4(a) Angle or Speed reference (deired) + - Error, Volt Controller (angle, peed) Control voltage, Vc Motor haft ω or θ Volt Senor Angle or Speed meaure e,.g Potentiometer, Tachometer Fig. 4(b) Fig. 4(a)(b): Two Block diagram repreentation of PMDC motor control [3]

6 Modeling, Simulation and Control Iue for a Robot ARM; Education and Reearch (III) 31 Fig. 4 (c): Preliminary Simulink model for negative feedback with forward compenation [3] 3.1 Senor Modeling To calculate the error, we need to convert the actual output robot arm poition, into voltage, V, then compare thi voltage with the input voltage V in, the difference i the error ignal in volt. Potentiometer i a popular enor ued to meaure the actual output robot (arm) poition, θ L,convert into correponding volt, V p and then feeding back thi value, the Potentiometer output i proportional to the actual robot arm poition, θ L, thi can be accomplihed a follow: The output voltage of potentiometer i given by (5), in thi equation: θ L :The actual robot arm poition. K pot the potentiometer contant; It i equal to the ratio of the voltage change to the correponding angle change, and given by Eq(5). Depending on maximum deired output arm angle, the potentiometer can be choen, for our cae V in = 0:12, and output angle = 0:180 degree, ubtituting, we have: V K * K p L pot pot (Voltage change)? (Degree change) V / degree The value (0.0667), mean that each one input volt correpond to 180/12= 15 output angle in radian, to obtain a deired output angular poition of 180, we need to apply 12 volt, to obtain an angular poition of 90 we need to apply ( 90*0.0667= Volt). 3.2 Control Strategy Selection and Deign Running the Simulink model of the robot arm cloed loop ytem without controller attached (K=1) hown in Figure 5(a), a well a the below MATLAB m.code, will return tep repone hown in Figure 5(b), the repone curve how that the arm ytem repond with a very huge value of ettling time,(approximately T S =500 econd) to reach teady tate output angle of 180 degree, that i not correponding to the required (5) deign pecification. A controller i to be deigned to meet deired pecification. In [3] different control trategie where applied to PMDC and it i found that, there are many motor control trategie that may be more or le appropriate to a pecific type of application each ha it advantage and diadvantage. The deigner mut elect the bet one for pecific application, where when applying lag-controller to PMDC ytem, the ytem tability i increaed, the ettling time, T i reduced and teady tate error i reduced, o called PD controller with deadbeat repone, enable deigner to atify mot required deign pecification moothly and within a deired period of time and can be applied to meet the deired pecification., applying internal model controller reult in improving ytem' both dynamic and teady tate performance, reducing overhoot, rie time and ettling time a well a diturbance rejection, when applying PID controller to PMDC ytem, the ytem tability i increaed, the ettling time T i decreaed and teady tate error i almot eliminated, and o on. By proper election the of the three PID gain, different characteritic of the motor repone are controlled. To achieve a fat repone to a tep command with minimal overhoot and zero teady tate error. We will, eparately, apply thee control trategie to our Robot arm ytem, and later to implify and accelerate the whole proce of robot arm ytem deign in term of deigning the mechanical arm and gear part a well a election and deigning the mot uitable control trategy, a general model in the form of function block with it function block parameter will be built. >> Vin=12; Jm=0.02 ; Jm=0.1267;bm =0.12 ;Kt =0.023 ; Kb =0.023 ; Ra =1 ; La=0.23 ; TL = 0 ;Tl = TL ;n=1; M=8;deired_max_angle=180; Arm_Length =0.4 ;b_arm= 0.09; Kpot =Vin/deired_max_angle; ; J_equiv= Jm+((M* Arm_Length ^2)/12)*(1/n)^2; b_equiv= bm + b_arm*(1/n)^2; num_arm_open = [Kt*n];%[Kt*n*(180/pi)] den_arm_open=[la* J_equiv (Ra* J_equiv + La* b_equiv) (Ra* b_equiv + Kt*Kb) 0]; dip(' Robot arm open loop tranfer function, (Arm angle)/volt')

