An Architecture for Adaptive Fuzzy Control in Industrial Environments

Transcription

1 An Archtecture for Adaptve Fuzzy Control n Industral Envronments Jérôme Mendes a, Ru Araújo a,b, Pedro Sousa c,b, Flpe Apóstolo c,b, Luís Alves a a DEEC-Department of Electrcal and Computer Engneerng Unversty of Combra, Pólo II; PT Combra, Portugal b ISR-Insttute of Systems and Robotcs; Unversty of Combra, Pólo II; PT Combra, Portugal c AControl - Automaton and Industral Control, Ltd; Parque Empresaral de Eras, Lote 5; PT Combra, Portugal Abstract The paper presents an archtecture for adaptve fuzzy control of ndustral systems. Both conventonal and adaptve fuzzy control can be desgned. The control methodology can ntegrate a pror knowledge about the control and/or about the plant, wth on-lne control adaptaton mechansms to cope wth tme-varyng and/or uncertan plant parameters. The paper presents the fuzzy control software archtecture that can be ntegrated n ndustral processng and communcaton structures. It ncludes four dstnct modules: a Mathematcal Fuzzy Lbrary, a Graphcal User Interface (GUI, Fuzzy Controller, and Industral Communcaton. Three types of adaptve fuzzy control methods have been studed, and compared: 1 drect adaptve, 2 ndrect adaptve, and 3 combned drect/ndrect adaptve. An expermental benchmark composed of two mechancally coupled electrcal DC motors has been employed to study the performance of the presented control archtectures. The frst motor acts as an actuator, whle the second motor s used to generate nonlneartes and/or tme-varyng load. Results ndcate that all tested controllers have good performance n overcomng changes of DC motor load. Keywords: Fuzzy Control, Adaptve Control, Lyapunov Stablty, Mathematcal Fuzzy Lbrary, Software Archtecture, Industral Communcaton, DC Motor. 1. Introduton The frst Fuzzy Logc Control (FLC system was developed by Mamdan and Asslan [1], [2], to be used n a small steam engne. Snce then, FLC has used for extensve applcaton n a wde varety of ndustral systems and consumer products and has attracted the attenton of many researchers. A major applcaton of fuzzy theory has been n control of nonlnear systems. Nonlnear processes are typcally dffcult to model and control. A lot of theoretcal research has been developed n ths feld. If the mathematcal model of the plant s known, then n many cases conventonal control may be used to provde a soluton. On the other hand, fuzzy logc control should be used n stuaton where mathematcal model s poorly undestood or unknown, and where expert human knowledge (e.g. experenced operators s avalable and can descrbe the control of the plant. A number of mportant complex control problems such as 1 stablzaton and trackng process output sgnals, 2 presence of nonlneartes, 3 presence of dsturbances, and 4 tme varyng parameters, are not suffcently studed and have to be further researched. In [3], a fuzzy controller s proposed 1 for controllng the temperature of a multple hearth furnace plant where fast and extensve changes n operatng condtons occur, complcated by non-lnear and tmevaryng behavor of the process and nteracton between the dfferent varables. In [4], an embedded statc fuzzy control system case study for machnng processes has been presented. However, such system would requre further work n order to refne the fuzzy controller s performance and so to mprove the transent response. In [5], a real-tme expermental study of a fuzzy PID control of a DC motor s presented. However, the system does not consder controller auto-adaptaton to mprove performance n face of plant changes. In [6], a Lnear Matrx Inequalty (LMI-based method wth pole-placement constrant s presented to desgn a stable fuzzy control system. In [7], genetc algorthms are employed to desgn a fuzzy logc controller n smulaton, and expermental results are presented. In [8], a PI predctve fuzzy controller s presented for electrcal drve speed control. In [6], [8], smulatons have valdated the feasblty of the proposed methods. The systems presented n [3] [8], use plant models, and do not consder controller onlne auto-adaptaton mechansms

