MECHATRONIC MODEL FOR THE DYNAMIC ANALYSIS OF A ROBOTIC SYSTEM

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1 Bulletn of the Translvana Unversty of Braşov Seres I: Engneerng Scences Vol. 6 (55) No MECHATRONIC MODEL FOR THE DYNAMIC ANALYSIS OF A ROBOTIC SYSTEM Monca ENESCU 1 Abstract: The present paper dscusses the co-smulaton methodology for a robotc system, whch s used n the spray pyrolyss process on a planar surface. Robot bodes, jonts and rotors are modelled as a rgd mult-body system. The MBS software envronment ADAMS was used to develop the dynamc model of a robotc system, whle the control system model s developed n MATLAB/Smulnk. The purpose s to verfy the mode n whch the control system (of the DC motors) s able to descrbe the trajectores of the end-effector, whch are prevously used to obtan the moton laws n the motor jonts (through the nverse knematc analyss as mult-body system). Key words: co-smulaton, spray pyrolyss, robotc system, dynamc model. 1. Introducton Today, sprayng s used for depostng coatngs onto varous artcles. Spray pyrolyss deposton s an aerosol process used to form a varety of materals n powder from ncludng ceramcs, superconductors and nanostructured materals. The spray pyrolyss s defned as a deposton technque whereby heat s used to break molecules nto elemental sources that are then spray deposted on a substrate. Spray Pyrolyss Deposton (SPD) s conssts of four man steps: 1) generaton of spray fro a precursor by a droplet generator, 2) spray transport by an ar flow durng whch solvent evaporaton occurs, 3) thermolyss of the precptated partcles at hgher temperatures to form nano partcles, 4) extracton of the partcles from the gas flow [5]. The advantages of the SPD technque are offer a better unformty n chemcal composton, a better regularty n shape, a lower cost for the preparaton of thn flms wth a larger area [7]. Robots are used for sprayng applcaton because of the repeatablty of the resultng surface fnshng, nclusve the beneft of removng humans from a hazardous envronment. Ther applcaton gves a better qualty of deposted surfaces due to the property of accurate control of robot [9]. The nozzle drecton generaton method s smlar to the generaton of the normal of a plane and the nozzle drecton s the opposte drecton of the normal of the plane. The nozzle velocty s determned by optmzng the sprayng process of a plane surface. The nozzle velocty can be calculated as a functon of the overlap dstance for a thckness. The relevance of ths paper s represented by the mportance for the feld of thn flm. Ths paper s structured as follows: Secton 1 Renewable Energy Systems and Recyclng Center, Translvana Unversty of Braşov.

2 16 Bulletn of the Translvana Unversty of Braşov Seres I Vol. 6 (55) No presents the ADAMS model, Secton 3 contans the MATLAB/Smulnk control scheme of the robotc system, Secton 4 presents some smulaton results and fnally, Secton 5 contans concludng remarks. 2. Dynamc Model of the Robotc System The robots are complex electromechancal systems, where varous electrc drves are used to control the movement of the artculated structures. For the model t was used jonts (brushless DC motors) connected to the robot structure by speed reducer. The whole electrcal part of the motor s represented n Fgure 1 by the block controller - motor. Fg. 1. The control system of a robotc system Blocks gearboxes contan mechancal part of motors and of ther speed reducers. The torque n the ar gap drves rotor to the motor. Robot bodes, jonts and rotors are modelled as a rgd mult-body system. The ADAMS software was used to develop the dynamc model of a robotc system. Ths model was then suppled under MATLAB/Smulnk envronment to be analyzed. The model s used n the control scheme to predct the behavor of the system usng a PD (Proportonal Dervatve) controller for poston. ADAMS and MATLAB/Smulnk were nterfaced to beneft a powerful tool to model the dynamc behavor of robotc system [4]. The need of a better desgn of the system lke n robotcs has led to the development of methods for the dynamc analyss as mult-body systems (MBS), whch facltate the self-formulatng algorthms. In ths approach, complex vrtual prototypes can be developed, whch exactly replcate the structure and the operatng condtons of the real physcal products. Vrtual prototypng, a new way of defnng dynamc smulatons s more complant wth tme and budget constrants [6]. Mostly, a vrtual prototypng platform ntegrates the followng software solutons [1-3]: CAD (Computer Aded Desgn), MBS (Mult-Body Systems), FEA (Fnte Element Analyss) and DFC (Desgn for Control). The CAD model mprove the model accuracy by the automatc calculaton of the nerta propertes of the all the parts of the robot. The CAD software s needed for creatng the geometrcal model (sold model) of the system. Ths model contans nformaton about the mass and nerta propertes of the rgd parts. In modelng usng CATIA, CAD software, robot model s dvded nto 11 parts. To mport the desgner model to ADAMS, the frst step s to save each of the parts of the robot n stp format, snce ths format s recognzed n ADAMS. The next step s to mport the model nto ADAMS. After transferrng model, nertal parameters of the parts are recorded n software database. The ADAMS software presents an alternatve to derve numercally the dynamc model for system. In Table 1 s shown the geometrc and dynamc characterstcs of the robotc system. A desgn s modeled under ADAMS (Fgure 2), and the dynamc model s determned n order to nvestgate the dynamc behavor.