7 32 Modeling, Simulation and Control Iue for a Robot ARM; Education and Reearch (III) Ga_arm_open=tf(num_arm_open,den_arm_open) Ga_arm_cloed=feedback(Ga_arm_open, Kpot/n), tep(12* Ga_arm_cloed) Fig. 5(a): Simulink model of cloed loop robot arm, with K=1 KI GPID () KP KD 2 KD KP KI 2 KP K KD KD K I D (6) The Simulink model of cloed loop robot arm, with DC motor, a ubytem and PID controller applied, i hown in Figure 6 (a). The repone of thi model i hown in Figure.6 (b). With optimal et of PID controller gain; K P, K I, K D, repone curve till how the exitence of teady tate error (e =0.0062) and overhoot of 0.024%. It i noted that the current can be controlled by adding and adjuting aturation block. The following MATLAB code can alo be ued to obtain tep repone Fig. 5(b(: Cloed loop robot arm ytem tep repone Angular Poition/time, Angular peed/time, Angular Acceleration / time, Current/time and Torque/time curve for 12 V input >> Kp= ; Ki = ; Kd= num_pid= [ Kd Kp Ki] ; den_pid= [1 0]; G_PID= tf(num_pid, den_pid) G_forward= erie(g_pid, Ga_arm_open); G_cloe_arm_PID = feedback(g_forward, Kpot/n) tep(v*g_cloe_arm_pid) axi([ ]) Controller Deign Uing PID Strategy: PID controller are commonly ued to regulate the time-domain behavior of many different type of dynamic plant [6]. The tranfer function of PID control i given by:

8 Modeling, Simulation and Control Iue for a Robot ARM; Education and Re earch (III) 33 Fig. 6 (a) Simulink model with PMDC mot or ubytem and PID controller G Lead () K K P K P K P P D P P KPP KP KDP KDP P Fig. 6(a): Step repone of cloed loop robot arm, with DC motor, a ubytem and PID controller 3.3 Controller Deign Uing Lead and Lag Compenator Lead compenator i a oft approximation of PDcontroller, The PD controller, given by G PD () = K P + K D, i not phyically implementable, ince it i not proper, and it would differentiate high frequency noie, thereby producing large wing in output. to avoid thi, PD-controller i approximated to lead controller of the following form [13]: G ( P PD ) G Lead ( ) K K P D P The larger the value of P, the better the lead controller approximate PD control, rearranging give: P GLead () KP KD P KP P KDP P Now, let KC K P K DP and KPP Z, K P K DP we obtain the following approximated controller tranfer function of PD controller, and called lead compenator: Z G ( ) K C P If Z < P thi controller i called a lead controller (or lead compenator). If Z > P : thi controller i called a lag controller (or lag compenator).the tranfer function of lead compenator i given by: Zo Glead () Kc ( P ) O Where : P Z, (7) The Lag compenator i a oft approximation of PI controller, it i ued to improve the teady tate repone, particularly, to reduce teady tate error of the ytem, the reduction in the teady tate error accomplihed by adding equal number of pole and zeroe to a ytem. KI GPI ( ) Glag ( ) KP KP KI K I KP K P (8)

