The Anthropomorphic Robot Arm Joint Control Parameter Tuning Based on Ziegler Nichols PID Renli WANG 1, a, Yueming DAI 2, b

Transcription

1 3rd Inernaional Conference on Mechanical Engineering and Inelligen Syses (ICMEIS 015) he Anhropoorphic Robo Ar Join Conrol Paraeer uning Based on Ziegler Nichols PID Renli WANG 1, a, Yueing DAI, b 1 Deparen of Inforaion and Elecric Engineering, Xuzhou Insiue of echnology, Xuzhou, 1111, China Deparen of Inforaion and Elecric Engineering, Xuzhou Insiue of echnology, Xuzhou, 1111, China a eail: renliwang@163.co, b eail: daiy63@163.co eywords: Anhropoorphic robo; Ziegler and Nichols paraeer uning; uli-join conrol; Criical sable Absrac. In order o ge he anhropoorphic robo accurae paraeers of he upper lib join conrol oor, a ehod based on Ziegler Nichols-frequency response of he adapive PID conroller is proposed. he conrol circui idenifies online iporan criical frequency response characerisics of process objec hrough inpu and oupu daa in he noral process operaion, and hen he syse online updae PID conroller paraeers based on Ziegler-Nichols seing rules or by he iproved ehod. he resuls show ha he ehod has sronger robusness and adapive abiliy. I can always guaranee conrol circui run in he bes condiion and alos copleely resisan o ouside inerference. he siulaion is no only an iporan guiding role o he design of anhropoorphic robo hand conrol node, bu also cerain reference significance for he dc oor closed-loop conrol. 1. Inroducion Anhropoorphic robo hand conrol node's ask [1][][3]is o receive robo "brain" (PC) insrucion and coplee he hand oor speed and posiion conrol. Personificaion robo hand oor osly adoped DC oor, ani-inerference abiliy of which is poor usually. o overcoe ouside inerference, decrease he speed flucuaion, obain high conrol accuracy and response speed, we pu forward he Ziegler Nichols [4][5]paraeer seing ehod: when he process variables and speed change, we esablish a se of epirical forula ha ransfor hese es resuls ino he righ perforance se paraeers. he Ziegler-Nichols frequency response ehod can online opiize ine hois speed regulaor paraeers in direc orque conrol syse, resrain he low speed orque ripple, and iprove he conrol precision of he syse. I can guaranee he conrol loop always run in he bes sae. By esablishing frequency converer speed odel, we consruced hois conrol syse siulaion diagra based on PID Ziegler-Nichols seing ehod. he siulaion resuls show ha he PID conroller based on Ziegler-Nichols PID seing ehod has good dynaic perforance on racking he se value response, less overshoo and good seady sae perforance. he syse has a srong abiliy o adap o he objec paraeers change.. he Maheaical Model of he DC Moor he acual easureen curve of he oor and heoreical forula are copared, open loop syse ie response funcion of anhropoorphic of robo hand oor [6] [7] is: d ω() dω() a + b + cω() = e() i (1) d d In he ype: a = 84.16; b = 18.97; c = d ω() dω() ω( ) = e( ) i () d d 015. he auhors - Published by Alanis Press 136

2 Join he inpu and oupu speed conversion link, o ee he syse requireens [8]: 1 Gs () = (3) S S he PID Conroller Paraeers Influence on Conrol Perforance [ ] [ ] D uk ( ) = uk ( ) uk ( 1) = ek ( ) ek ( 1) + ek ( ) + ek ( ) ek ( 1) + ek ( ) (4) P I D k uk ( ) = P ek ( ) + e( j) + ek ( ) ek ( 1) I j= 0 D [ ] (5) Forula (4) is called increenal PID conrol forula; Forula (5) is called posiion ype PID conrol equaion [8]. D In he ype: p is proporional coefficien, I = P is inegral coefficien and D = P is I differenial coefficien. 3.1 he coparison of wo kinds of PID conrol algorih Because posiion ype PID conroller adops oal oupu, is oupu is he acual posiion of he acuaor, and each oupu is associaed wih he pas sae and calculaion of deviaion accuulaion. So large aoun of calculaion work us run, once he daa processing copuing chips appear proble, he syse will ake he oupu volailiy and resul in high volailiy in he acuaor, which causes big accidens. he increenal PID algorih is beer. In increenal algorih, he proporional and inegral ie sybols have he following relaions: if he conrolled variables o coninue deviaes fro he given value, he wo sybols are he sae; and when he conrolled variables o he given value direcion changes, he wo sybols insead. his algorih can ake he dynaic process of conrol syse accelerae. 3. he PID conroller paraeers influence on conrol perforance (1) Proporional coefficien p: he role is o accelerae he response speed of syse and iprove he adjusen accuracy of syse. When he syse once appeared deviaion, proporional conrol will produce an iediae adjusen o reduce error. he greaer he p, he faser he syse response. Bu i will produce overshoo and oscillaion even lead o syse insabiliy, so he value canno selec oo uch; Bu if he value is oo sall, i will reduce regulaion accuracy and syse response speed, hen i prolong o adjus ie and ake he syse saic and dynaic characerisics worse. () he inegral coefficien i: is role is o eliinae he seady-sae error of he syse and iprove he degree of no error. he bigger he i, he faser he saic error is eliinaed. Bu if i is oo big, i can produce inegral sauraion phenoenon a he beginning of he response process, and cause a big overshoo o ake he dynaic perforance worse; Bu if he value is oo sall, i will ake inegral effec weakened, and he syse saic error is difficul o eliinae, so ransiion ie is longer. he syse can' reach a seady sae as soon as possible, hen affec he syse conrol precision and dynaic characerisic. (3)Differenial coefficien d: is role is o iprove he syse dynaic characerisics, reflec he deviaion signal change rae, and foresee he deviaion change rend. I can produce advanced conrol funcion, reduce he overshoo of syse, and increase he syse sabiliy. Bu i s no oo uch, Oherwise i no only ake he response process braking ahead of ie and prolong syse adjusen ie, bu also ake he ani-inerference of he syse worse. he purpose of paraeer seing is by adjusing he hree paraeers of PID p, i and d o ake he closed-loop characerisic roo of syse disribue a paricular doain in he lef half plane of s doain, o ensure ha he syse has enough sabiliy argin and saisfy he given perforance arge. 137

