Control of SIMO Systems in Simulation: The Challenge of the Multiple Axes Actuating Pneumatic Arm

Transcription

1 Internatinal Jurnal f Cmputer Applicatins ( ) Vlume 168 N.10, June 2017 Cntrl f SIMO Systems in Simulatin: The Challenge f the Multiple Axes Actuating Pneumatic Arm G. P. Smyrnaiu Dept. f Autmatin M. Paputsidakis Dept. f Autmatin A. Xatzpuls Dept. f Autmatin D. Tseles Dept. f Autmatin ABSTRACT In this paper a cmparative study f the classical cntrl methds fr the testing f a mathematical mdel, which cntrls six actuatrs f a six degrees f freedm rbtic arm with a single cntrller, is illustrated, aiming t the cnstructive simplificatin f the system. In mre detail, a mathematical mdel f the system is designed which simulates all mechanical parts, including 5-way directinal pneumatic valve, the pneumatic actuatrs/pistns and the mathematical mdel f the cntrller. The purpse f the abve is the tuning f a Single Input, Multiple Outputs (SIMO) cntrller which will direct the mtin f the six pneumatic pistns. The thrugh analysis f the implementatin f the pneumatic system in Matlab/Simulink envirnment is fllwed by experimentatin and results using Prprtinal (P), Prprtinal-Integral (PI), Prprtinal- Derivative (PD) and Prprtinal-Integral-Derivative (PID) cntrllers. The simulatin results shw the advantages f the abve classical cntrl methds n the rbtic human arm which imitating human mtin and made by a well-knwn cmpany in the field f pneumatic autmatin. Keywrds Single input-multiple utput systems, pneumatic psitining systems, simulatin envirnment, PID cntrller design. 1. INTRODUCTION In mdern industry pneumatic systems (PS) are used with an increased rate. A pneumatic system uses cmpressed air as a mean t transfer the mtin, and have as a final result the mvement f a pistn r in rare cases the rtatin f a mtr. Pneumatic Systems find applicatin in cases where small frces shuld be applied and great velcity is needed. This is the main reasn they are widely used in the industry. Pneumatic systems als stre and transfer energy with ease and can prduce lw cst, linear mvement with relatively high speed, easily adjustable [1]. Cylinders are cnsidered the basic elements f mtins in Pneumatic Systems, which cnvert the pneumatic frce int a linear mtin. Pneumatic cylinders cnsist f a chamber and prts frm where the air enters and exits, perfrming, that way, the linear mvement. The pistn s chamber is tight t avid any leakage and is highly durable s that it can endure the high pressure [2]. There are three distinguished categries fr the pneumatic cylinders: In the single-acting cylinders, which are divided int single-acting cylinders with and withut rebund spring. In the duble-acting cylinders, which are divided int duble acting cylinders with a single rd, with dublerd, telescpic and with delay. In the Tandem cylinder, which includes tw separated duble-acting cylinders f cmpressing air, in a rw fr additinal pwer. This setup dubles the air pressure prvided by the pistn because f its increased [3], [4]. Fr the crrect functin f the pneumatic actuatrs a cntrller is required. The valves are devices that help regulate the starting r stpping f the pistn, and als assist in determining the cmpressed air flw directin. The valve cntrls the mtin f the rd and the valve respectively is tuned by a classic cntrller [4]. Valves are distinguished in the fllwing categries: Directinal valves, Signal valves, Pressure cntrl valves Return / check valves [2]. The requirements f mdern times and particularly the last five years have impsed a rapidly develping technlgy in the hydraulic autmatin area. As a result, a new technlgy sectr appeared: hydraulic. This remarkable grwth is mainly due t the cntributin f the cnstructin f hydraulic cmpnents and P.L.C, general. By hydraulic system we mean that a device used t transmit mtin and pwer transmissin frm the mtr t the driven machine. The analysis, design and mdeling hydraulic autmatin systems, based n principles and laws, is widely applicable in fields such as the autmtive industry and in rbtics. 2. CONTROL DESIGN IN SIMULATION ENVIRONMENT 2.1 Nn-Linear Mathematical Mdel A pneumatic system cnsists f a cylinder, a valve, exhaust and supply tubes, psitin sensrs and pressure sensrs. The lad is the rest f the mechanical parts that are cnnected t the pneumatic pistn. A nn-linear pneumatic system is illustrated in the fllwing Figure. 1