Enescu, M.: Mechatronc Model for the Dynamc Analyss of a Robotc System 17 Inerta parameters of the system Table 1 Parameter Mass [kg] Moment of nerta [Kg.m 2 ] Lnk 1 m 1 = 93.8 I xx = 5.

95 10 6 I yy = 1.95 10 6 I zz = 4.2 10 4 Lnk 5 m 5 = 0.3 I xx = 184.9 I yy = 116.03 I zz = 107.7 Lnk 6 m 6 = 0.12 I xx = 112.8 I yy = 112.5 I zz = 15.

The dynamc model generated by ADAMS/Controls Once the model s fnalzed, the dynamc model s generated by ADAMS/Controls and exported under the MATLAB/ Smulnk.

3 Enescu, M.: Mechatronc Model for the Dynamc Analyss of a Robotc System 17 Inerta parameters of the system Table 1 Parameter Mass [kg] Moment of nerta [Kg.m 2 ] Lnk 1 m 1 = 93.8 I xx = I yy = I zz = Lnk 2 m 2 = 35.4 I xx = I yy = I zz = Lnk 3 m 3 = 14.6 I xx = I yy = I zz = Lnk 4 m 4 = 20 I xx = I yy = I zz = Lnk 5 m 5 = 0.3 I xx = I yy = I zz = Lnk 6 m 6 = 0.12 I xx = I yy = I zz = 15.8 a connecton so that any change n one of the programs affects the other one [8]. Fg. 3. The dynamc model generated by ADAMS/Controls Once the model s fnalzed, the dynamc model s generated by ADAMS/Controls and exported under the MATLAB/ Smulnk. The block adams_sub (Fgure 4) s the fle exported from ADAMS whch s contanng the dynamc model wth all the smulaton parameters. Fg. 2. ADAMS model of the robotc system In ths study t was been used a system wth sx nputs (control torques), respectvely twelve outputs (the angle and angular velocty) (see Fgure 3), where w s the velocty, Tetha represent the angular poston and T s the torque, for = 1 6. The objectve of co-smulaton s to make Fg. 4. Archtecture of the Adams_sub block The blocks: ADAMS_uout, ADAMS_yout and ADAMS_tout are the nput and output varables, respectvely the smulaton tme. ADAMS Plant s the dynamc model of the robotc system.

4 18 Bulletn of the Translvana Unversty of Braşov Seres I Vol. 6 (55) No By havng Adams_sub block n MATLAB/Smulnk, the robot model s sutable for control and moton smulaton as a defned system n MATLAB. The man objectve of the research s to generate varous paths on the planar and curved surfaces (for ths paper, we have consdered a planar trajectory). Wth other words, we ntend to verfy the mode n whch the control system (of the DC motors) s able to descrbe the trajectores of the end-effector, whch are prevously used to obtan the moton laws n the motor jonts (through the nverse knematc analyss as mult-body system). 3. The Control Scheme The robots are complex electrcal and mechancal systems wth electrc drves whch are used to control the movement of the artculated structures. For ths study, the electrc drves were facltated by the Electrc Drves lbrary n MATLAB/ Smulnk. Ths module can be used to model the motor drve, the speed reducer, the mechancal model of the arm and the controller. For each motor drve, a proportonal-dervatve (PD) controller s used. The control scheme used n ths paper s present n Fgure 5. The advantage of the PD controller s that ths does not requre a deep knowledge of the dynamc model of the robotc system. In ths paper, we wll be nterested n the PD controller. The PD control algorthm s gven by: ( t) K e( t) K e ( t), (1) P D where τ(t) s the drvng torque generated by the controller, K P, K D are the proportonal and dervatve gans, respectvely, e(t) s the poston error and e (t) s the velocty error, they are calculated by: e( t) xd x( t); e ( t) x ( t) (2) where x d s the desred poston and x(t) s the actual poston. The control system used n ths study s the type of control loops desgned usng Smulnk blocks for each of the sx control postons. The robot s axes are drven by DC motor that are modeled by permanent magnet synchronous motors. The speed reducers and the gearbox are needed to transmt torque from the motors to the jonts. The motor s fed by a three phase nverter operatng n current controlled mode. The block model of the poston controller s shown n Fgure 6, wth the followng notatons: teta_ref - the desred reference angle, teta - the current jont angle, w - the correspondng rotatonal velocty, Kp - proportonal gan, Kd - dervatve gan, Nref - the reference rotor speed. The Saturaton block mposes upper and lower bounds on the sgnal. Fg. 5. The control scheme of the robotc system Fg. 6. The PD scheme of the poston controller

composed of three terms: T d 2 J 2 dt d C dt G, (3) where θ s jont poston, J s nerta, C s centrfugal and Corols coeffcent, G s gravtatonal coeffcent.