3 4. Ziegler Nichols Mehod o Realize he PID Paraeer Seing Ziegler and Nichols ehod has developed online paraeers seing beween experience and calculaion ehod. Ziegler Nichols ehod ay deerine very precise paraeers for conroller, i also can fine-une afer his Ziegler Nichols PID paraeer seing ehod: (1)Build a closed loop conrol circui, deerine he sabiliy lii. () According o he forula o calculae he conroller paraeers. he sabiliy lii is deerined by he P coponen. When here is a seady oscillaion o reach his lii, he criical coefficien pcri and criical oscillaion cycle cri are generaed. Afer deerining he criical coefficien pcri and criical oscillaion period cri, we calculae oher paraeers according o a forula in he able 1. According o he experience forula of following able and he corresponding conroller ype se corresponding PID paraeers, and hen conduc siulaion validaion and fine-uning: he conroller ype P able 1 PID paraeers calculaing forula I Characerisic daa D PID 0.6 Pcri 0.5 cri 0.1 cri i I P D P D For he ransfer funcion of a given conrolled objec, we selec he inersecion poin beween roo locus diagra of discree syse and z plane uni circle on he roo locus diagra, hen we gain and his poin ω value naelyω. Seing forula is as follows: p = 0.6, Pπ pω d =, i = (6) 4ω p In forula, is he p values of he syse iniiae oscillaion, ω for he oscillaion frequency. Oscillaion frequency ω can be deerined by he pole Angle θ locaed on he uni circle, ω =θ/ ( for he sapling period). 4. he Malab seing progra ake sapling period: =0.5s; he aplifier aplificaion coefficien: p=50. he operaion resul is shown in Figure

4 Selec a poin in he graphics window. k =5.7977e+07 pole = i i kp =3.4786e+07 kd =3.5469e+06 ki =8.59e he Siulink Siulaion 5.1 o consruc a syse of Siulink odel Fig.1. Roo locus diagra of progra Based on he analysis of he echanical heory as he foundaion, designed he soccer robo pick he ball insiuions opial design process[9] [10], found ai funcion, selec design variables and he corresponding opiizaion algorih o opiize a coplee se of insiuions. A las hrough he es he final perforance paraeers of he insiuion are obained. Experiens show ha he syse has higher accuracy and sabiliy, he new opiize pick he ball have design basic requireens, and achieved good ideal conrol effec. Fig. Syse siulaion odel 139

5 5. he resuls of Siulaion he experienal resuls show ha he syse has a good response speed, sabiliy and accuracy, and srong robusness. 6. Conclusion Fig.3 Adapive PID dynaic response based on Ziegler Nichols - frequency ehod In a closed loop conrol syse, he inegral conrol link iproves he seady-sae error accuracy of he syse. Due o he consanly accuulaed error, i can eliinae he error quickly, bu i ake he syse produces overshoo; And differenial conrol can increase he daping of he syse and iprove he dynaic response speed. Because he PID conroller can copensae he vas ajoriy of he conrol syse, he seing ehod is siple and good robusness; herefore i is currenly he os widely used conroller. Ziegler-Nichols ehods are ehod of PID seing based on syse sabiliy analysis. Ziegler-Nichols ehod can quickly and accuraely calculae he corresponding paraeer nuerical, hen only need o fine-une he ideal conrol effec can be go. By Ziegler Nichols - frequency ehod, we ge a se of paraeers for he p = e+07; d =3.5469e+06; i =8.59e+07. According o he above paraeers, he syse has finally a high conrol precision, faser response speed, ore ousanding conrol sabiliy, alos copleely resisan o ouside inerference. his ehod can realize he PID conroller adapive and ensure he conrol loop always work in he bes condiion even under he operaing condiions change. I is of grea significance for indusrial enerprises he energy-saving eission reducion and iproving he operaion efficiency of process equipen. Reference [1]Ming-Hsun Chiang, Fan-Ren Chang, Anhropoorphic Design of he Huan-Like Walking Robo[J], Journal of Bionic Engineering,013:10(), []Chung Yik Lau, Alon Chai, he Developen of a Low Cos Pneuaic Air Muscle Acuaed Anhropoorphic Roboic Hand[J], Procedia Engineering,01(41), [3]F.J. Brosed, J. Sanolaria, J.J. Aguilar, D. Guilloía, Laser riangulaion sensor and six axes anhropoorphic robo anipulaor odelling for he easureen of coplex geoery producs[j], Roboics and Copuer-Inegraed Manufacuring, 01:8(6),

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