8th WSEAS Int. Conf. on ROBOTICS, CONTROL and MANUFACTURING TECHNOLOGY (ROCOM '08), Hangzhou, China, April 6-8, 2008

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1 th WSEAS Int. Conf. on OBOTICS, CONTO and MANUFACTUING TECHNOOGY (OCOM '), Hanghou, China, April -, PID CONTO OF A BIPED OBOT IAQUAT AI HAN, UWAIIYAH NAEEM, UMA HAN, S. ZAHID HUSSAIN Department of Mechatronic Engineering AI Univerity E-, Ilamaad PAISTAN liaquat@yahoo.com,,, ABSTACT Human are the mot complicated tructured root poile. The world today i triving to mae root that replicate the human tride. While waling human, contantly hift their weight from one leg to the other to alance the COG (center of gravity). Biped root mot cloely reemle the human wal. However, current iped root lac adaptaility and taility. Thi paper preent the deign of a Proportional Integral Derivative control for a - DOF (Degree of Freedom) Biped oot that enure maximum taility during it wal. The ytem i analyed with the aion of PI, PD and PID control to the ytem tranfer function. The effectivene of the deign i verified y computer imulation. EYWODS: oot, PID control, inverted pendulum, control ytem. INTODUCTION An inverted pendulum i a ueful tool that wor efficiently to contantly hift the weight of the root. The root under cuion hown in fig. [] ue an inverted pendulum for weight alancing. The ytem ue four DC motor in all It ue one DC motor to operate the hip joint two motor to control the leg movement, one DC motor to perform the turning operation and one for weight hifting (to operate the inverted pendulum) a hown in fig. The paper carrie out a force analyi and mathematical modeling of the oot. Then PI, PD and PID are added to the tranfer function one y one. The ytem i analyed through hit and trial y a numer of imulation carried out in MATAB and SIMUIN.. INETED PENDUUM Under ideal contion, the ehavior of the pendulum i governed completely y the econd-order fferential equation mentioned previouly. Thi mae it a perfect candate for PID (Proportional- Integral-Derivative) control. The idea ehind PID control i that the magnitude of the output ignal of a ytem hould e a linear comination of the input ignal, it integral up to the current time, and it derivative in order to create a tale ytem, that i, one that achieve equilirium. Thi mae ene in the context of alancing a pendulum. Firt, the olution to the ero of the pendulum' governing equation mae clear the need for power output in proportion to the placement. But thi alone can quicly ecome untale and doen't account for the full tate of the pendulum. For example, if the pendulum i far off equilirium ut ha a velocity that i rapidly moving it ac to center, a fferent power hould e upplied than if the pendulum i placed and falling in the other rection, hence the need for ISBN: ---- ISSN: -

2 th WSEAS Int. Conf. on OBOTICS, CONTO and MANUFACTUING TECHNOOGY (OCOM '), Hanghou, China, April -, a derivative term. Finally, the need for integral control ecome apparent when conidering what happen when the acceleration of the cart exactly compenate for that of gravity: the pendulum i temporarily in an untale equilirium, neither riing nor falling. The derivative term i ero, o it can't motivate the power output. The placement in't changing, o the proportional term i already giving all it' going to give. The integral term erve to detect thi ituation and provide for power when the proportional term in't cutting it. Fig-. Two legged root model Fig-. Dynamic model. PID Control The PID control algorithm i ued for the control of almot all loop in the proce indutrie, and i alo the ai for many advanced control algorithm and trategie. In order for control loop to wor properly, the PID loop mut e properly tuned. Standard method for tuning loop and criteria for judging the loop tuning have een ued for many year, ut hould e reevaluated for ue on modern gital control ytem. While the aic algorithm ha een Unchanged for many year and i ued in all triuted control ytem, the actual gital implementation of the algorithm ha changed and ffer from one ytem to another and from commercial equipment to academia. Thi paper will cu controller tuning method and criteria. Alo cued will e the gital PID control algorithm, how it wor, the variou implementation method and option, and how thee affect the operation and tuning of the controller.. Mathematical Model. Pendulum: The modeling equation for the pendulum i given elow. Thi i a nonlinear equation that need to e normalied later. The ytem i linearied at ψ Π ( M I) Mx co mgin...(.). Motor: Each of the four motor eing ued to operate the leg and hip aemly will have almot the ame modeling equation. The ma of each of ISBN: ---- ISSN: -