2 Internatinal Jurnal f Cmputer Applicatins ( ) Vlume 168 N.10, June 2017 value, the flw will attain snic velcity (chked flw) and will depend linearly n the upstream pressure. If the pressure rati is smaller than the mass flw depends nnlinearly n bth pressures. The standard equatin fr the mass flw thrugh an rifice f area is: Where is the mass flw thrugh valve rifice, is the supply rate, is the value f the upstream pressure and is the value f the dwnstream pressure. C1 and C2 are cnstants f a given fluid, in this case the air: Fig. 1: Standard pneumatic cylinder-valve mdel The equatin f mtin fr the pistn-rd-lad assembly can be expressed as: Where is the external mass f the lad, is the mass f the pistn, is the current psitin f the rd, is the speed f the pistn, is the acceleratin f the pistn, is the frictin cefficient, is the frictin frce (Culmb), is the external frce, P1 and P2 are the abslute value f the air pressure f the actuatr s chamber, is the abslute value f the envirnment pressure, A1 and A2 are the pistn effective areas, is the rd crss sectinal area. The abve equatin represents the frce f the actuatr generated by different pressures acting n the ppsite sides f the pistn, in rder t cntrl the actuatr s utput. The time derivative fr the pressure in the pneumatic cylinder chambers can be expressed as: Where P is the pistn s pressure, R is the ideal gas cnstant, T is the temperature, is the inactive vlume at the end f strke and admissin prts, is the pistn effective area, L is the pistn strke, x is the pistn psitin, and are the mass flws entering and leaving the chamber, and and taking values between 1 and k, depending n the actual heat transfer during the prcess. The first term f the abve equatin represents the effect f the pressure f the air flw int r ut f the cylinder chamber, while the secnd term describes the effect f the mtin f the pistn. The pressure drp acrss the valve rifice is usually large, and the flw has t be treated as cmpressible and turbulent. If the upstream t dwnstream pressure rati is larger than a critical Where k is the cnstant f air value [5],[6]. 2.2 Simulatin f the Pneumatic System with 6 Actuatrs and P Cntrller The pneumatics system simulatin mdel with six parallel cnnected pistns with analg cntrl is illustrated in belw Figure 2: This mdel represents an integrated pneumatic system with six cntrllable actuatrs/ pistns. The cmpnents are described belw: A directinal cntrl valve 5/3 This is a five-way valve and three-psitin (5/3 valve) which is used t cntrl the cmpressed air s flw int and ut thepistn, having as an utput the return f the pistn. This valve has an intermediate psitin, which is clsed, the transits B-X and A-S stay clsed. That way the cmpressed air gets trapped in the champers f the pistn. The plunger balances under the influence f the tw pressures, and stp in an intermediate psitin, with a relative accuracy. The plunger is immbilized that way and the rd remains stable. As shwn in Fig.2, the supplied pressure is inserted in prt P and the pneumatic actuatr is cnnected t prts A and B. R and S are return paths f the A and B prts respectively. Duble-acting Cylinder The Pneumatic System uses a duble-acting cylinder with a single rd that frces the cmpressed air t mve the rd in bth directins. Flw Rate As shwn frm Fig. 2, the blck diagram f the flw rate f the pneumatic system is cnnected with a directinal valve t drive the cmpressed air t the actuatrs prts s that he can mve accrdingly. The Flw rate blck diagram cntains a subsystem which cnsists: Mass & Heat Flw Sensr, which is a device that cnverts the mass flw rate and heat flw rate between the tw pneumatic ndes int physical measurement signals G and Q. The psitive directin f the sensr is frm the prt A t prt B. PS-Simulink Cnverter which cnverts the input Physical Signal t a unit less Simulink utput signal in this case Kg/s. 2