2 to take nto account and overcome complex and/or unknown tme-varyng plant behavor and system dsturbances, and n partcular to mprove performance under such condtons. The development of adaptve fuzzy control methodologes can be used to cope wth the above mentoned dffcultes [9] [13]. Adaptve systems are generally used to control structures whose parameters are unknown and/or tme-varyng. Adaptve fuzzy controllers can be classfed nto two categores [14]: drect and ndrect adaptve controllers. In drect adaptve fuzzy control, the parameters of the controller ntally constructed from human control knowledge, and the teratvely adjusted to reduce the output error between the plant and a reference model. Indrect adaptve fuzzy control, are ntally constructed from human knowledge about the unknown plant, and then teratvely adjusted to reduce the output error between the plant and a reference model. Ths paper presents a general purpose archtecture for adaptve fuzzy control of ndustral systems. Both conventonal and adaptve fuzzy control can be desgned. The control methodology can ntegrate a pror knowledge about the control and/or about the plant, wth onlne control adaptaton mechansms to cope wth tmevaryng and/or uncertan plant parameters. Integraton of a pror knowledge s performed n the form of fuzzy If-Then rules not requrng specfc mathematcal/physcal models. The paper presents the fuzzy control software archtecture that can be ntegrated n ndustral processng and communcaton structures. It ncludes four dstnct modules: a Mathematcal Fuzzy Lbrary, a Graphcal User Interface (GUI, a Fuzzy Controller, and Industral Communcaton. Three types of adaptve fuzzy control methods have been studed, and compared: 1 drect adaptve, 2 ndrect adaptve, and 3 combned drect/ndrect adaptve. The adaptve control schemes use fuzzy systems to approxmate unknown nonlnear functons of the plant. Ths s theoretcally supported by the fact that fuzzy logc systems are unversal approxmators [15]. The parameters of fuzzy systems are adjusted by adaptve laws desgned wth Lyapunov methods [16]. The stablty s guaranteed by the Lyapunov synthess approach [9]-[11]. An expermental benchmark composed of two mechancally coupled electrcal DC motors has been employed to study the performance and demonstrate the effectveness of the presented control archtectures. The frst motor acts as an actuator, whle the second motor s used to generate nonlneartes and/or tme-varyng load. Results ndcate that all tested controllers have good performance n overcomng changes of DC motor load. The system 2 exhbts nose, parastc electro-magnetc effects, frcton and other phenomena commonly encountered n practcal applcatons. The paper s organzed as follows. Secton 2 ntroduces the fuzzy logc system. Secton 3 presents adaptve fuzzy controllers. The software archtecture s descrbed n Secton 4. Secton 5 presents the expermental setup. In secton 6, the results of experments are presented and analysed. Fnally, Secton 7 makes concludng remarks. 2. Fuzzy Systems Ths secton brefly overvews the man concepts of fuzzy systems. Fuzzy systems can be used to mplement fuzzy controllers. A fuzzy system s a knowledge-based system defned by a group of IF-THEN rules. The followng s an example of such a rule: IF the speed of a car s hgh, (1 THEN apply less force to the accelerator where speed and force are nput and output varables, respectvely. These varables are defned by semantc terms, assocated to fuzzy sets hgh and less. A fuzzy set A s characterzed by a mappngµ A (x=u [0, 1]. Fgure 1: Basc confguraton of fuzzy logc systems. The confguraton of the fuzzy system s shown n Fg.1. It conssts of four elements: knowledge base, fuzzfer, fuzzy nference engne and defuzzfer. The knowledge base conssts a rule base composed of a set of N fuzzy IF-THEN rules R j of the form R j : IF x 1 s A j 1, and... and x n s A j n THEN y s B j, (2 where j=1, 2,..., N, x (=1, 2,..., n are nput varables of the fuzzy system, y s the output of the fuzzy system. The knowledge-base s an mportant component of the fuzzy system snce all other components use t, and t s here that system knowledge resdes.