In the smulaton, the nputs were requred to move the end-effector (nozzle) from ts orgnal poston to the new poston followng the descrbed path.

5 Enescu, M.: Mechatronc Model for the Dynamc Analyss of a Robotc System 19 For each of the sx jonts, we have consdered the effect of the other lnks as a sngle load, reflectng to the jont a torque that s composed of three terms: T d 2 J 2 dt d C dt G, (3) where θ s jont poston, J s nerta, C s centrfugal and Corols coeffcent, G s gravtatonal coeffcent. In ths analyss, the parameters J, C, G are functons of jont postons. a) 4. Smulaton and Results The robotc system s a robot wth sx degrees of freedom and has the parameters gven n Table 1. In the smulaton, the nputs were requred to move the end-effector (nozzle) from ts orgnal poston to the new poston followng the descrbed path. The smulaton s performed usng a tme step of 45 seconds, and the responses of the smulaton for sx axes are shown on one scope connected to the output varables of the robot blocks. In the smulaton the both of software are workng n the same tme, ths fact leads to the possblty to obtan results n the both software. In ths study the results (the angular velocty varaton dependng on tme, the angular dsplacement dependng on tme) are obtan wth MATLAB/Smulnk and ADAMS software. In Fgures 7 and 8 are shown the dagrams were obtaned by co-smulate released for the mechancal structure developed n MBS concept n ADAMS and the control system released n MALTAB/Smulnk for the planar trajectory, the smulaton was performed for 45 seconds. In Fgure 7 (a - result from MATLAB, b - result from ADAMS) are represented n the graphc mode the velocty of the frst jont n the analyzed robotc system. b) Fg. 7. The angular veloctes of the system In Fgure 8 (a - result from MATLAB, b - result from ADAMS), there are generated the poston dagrams for the frst jont of the robot wth sx degrees of freedom. a) b) Fg. 8. The angular poston of the system

6 20 Bulletn of the Translvana Unversty of Braşov Seres I Vol. 6 (55) No Conclusons In ths paper, we developed the vrtual prototypng of the robotc system. The robotc system was desgned under ADAMS envronment then ts dynamc model was exported to MATLAB/Smulnk for the cosmulaton. The MBS model of the robotc system (shown n Fgure 2) was ntegrated n the control system model (Fgure 5). The mechancal model and the control system were been co-smulated (tested together). Dfferent sets of dynamc parameters can be selected accordng to purpose wthout changng the model. The physcal robot exsts wthn the Department of Renewable Energy Systems and Recyclng, and the moton laws n jonts (obtaned by smulatng the vrtual prototype) wll be mplemented on the physcal robot for generatng the desred trajectory. Varous trajectores wll be tested to obtan a better unformty of the flm by dfferent overlappng sprayng cones, n order to acheve the desred deposted surface. References 1. Alexandru, C., Comşţ, M.: The Energy Balance of the Photovoltac Trackng Systems usng Vrtual Prototypng Platform. In: Proceedngs of the 5 th Internatonal Conference on the European Electrcty Market - EEM, Lsbon, 2008, p Alexandru, C., Pozna, C.: Vrtual Prototype of a Dual-Axs Trackng System used for Photovoltac Panels. In: Proceedngs of the 2008 IEEE Internatonal Symposum on Industral Electroncs - ISIE, Cambrdge, 2008, p Alexandru, C.: Software Platform for Analyzng and Optmzng the Mechancal Systems. In: Proceedngs of the 10 th IFToMM Internatonal Symposum on Scence of Mechansms and Machnes - SYROM, Braşov, 2009, p Cheraghpour, F., Vaez, M., et al.: Dynamc Modelng and Knematc Smulaton of StäublTX40 Robot usng MATLAB/ADAMS Co-Smulaton. In: IEEE Internatonal Conference on Mechatroncs - ICM, 2011, p Eneşca, A., Duţă, A.: The Influence of Organc Addtves on the Morphologc and Crystallne Propertes of SnO2 Obtaned by Spray Pyrolyss Deposton. In: Thn Sold Flms 519 (2011), p Ferrett, G., Magnan, G., et al.: Vrtual Prototypng of Mechatronc Systems. In: Annual Revews n Control 28 (2004), p Iene, E., Isac, L., et al.: Characterzaton of Al/Al (2) O (3) /NO (x) Solar Absorber Obtaned by Spray Pyrolyss. In: Sold State Scences 12 (11) (2010), p Lăpuşan, C., Măteş, V., et al.: Modelng and Smulaton Methods for Desgnng Mechatronc Systems. In: Journal of Engneerng Studes and Research 16 (4) (2010), p Potkonjak, V., Dordevc, D.G.S., et al.: Dynamcs of Anthropomorphc Pantng Robot: Qualty Analyss and Cost Reducton Ion. In: Robotcs and Autonomous Systems 32 (1) (2000), p

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