3 the leg i concentrated in a. Hence the ma moment of inertia of the (leg) i calculated a follow mr / And the modeling equation are a follow. i i..(.) i i.(.) i I.(.). State pace In the tate-pace form, the equation aove can e expreed y chooing the rotational peed and electric current a the tate variale and the voltage a an input. The output i choen to e the rotational peed.. inearied Pendulum Tranfer Function: U.. [ ] Y The tranfer function i otained uing the tate-pace method. For m arm.g, g.m/,.m.hence, the pendulum tranfer function ecome,.. ) ( ) ( U G pen ower aemly tranfer function: [ ] Y Hence, for (friction) N/m, (for the pring contant of Aluminum), (output reitance) Ω and (Inductance) H, the tranfer function of the lower aemly i calculated uing tate pace.. Unit Step epone of the Tranfer Function The Tranfer function had the following unit tep repone Fig-. Unit Step epone th WSEAS Int. Conf. on OBOTICS, CONTO and MANUFACTUING TECHNOOGY (OCOM '), Hanghou, China, April -, ISBN: ---- ISSN: -

4 th WSEAS Int. Conf. on OBOTICS, CONTO and MANUFACTUING TECHNOOGY (OCOM '), Hanghou, China, April -, control) PID (overhoot) PID (ome over hoot) PID (no overhoot). c.t c.t c. c.t c.t c. c.t c.t c Tale-: Ziegler Nichlo tuning parameter. PID Control Fig-. oot ocu The PID control tranfer function I igc ( ) p d. By changing the value of P, I and D we can reach a value of PID for which the ytem ecome tale. The proportional controller i a pure gain adjutment, acting on the error ignal to provide the driving input to the proce. The P- controller i alo ued to adjut the peed of the ytem. With the aion of the P-controller the ytem will have an overhoot ut it will ettle down quicly. The integrator controller i implemented with the introduction of an integrator. Integrator control i ued to provide the required accuracy for the control ytem. The derivative action i normally introduced to increae the damping in the ytem. The derivative controller alo increae the noie in the ytem which may caue prolem inclung intaility. The value of (critical gain) c and (critical Time) T c ; the ytem requirement i ero teady tate error, /- ec ettling time, ie Time hould e ec and only < %. Fig-: PID with ow gain Fig-. PID with High gain Control p I d P only. c PI. c.t c PID (tight. c.t c.t c Fig-. oot locu with PID ISBN: ---- ISSN: -

5 th WSEAS Int. Conf. on OBOTICS, CONTO and MANUFACTUING TECHNOOGY (OCOM '), Hanghou, China, April -,. Concluion Uing PID control ha greatly implified the control of the ipedal root. Some of the value have een aumed to cloe approximation however the reult can e further improved y uing exact value.. eference [] Y. Aya, B. Afal,M. Saeed, S.ehman, Deign, Farication and Control of a Two-egged Waling oot Fourth International Worhop on oot Motion and Control, pp -, une -,,Poland. [] M. Doi, Y. Haegawa, T. Fuuda, Paive Dynamic Autonomou Control of Bipedal Waling International ournal of Humanoid ootic, world cientific pulihing company, Octoer,., apan [] M. Guihard, P. Gorce, Dynamic Control of Biped uing Anle and Sip Strategie, proceeng of the IEEE/S Intl. Conference on Intelligent oot and Sytem EPF, auanne, Octoer, Switerland. [] Etal. A. Irfan,. Ahraf, W. Ahmed, Inverted Pendulum, pulihed in the journal of AMSE Dec ol, pg no,,france. [] Modeling an inverted pendulum, Control Tutorial for Matla. ISBN: ---- ISSN: -