3 Table 1: S-Norms and T-norms S-norm (OR T-norm (AND Maxmum max(a, b Mnmum mn(a, b Bounded sum mn(1, a + b Bounded product max(0, a + b 1 Algebrac sum a + b ab Algebrac product ab The fuzzy rules are composed of two parts: the antecedent (IF part and consequent (THEN part. A j and B j are lngustc terms characterzed by fuzzy membershp functonµ A j(x andµ B j (y, respectvely. Examples of membershp functons are represented n Fg.2. The fuzzfer maps the real values of x of the nput lngustc varables nto fuzzy sets descrbed by membershp functons X. The fuzzy nference engne (FIE uses the collecton of fuzzy IF-THEN rules to map the nput fuzzy set X nto the rules consequents fuzzy sets B j. The collecton of fuzzy outputs of the rules s combned nto an overall nferred fuzzy output Y. In the FIE, the frst step s to process each rule ndvdually. The processng of the rules antecedents composed of propostons connected by the fuzzy AND operator s performed usng T-norms. OR operators can also be employed to connect antecedent propostons. OR operators are mplemented usng S -norms. Table 1 presents examples of T-norms and S -norms. The fuzzy NOT operator can also be used n fuzzy propostons: t s processed by fuzzy complement operators. After calculatng the antecedent value, fuzzy propostons (antecedent and consequent are nterpreted as fuzzy relatons usng an mplcaton operator. In fuzzy logc, the sentences IF A THEN B can be wrtten as A B, where A and B are the fuzzy propostons whose values are fuzzy sets, and s a fuzzy mplcaton. Typcally used mplcaton operators are the Mamdan Mnmum and Mamdan Product mplcatons. Assumng C=A B, a=µ A (x, b=µ B (x, c=µ C (x, then Table 2a defnes these two operators. The next step s to aggregate the outputs of all fuzzy rules wth aggregaton methods. In ths process the output fuzzy sets of rules are combned nto an overall output fuzzy set of the system, whch s used as the nput to the defuzzfer. Table 2b gves examples of aggregaton methods where the fuzzy outputs A, and B, of two rules are combned nto a fuzzy set C. There s Table 2: a Fuzzy mplcaton methods for C = A B, b Man aggregaton methods. Aggregaton of A, and B nto C. (a Mnmum mn(a, b Product c ab (b Bounded sum mn(a + b, 1 Maxmum max(a, b c Fgure 2: Examples of trapezodal, trangular and gaussan membershp functons. 3 a varety of choces for the fuzzy nference engne, dependng on the employed operators for the S -norm and T-norms, and the mplcatons and aggregaton methods [14]. An example s the Product Inference Engne whch uses the Mamdan product mplcaton, algebrac product for the T-norms and maxmum for S -norms. The defuzzfer s defned as a mappng from a fuzzy set Y (n ths case, correspondng to the output lngustc varable of the fuzzy nference engne nto a real valued output, y. There are also several possble choces for the defuzzfer to be assocated wth the fuzzy nference engne. The choces are avalable for the control desgner and can take nto account, for example, the computatonal effcency. Let y, and hgt(y be the center and heght (maxmum attaned membershp value of fuzzy set Y, respectvely. Center of gravty, centre of area, frst of maxma, last of maxma, and the center average are commonly used defuzzfers n fuzzy control (Table 3, and [14]. 3. Adaptve Fuzzy Control To desgn the ndustral fuzzy control archtecture consder a class of nonlnear dynamc systems modeled by the followng dfferental equaton, whch encompasses a wde range of relevant ndustral systems: x (n = f (x+g(xu, (3 y = x, where x=[x 1, x 2,, x n ] T = [ x, ẋ,, x (n 1] T s the state vector, u s the control nput, y s the output of the system, and f (x and g(x are unknown contnuous functons. Wthout loss of generalty, t s assumed that g(x > 0. The adaptve control methodologes presented n the sequel are able to cope wth sgnfcant msmatches between the real plant and model (3.