3 Internatinal Jurnal f Cmputer Applicatins ( ) Vlume 168 N.10, June 2017 Pressure Surce This is an ideal air cmpressr which maintains a fixed pressure differential, irrespectively the flw rate. The cmpressr des nt add extra heat t the system. A psitive pressure difference results in the pressure in prt B t be greater than the pressure in the prt A. The cmpressr differential pressure is 6 bar. Subsystem blck and Time scpe blck Fr the pneumatic system Simulatin, the Simulink library was used. Time scpe blck is used and the six actuatrs are cnnected and als the input step. A Subsystem blck is created which includes the 5 pneumatic pistns and it s cnnected with the first ne (Master-slaves) as illustrated in the fllwing figure. Fig 2: Simulatin Mdel f the Overall System Fig 3: Subsystem Blck 3

4 Internatinal Jurnal f Cmputer Applicatins ( ) Vlume 168 N.10, June 2017 The Step input is set t start frm 0 sec. Step s range value starts frm 0 t 1. As final value in the stke parameter f the pistn is set 0.05 m height and the strke length is set in 0.1 m. Frm the Simulink library a PID cntrller is selected (Prprtinal Integral Derivative) the P value is set t and the rest f the parameters are eliminated (0) t achieve Prprtinal cntrl. Simulatin time is set t T=0.5 sec, air supply pressure is set t 6 bar, [ Pascal]. The systems respnse and the psitin f the six actuatrs with Prprtinal cntrl are shwn in the fllwing figure. shwn in the fllwing figure. Simulatin time is set t T=0.5 sec, air supply pressure is set t 6 bar, [ Pascal]. Fig 4: P cntrller s Step Respnse The fig. 4 results fr, where the pistns have settled in the Set value. Fr lwer values a steady state errr ccurs in the systems respnse and fr greater values the steady state errr is lifted. At this pint it shuld be mentined, that the steady state errr is nt erased cmpletely, but instead it is getting smaller. The Step input is set t start frm 0 sec. As final value in the stke parameter f the pistn is set 0.05 m height and the strke length is set in 0.1 m. The PID cntrller is tuned (Prprtinal Integral Derivative) t and t achieve Prprtinal-integral cntrl. Simulatin time is set t T=0.5 sec, air supply pressure is set t 6 bar, [ Pascal]. The fllwing figure illustrated the pneumatic system respnse. Fig 6: PD cntrller s Step Respnse The abve figure, results fr and and filter cefficient N=100, where the pistns have settled in the Set value. Increasing the cefficient a steady state errr ccurs with values n the psitin f the pistns less than 0.05 m. The Step input is set t start frm 0 sec. As final value in the stke parameter f the pistn is set 0.05 m height and the strke length is set in 0.1 m. The PID cntrller is tuned (Prprtinal Integral Derivative) t, and t achieve Prprtinal-Integral-Derivative cntrl in the pneumatic system. The systems respnse and the psitin f the six actuatrs with Prprtinal-Integral- Derivative cntrl is shwn in the fllwing figure. Simulatin time is set t T=0.5 sec, air supply pressure is set t 6 bar, [ Pascal]. Fig 5: PI cntrller s Step Respnse The abve figure s results fr, where the pistns have settled in the Set value. Fr increased the gain, a steady state errr appears in the system with values f the psitin f the pistns greater than 0.05 m. The Step input is set t start frm 0 sec. As final value in the stke parameter f the pistn is set 0.05 m height and the strke length is set in 0.1 m. The PID cntrller is tuned (Prprtinal Integral Derivative) t and t achieve Prprtinal-Derivative cntrl in the pneumatic system. The systems respnse and the psitin f the six actuatrs with Prprtinal-Derivative cntrl is Fig 7: PID cntrller s Step Respnse The abve figure results fr, and filter cefficient N=100, the pistns have settled in the Set value. Increasing the gains values changes ccur in the steady state errr. Als distrtin may appear n sme situatins fr increased gain values. Increasing the Prprtinal gain while leaving the ther tw gains aside it is bserved, that the system s respnse tries t fllw the input set t it but a steady state errr ccurs. Increasing its value the steady state errr is getting smaller but it is never eliminated. Increasing the Integral gain and leaving the ther cefficients intact the steady state errr is getting smaller but we have distrtin. By increasing the Derivative gain the versht is getting reduced, as well as the settling time while the steady state errr get smaller changes. With the Prprtinal cntrl methd the Pneumatic system respnse gets accurate by chsing the crrect value and acts fast with settling time =492.4 ms (Fig.4). When the applicatin requirements are increased then this methd f 4