9 34 Modeling, Simulation and Control Iue for a Robot ARM; Education and Reearch (III) Since PI controller by it elf i untable, we approximate the PI controller by introducing value of P o that i not zero but near zero; the maller we make P o, the better thi controller approximate the PI controller, and the approximation of PI controller will have the form: Zo Glag ( ) K c ( P ) O (9) Where: Z o > P o, and Z o mall number near zero and Z o =K I /K P, the lag compenator zero. P o : mall number,the maller we make P o, the better thi controller approximate the PI controller. The Simulink model of both Lead and Lag compenator i hown in Figure.7 (a). The tep repone are hown in Figure.7(b). Fig. 7 (a): Simulink model of both Lead and Lag compenator trategy, Two model in the form of function block with it function block parameter will be built, firt imple uing only PID controller and a econd general model with mot control trategie applied to Robot arm deign and control PID Controller Function Block for Robot ARM Deign and Analyi Fig. 7 (b): Poition tep repone applying eparately lead and lag compenator, tep 12 volt, output 180 degree 3.4 Function Block for Sytem Deign and Analyi To implify and accelerate the whole proce of Mechatronic robot arm ytem deign in term of deigning mechanical part; arm and gear, a well a election and deigning the mot uitable control A uggeted Function Block model for robot arm deign, controller election, deign and robot ytem analyi i hown in Figure.8 (b), the function block ubytem i hown in Figure.8 (a). thi model allow deigner to apply Simulink PID controller block and it ubytem (P, PI, PD and PID) tuning capabilitie and feature to elect controller and analyze reulting robot arm repone, by defining parameter of Robot arm ubytem (Arm, gear, and DC motor) electing controller (PID), and running model, will reult in peed/time and poition/time curve hown in Figure.8(c). By changing the potentiometer contant, K pot, the output angle range will change, Running thi function block for the given robot arm, for an applied voltage of 0 to 12 volt and with K pot = will correpond

10 Modeling, Simulation and Control Iue for a Robot ARM; Education and Reearch (III) 35 linearly to an output arm angle of 0 to 90, peed/time and poition/time curve are hown in Figure.9(a), where Running thi function block, for an applied voltage of 0 to 12 volt and with K pot = will correpond linearly to an output arm angle of 0 to 45 degree, a 45 degree poition tep repone i hown in Figure.9(b) Fig. 8 (a) Robot arm function block ubytem, uing only PID Controller Fig. 8 (b) Function Block uing PID for robot arm analyi and deign

11 36 Modeling, Simulation and Control Iue for a Robot ARM; Education and Reearch (III) A Propoed Function Block with It Function Window Parameter, For Robot Arm Deign, Controller Selection, Deign and Verification Fig. 8 (c) Speed/time and poition/time repone of function block uing PID controller, K pot =0.066, and Arm angular poition θ = 180 Fig. 9(a) Speed/time and poition/time repone of function block uing PID controller, K pot , output angular poition of θ = 180. The uggeted general function block i hown in Figure 10(b) baed and ubytem in Figure 10(a), thi model include mot control trategie applied to Robot arm deign and control election,thi model allow deigner to define robot arm ubytem parameter, e.g. arm length, weight, gear ratio, damping factor, a well a to define electric motor parameter, e.g. V in =12;J m =0.02. after defining all parameter, model allow uing manual witch, elect any control trategy, finally run the model and analyze repone curve of a given robot arm ytem. the control trategie included in thi model are, P, PI, PD, PID included in PID Simulink block, lead, lag compenator, PD with deadbeat, lead-integral controller, model will return all the following repone curve for any input from zero to 12 volt, Angular Poition/time, Angular peed/time, Angular Acceleration / time, Current/time and Torque/time curve for 12 V input, thi model, alo, allow deigner to ue Simulink tuning capabilitie of PID controller and it feature. Switching model to PID controller, running imulation, will reult in Arm poition/time repone curve hown in Figure.10 (c). Thi model can be modified to include other control trategie. Fig. 9(b) Output Speed/time and poition/time, (θ = 45), K pot = Fig. 10 (a) Robot arm function block ubytem