5 Internatinal Jurnal f Cmputer Applicatins ( ) Vlume 168 N.10, June 2017 cntrl gets unsuitable and the systems respnse with a lad gets unpredictable [7]. Therefre this methd f cntrl cannt deal with all the scenaris that can ccur in the industrial envirnment and needs furthermre assistance frm a subsystem. The secnd methd f cntrl that was used in the pneumatic system was the Prprtinal-Integral methd which accrding t the thery using the integratin term is intended t eliminate the steady state errr in the system. The steady state errr theretically shuld have been eliminated by the integral term while adding sme minr distrtin n the systems respnse, has settling time =488.6 ms desn t eliminate the stead state errr =0.05 m as expected even at the maximum value (Fig 5). In simulatin envirnment the PI cntrller desn t add scillating behavir, nr creates versht in the pneumatic system. In reality studies have shwn that the Integral cefficient n a Nn-linear system adds cnstantly frce in the system creating disturbances [7],[8],[9],[10], and unbalancing the systems respnse. That is the main reasn that the PI cntrller is avided in general in bth simulatin experiments as well as in real nce. The next methd f cntrl that was applied in the pneumatic system was the PD cntrller (Prprtinal-Derivative). The- D cefficient shuld minimize the systems versht. With experimental testing it is cnfirmed that the PD cntrller helps stabilize the Pneumatic system respnse with =498.7 ms and eliminates the ver sht with a =0.05 (Fig.6). The last cntrller tested was the three-term PID cntrller (Prprtinal-Integral-Derivative) t cmplete the cmparisn between all the cntrllers. The respnse time f the PID cntrller it s the same as the PD s. =498.5 ms (Fig.7). In simulatin envirnment, PID cntrller has distrtin when the cefficients value are t high but he is eliminating the versht effect. In reality the presents f the I-term is creating lw frequency signals that are hard t eliminate and adds unpredictable behavir in the system s respnse [7],[8],[9],[10], making it hard t justify its usage n a nn-linear mdel as this ne. Therefre the mst ptimal respnse fr the six actuatr pneumatic systems is given by PD cntrller in Simulatin as well as in real experiments. 3. CONCLUSIONS AND DISCUSSION In the current study a cmparisn was perfrmed between classic methds f cntrl in simulatin envirnment that included a six actuatr rbtic arm with six degrees f freedm and a single classic cntrller. The design and implementatin f the pneumatic system was described (Matlab/Simulink). The mathematical mdels f the directinal valve, the actuatrs and the cntrllers were described. The experimental result where Prprtinal (P), Prprtinal-Integral (PI), Prprtinal Derivative (PD), and Prprtinal-Integral-Derivative (PID) were used, were illustrated. The innvative pneumatic system simulatin mdel f an input and multiple utput (Single Input, Multiple Outputs - SIMO), gives the user the ability t tune in a single cntrller that can simultaneusly drives six parallel cnnected drive pistns. After the experiments cmpletin it was shwn that the Prprtinal Derivative (PD) prvided the system with the mst ptimal respnse. Mrever, the specific pneumatic system with the given rbustness and repeatability, as recrded by the experimental prcedure, created a clear practical prmises fr the usage f the rbtic hand ExHand f Fest which can be used as an uter skeletn that can be wrn as a glve by the human hand. The fingers can be actively mved and their strength amplified the peratr s hand mvements are registered and transmitted t the rbtic hand in real time. The exskeletn hand has all the principal physilgical degrees f freedm f its human cunterpart. It thus supprts the human hand s diverse techniques fr grasping and handling bjects. The bjectives are t enhance the strength and endurance f the human hand, t extend humans scpe f actin and t secure them an independent lifestyle even at an advanced age. Since all the jints and their drive units are lcated utside the actual hand in the frm f the exskeletn, this manual rthsis can be fitted nt nly ver the human hand, but als ver an artificial handmade f silicne. Using the same hardware, this enables a scenari that creates a link between rbtics and rthtics in a cmpletely new way. The ExHand cmbines human intelligence with the capabilities f a rbt. While machines are precise, rbust and pwerful, their