12 Modeling, Simulation and Control Iue for a Robot ARM; Education and Reearch (III) 37 Fig. 10 (b) Function block with it function block parameter window for robot arm deign, controller election, deign and verifi cation V_max = input(' Enter maximum allowed voltage, V max :'); Angle_max = input( ' Enter maximum allowed angle for robot arm : '); Fig. 10 (c) Arm poition/time repone of function block 3.5 A Propoed m.file for Robot ARM Reearch and Education The following m.file can be ued to return tranfer function, open loop and cloed loop, with and without applying controller a well a correponding repone and performance pecification. clc, clear all, cloe all Jm = input(' Enter Motor armature moment of inertia (Jm) :'); bm = input(' Enter damping contant of the the motor ytem (bm):'); Kb = input(' Enter ElectroMotive Force contant (Kb):'); Kt = input(' Enter Torque contant (Kt):'); Ra = input(' Enter electric reitance of the motor armature (ohm), (Ra):'); La =input(' Enter electric inductance of the motor armature,henry,(la) :'); V = input(' Enter applied input voltage Vin :'); M= input(' Enter robot arm ma, M='); Length = input(' Enter robot arm Length, L='); b_arm= input(' Enter damping factor of robot arm, b_arm ='); n= input( 'Enter gear ratio n = '); %obtaining open loop tranfer function of DC motor ytem and tep repone num1 = [1]; den1= [La,Ra]; num2 = [1]; den2= [Jm,bm]; A = conv( [La,Ra], [Jm,bm]); TF1 =tf(kt*n, A); dip('dc motor open loop tranfer function, Speed/Volt: ') Gv= feedback(tf1,kt) dip(' DC motor open loop tranfer function, Angle/Volt: ') Ga=tf(1,[1,0] )*Gv ubplot(4,2,1), tep (V*Ga); title(' Poition tep repone of open loop DC motor ytem') ubplot(4,2,2) tep (V*Gv) title(' velocity tep repone of open loop DC motor ytem') %{ or baed on open loop tranfer function,the following code can be ued num = [Kt*n];

13 38 Modeling, Simulation and Control Iue for a Robot ARM; Education and Reearch (III) den=[la*ja (Ra*Ja+Lm*bm) (Ra*bm+Kt*Kb) 0] dip(' Robot arm open loop tranfer function, Angle/Volt: ') Ga =tf(num,den) tep (V*Ga) %} % obtaining open loop tranfer function of robot arm ytem and tep repone J=((M* Length^2)/12)+Jm; b= bm + b_arm; num_arm_open = [Kt*n*(180/pi)]; den_arm_open=[la*j (Ra*J+La*b) (Ra*bm+Kt*Kb) 0]; dip(' Robot arm open loop tranfer function, (Arm angle)/volt') Ga_arm_open=tf(num_arm_open,den_arm_open) ubplot(4,2,3) tep(v*ga_arm_open); title(' Poition tep repone,open loop arm ytem') ubplot(4,2,4) comet(tep(v,ga_arm_open)) title(' Poition tep repone') % Obtaining cloed loop tranfer function of robot arm ytem and tep repone Kpot=V_max /Angle_max; % potentiometer G_cloe_arm= feedback(ga_arm_open,(kpot/n)) ubplot(4,2,5), tep(v*g_cloe_arm); title(' cloed loop poition tep repone') ubplot(4,2,6) comet(tep(v*g_cloe_arm)) title(' Robot arm Poition tep repone') xlabel(' ') % Controller Deign : PID Controller Kpro=input(' Enter Proportional gain Kp :'); Ki=input(' Enter Integral gain Ki :'); Kd=input(' Enter derivative gain Kd :'); num_pid=[kd Kpro Ki] ; den_pid=[ 0 1 0]; dip(' PID tranfer function') G_PID=tf(num_PID,den_PID); G_forward= erie(g_pid, Ga_arm_open); dip(' TF of Robot arm with PID controller, (Arm angle)/volt') G_cloe_arm_PID = feedback(g_forward, Kpot/n) % tep(v*g_cloe_arm_pid) ubplot(4,2,7) tep(g_cloe_arm_pid) IV. Concluion To implify and accelerate the proce of robot arm ytem deign in term of motor ubytem izing, deigning the mechanical ubytem, a well a election and deign of the mot appropriate control trategy to achieve deired performance, two Simulink model firt for open loop DC ytem motor election and performance analyi and econd for overall arm ytem performance analyi are propoed and teted. Introduced model can be ued to elect and analyze the performance of open and cloed loop ytem and obtaining the Angular Poition/time, Angular peed/time, Angular Acceleration / time, Current/time and Torque/time repone curve for given input voltage; finally for reearch and education purpoe, a MATLAB m.file i written, to return tranfer function, open loop and cloed loop, with and without applying controller, a well a correponding repone and performance pecification. Analyzing obtained repone curve for different input voltage value, when different control trategie i applied, how the accuracy and applicability of derived model for reearch purpoe in election, performance analyi and control of mechatronic ytem requiring output poition control. Reference [1] Chun Htoo Aung, Khin Thandar Lwin, and Yin Mon Myint, Modeling Motion Control Sytem for Motorized Robot arm uing MATLAB, World Academy of Science, Engineering and Technology [2] Ahmad A. Mahfouz,Mohammed M. K., Farhan A. Salem, Modeling, Simulation and Dynamic Analyi Iue of Electric Motor, for Mechatronic Application, Uing Different Approache and Verification by MATLAB/Simulink (I). IJISA Vol. 5, No. 5, April [3] Norman S. Nie, Control ytem engineering, ixth edition, John Wiley & Son, Inc, [4] Farhan A. Salem, Modeling controller election and deign of electric DC motor for Mechatronic application, uing different control trategie and verification uing MATLAB/Simulink, Submitted to European Scientific Journal, 2013 [5] M.P.Kazmierkowki, H.Tunia "Automatic Control of Converter-Fed Drive", Warzawa [6] R.D. Doncker, D.W.J. Pulle, and A. Veltman. Advanced Electri-cal Drive: Analyi, Modeling, Control. Springer, [7] Grzegorz SIEKLUCKI,Analyi of the Tranfer- Function Model of Electric Drive with Controlled Voltage Source PRZEGL AD ELEKTROTECHNICZNY (Electrical Review), ISSN , R.88NR7a/2012. [8] An educational MATLAB m.file applied to PMDC motor controller deign comparion, election and analyi Ahmad A. Mahfouz, Farhan A. Salem [9] B. Shah, Field Oriented Control of Step Motor, MSc. Thei, SVMITB haruch, India, Dec