respnses t cmplex situatins are limited. They nrmally rely n the visual and tactile perceptin and decisin-making capacity f a human peratr. With the ExHand the peratr has the sensatin f feeling the shape f the remte bject. The human sense f tuch can thus be implemented ver lng distances and can even be applied at the interface f the real t the virtual wrld. The system amplifies the strength f the human hand and helps emplyees remain in the wrk prcess fr a lnger time withut suffering permanent physical effects. T prevent fatigue, the ExHand can be wrn fr activities carried ut in the assembly prcess, thereby functining as an assistance system that makes fr mre pleasant wrking cnditins in the assembly envirnment. The ExHand mving by eight pneumatic actuatrs which ensure the precise mvement f the rbtic arm. The frces, the angles and distances recrded by sensrs [13]. Given the fact that the cnstructin is fully peratinal, but there is n literature t be fund with sme effrt t make simulatins in the MatLab Simulink, neither any experimental results f its usage. The mdel f this paper perfrms rbust cntrl and can simulate human mvement using six pneumatic actuatrs, which in fact will ensure the accurate mvement f the rbtic hand in real time. Fig 8: A Well Knwn Pneumatic Arm 4. WHAT IS TO FOLLOW By taking advantage f the pssibilities given by Matlab/Simulink the pneumatic system that was designed fr the purpse f finding the mst ptimal methd f cntrl, culd be benefit by adding fuzzy lgic cntrller. The particular cntrller is nt fund in the literature, but culd be 5

6 Internatinal Jurnal f Cmputer Applicatins ( ) Vlume 168 N.10, June 2017 used t cntrl the psitin f the six pistns f the system, prviding new cmparisn data and therefre new results. Als, checking the psitin f the six parallel-cnnected pistns culd be dne by placing in the system a Linear Variable Differential Transfrmer LVDT. In mre details, Fuzzy lgic is a wide scientific field created by the need t bypass the strict traditin f binary lgic in which nly the statement true r false exist. Fuzzy lgic inserts the definitin f truth degrees which measure whether an bject is invlved in a fuzzy set. The truth degree value is define by the membership functins which take values between 0 and 1 that describe whether an bject is invlved in a fuzzy set. Fuzzy cntrl ccurred frm the need fr a cntrl strategy that is nt based n a mathematical mdel system, which usually differs frm the real. The cntrllers designed based n fuzzy lgic have the capacity t handle fuzzy data and nise data. They are based n the human ability t perceive the behavir f qualitative rules system. Thrugh a series f simple linguistic rules, fuzzy lgic can mdel the knwledge and experience f an experienced user. That way a knwledge based system is frmed t guide basic mdels t be mre receptive f the human lgic. That way fuzzy lgic cntrl succeeds where ther classic methds f cntrl can t. The main structural elements f a fuzzy lgic cntrller are the fllwing: Knwledge base in which the rules are stred t cntrl the prcess (if-then rules) Fuzzy sets, which are used t represent the input and utput variables f the verbal terms. Fuzzifier which cnverts the real input values in fuzzy sets Inference engine, which prcesses the utputs f the Fuzzifier and uses the knwledge base t extract the fuzzy sets and the cnclusins Defuzzifier, which cnverts the cnclusins int real terms, s that it can be transferred int cntrl actin f the prcess. There are varius types f fuzzy cntrllers in which the main difference lies in the inference mechanism. Essentially, entailment wherein the inference mechanism is based n statements and the type f the cntrller. The main types f cntrllers are: Mamdani, defined as: "If x is A then y is B" was named after Ebrahim Mamdani, wh was amng the 1 st t establish the fuzzy The utputs f the rules f this methd are fuzzy sets. Sugen Takagi, which is defined as: "If x is A then y is c", where c is a number r a crisp fuzzy set. Takagi - Sugen Kang r Τ-S-K, is an extensin f the previus rule and is ne f the mst imprtant rules wh is used in advanced fuzzy systems "If x is A then y is c0 + c1 x", where c0, c1 Є R [11]. Anther future challenge is t undertake the simulatin f a Linear Variable Differential Transfrmer LVDT is actually a sensr fr the linear displacement. The range f the measured displacement varies frm 0,1mm t 1000mm. Linear variable differential transfrmers are instruments with precisin and have lw divergence (±0.5%), because their cre is nt in cntact with the cils, resulting in a very lw mechanical frictin. Despite their advantages LVDT are instruments used fr measuring small displacements, but they are quite sensitive and are affected by vibratins and temperature. The device cmprises three cils, tw secndary and a primary ne, the centre f the primary is a cre made f sft magnetic material (sft irn, amrphus wire, FeSiB etc.). The primary is pwered with high frequency vltage and the secndaries are cnnected in series with ppsite plarity. When the magnetic cre is lcated in the centre, due t symmetry f the vltages induced in the secndary cils are equal and ppsite cnnected, the utput is zer. Mvement f the cre generates a signal (alternating vltage) in the utput amplitude is prprtinal t the displacement and the phase indicates the directin f mtin. The name f a specific sensr is described in the wrking principle: 1. The adapter is subjected t the electrmagnetic inductin principles. 2. It has ne primary and tw secndary cils, which are cnnected and prvide the difference in the trends in their respective utputs, fr this reasn it s called differential. 3. The magnetic cupling between the cils can be changed by affecting the magnitude f the induced electrmtive frce, fr this reasn it is cnsidered variable. 4. LVDT is designed in a specific way, s that the changes f the magnetic cupling between the cils can be linear. The functin fr the primary is given belw: The LVDT finds multiple applicatins in the industrial department because f his many benefits: T cntrl the water level in a tank. In engineering wrkshps. In rbtics. In frce, pressure and acceleratin measurement systems. Fr psitin cntrl in hydraulic and pneumatic rams. Fr crane cntrl [12]. The LVDT can be used fr the successful cntrl f the psitin f ne r mre pneumatic actuatrs f a system, prviding prper cntrl and reliable results. Fig 8: LVDT system with single-rd 6

7 Internatinal Jurnal f Cmputer Applicatins ( ) Vlume 168 N.10, June ACKNOWLEDGMENTS All authrs wuld like t express their gratitude t the Pst- Graduate Prgram f Studies Autmatin f Prductins and Services f PUAS, fr the financial supprt t undertake this research prject 6. REFERENCES [1] Hydraulic-Pneumatic systems and Applicatins, Athanasis T. Rutulas, Cntemprary Publicatins, Athens,, [2] Thesis: Mvement cntrl in the pneumatic systems, N. Themelis, Department f Mechanical, Natinal Technical University f Athens,, [3] Infrmatin paper: Intrductin t Pneumatic Systems, I. Ligns, P. Buslis, G. Plitis, G. Chamilthris, Electrical Sectr, Regin Training Center, Iannina,, [4] Autmatin and Autmatic Cntrl Systems, Part A, I. Ligns, P. Buslis, G. Plitis, G. Chamilthris, Electrical Sectr, Athens, [5] Paper #: A High Perfrmance Pneumatic Frce Actuatr System Part 1 - Nnlinear Mathematical Mdel, Edmnd Richer and Yildirim Hurmuzlu, Suthern Methdist University, Schl f and Applied Science, Mechanical Department, Dallas, [6] Paper #: Mathematical And Simulink Mdel Of The Pneumatic System With Bridging Of The Dual Actin Cylinder Chambers, Vladislav Blagjević, Midrag Stjiljkvić, Faculty f Mechanical Niš, University f Niš, Vl. 5, N 1, [7] Thesis: A cmparative Investigatin Int Prprtinal- Integral-Derivative Cntrl Methds fr Accurate Psitin Cntrl f Linear Pneumatic Actuatrs, M.G. Paputsidakis, University f the West f England, Bristl, UK, [8] Paper #: An Analysis f a Pneumatic Serv System and Its Applicatins t a Cmputer-Cntrlled Rbt, S. Liu and J. E. Bbrw, Jurnal f Dynamic Systems, Measurement and Cntrl, vl 110, PP , [9] Paper #: Nn-cnventinal adaptive cntrl f a servpneumatic unit fr vertical lad psitining, C. Ferraresi, P. Giraud, G. Quaglia, West Technical Cnference, [10] Paper #: Variable Structure Cntrl f a Pneumatic Actuatr, Tang J. and Walker G., Transactins f the ASME, vl.117, pp.88-92, [11] Thesis: Cntrl wind turbine inductin mtr squirrel cage using fuzzy lgic, C. Kkktas, Department f Electrical and Cmputer, University f Patras,, [12] Lab Ntes: Sensrs-Interfaces, C. Tsns, Department f Electrnics, University f Applied Sciences, Central, [13] New scpe fr interactin between humans and machines rsch_fc_exhand_en_l.pdf IJCA TM : 7