14 Modeling, Simulation and Control Iue for a Robot ARM; Education and Reearch (III) 39 [10] Jamal A. Mohammed, Modeling, Analyi and Speed Control Deign Method of a DC Motor Eng. & Tech. Journal, Vol. 29, No. 1, 2011 [11] R.C. Dorf and R.H. Bihop, Modern Control Sytem,10th Edition, Prentice Hall, 2008 How to cite thi paper: Farhan A. Salem,"Modeling, Simulation and Control Iue for a Robot ARM; Education and Reearch (III)", International Journal of Intelligent Sytem and Application(IJISA), vol.6, no.4, pp.26-39, DOI: /ijia Appendix: Table 1 Nomenclature Symbol Quantity Unit V, or V in The applied input voltage Volte, V R a Armature reitance, ( terminal reitance) Ohm,Ω R f Stator reitance Ohm,Ω i a Armature current Ampere, A K t Motor torque contant N.m/A K e Motor back-electromotive force cont. V/(rad/) ω m Motor haft angular velocity rad/ T m Torque produced by the motor N.m J m Motor armature moment of inertia kg.m 2 J total Total inertia=jm+jload kg.m 2 L a Armature inductance Henry, H b m e a,emf: Vicou damping, friction coefficient The back electromotive force, EMF =K bdθ/dt N.m/rad. e a,emf: θ m Motor haft output angular poition radian ω m Motor haft output angular peed rad/ec V R = R*i The voltage acro the reitor Voltage V L=Ldi/dt The voltage acro the inductor Voltage T load Torque of the mechanical load T load T α T ω T EMF Torque du to rotational acceleration Torque du to rotational velocity The electromagnetic torque. Author' Profile Farhan A. Salem: B.Sc., M.Sc and Ph.D., in Mechatronic of production ytem, Now he i with Taif Univerity, Mechatronic program, Dept. of Mechanical Engineering and gen. director of alpha center for engineering tudie and technology reearche.