4 Table 3: Commonly used defuzzfer methods. Center of gravty y = Centre of area y = y, y Frst of maxma Last of maxma Center average y = max mn yµ Y (ydy max mn µ Y (ydy mn µ Y(ydy= max y µ Y (ydy y = n f{y hgt (Y} hgt (B ={y v µ Y (y=sup y v µ Y (y} y = sup{y hgt (Y} hgt (Y={y v µ Y (y=sup y v µ Y (y} Ml=1 y l hgt(y l Ml=1 hgt(y l A generc adaptve control scheme s represented n Fg. 3. As can be seen, the scheme conssts of the plant, the controller and the adaptaton law. In ths work, the fuzzy controller s composed of fuzzy systems (7 whch have adjustable parameters to be adjusted by an adaptaton law. Let functons f (x and g(x be known, k = [k n,, k 1 ] T be chosen such that the roots of polynomal h s = s n + k 1 s n 1 + +k n are n the open left-half plane, and the control law be: u = 1 [ f (x+y (n m + k T e ], (4 g(x where y m s the reference model output sgnal, e = [ e, ė,, e (n 1 ] T and e = y ym. If control law (4 s appled to (3 then the followng equaton holds e (n + k 1 e (n k n e=0, (5 and lm t e (t=0 whch s the man objectve of control. The fuzzy logc systems (Fg. 1 used on adaptve fuzzy controllers presented n ths paper are composed by: sngleton fuzzfer (drect representaton of a number by a fuzzy set, center-average defuzzfer, and the product nference engne [9]. In these condtons, consderng rules (2, the fuzzy system mplements the followng functon: h (x= N j=1 y j ( n =1 µ A j (x N n=1 j=1 µ A j (x, (6 where y j s the center of B j. Equaton (6 can be rewrtten as: h (x=θ T ξ (x (7 whereθ= [ ] y 1,, y T N s a parameter vector wth adjustable parameters andξ (x= [ ξ 1 (x,,ξ N (x ]T s a vector defned as: n=1 µ A j (x ξ j (x= n=1, j=1,..., N. (8 µ j A (x N j=1 Is has been proven that fuzzy logc systems (6 are unversal approxmators [17]. Thus, they wll be used to approxmate unknown nonlnear functons. 4 Fgure 3: Generc adaptve control scheme Indrect adaptve control It s assumed that functons f (x and g(x are unknown. Some plant knowledge about f (x and g(x s employed to desgn the ntal control soluton n the ndrect adaptve fuzzy controller. Fuzzy systems n the form of (7 are used to approxmate f (x and g(x. The knowledge about the plant s assumed to be expressed wth the followng two sets of fuzzy IF-THEN rules (wth j=1,..., N of the form (2 to descrbe the behavor of f (x and g(x, respectvely: R f j : IF x 1 s F j 1, and... and x n s F j n THEN f (x s C j (9 R g j : IF x 1 s G j 1, and... and x n s G j n THEN g(x s D j (10 Thus, the followng fuzzy systems of the form (7 are used to approxmate f (x and g(x: ˆ f ( x θ f =θ T f ξ f (x, (11 ĝ ( x θ g =θ T g ξ g (x, (12 where θ f and θ g are adjustable parameters, and [ ξ f (x = ξ f,1 (x,,ξ f,n (x ] T and ξ g (x = [ ξg,1 (x,,ξ g,n (x ] T are defned smlarly to (8 [but now for rules (9-(10]. They are the centers of consequent fuzzy sets of rules (9-(10 whch are to be adapted. If functons f (x and g(x are replaced wth ther fuzzy approxmatons (11 and (12, then the followng control law s obtaned: u= 1 ĝ ( x θ g [ ˆ f ( x θ f + y (n m + k T e ] (13

5 The adaptve laws are derved by Lyapunov synthess wth the followng Lyapunov functon [9]: V= 1 2 et Pe+ 1 2γ f φ f T φ f + 1 2γ g φ g T φ g (14 whereγ f andγ g are postve constants. Functon (14 takes n account the trackng error e and the adjustable parameter errorsφ f = ( θ f θ f andφg = ( θ g θ g, whereθ f andθ g are the optmal parameters ofθ f and θ g, respectvely, to attan optmal mn-max approxmaton error of f (x and g(x. P s s a postve-defnte matrx satsfyng the followng Lyapunov functon: Λ T P+PΛ= Q (15 where Q s an arbtrary n n postve-defnte matrx, andλs a matrx that can be drectly depends on k, and can be desgned to attan the desred error dynamcs (5 [9]. The employed adaptaton laws are [9]: θ f = γ f e T p n ξ f (x (16 θ g = γ g e T p n ξ g (xu (17 where p n s the last column of P Drect adaptve control Instead of knowledge about the plant (as n Sec. 3.1, to desgn a drect adaptve fuzzy controller some knowledge about adequate plant control actons are used to desgn an ntal control soluton. The control knowledge can be provded for example by human knowledge, and s assumed to be expressed as a set of N fuzzy IF-THEN rules of the form: R D j : IF x 1 s U j 1, and... and x n s U j n THEN u s E j (18 To use the knowledge about the control (18 the followng fuzzy system of the form (7 s used for the controller: u=u (x θ D =θ T D ξ D (x, (19 where θ D s a vector of adjustable parameters, and ξ D (x= [ ξ D,1 (x,,ξ D,N (x ]T s defned smlarly to (8 [but now for rules (18]. Let u be the deal control (4 that would be obtaned f f (x and g(x were known. Smlarly to the ndrect case (Sec. 3.1, the adaptve laws are derved by Lyapunov synthess. The followng Lyapunov functon used [9]: V= 1 2 et Pe+ 1 2γ D ( θ D θ D T ( θ D θ D (20 whereγ D s a postve constant, andθ D are the optmal values of the parametersθ D that optmze the mn-max 5 approxmaton error between u and u. The employed adaptaton law s [9]: where p n s the last column of P Combned adaptve control θ D =γ D e T p n ξ D (x, (21 In the combned adaptve control approach, the control s composed of a weghted average of ndrect (Sec. 3.1 and drect (Sec. 3.2 adaptve controls. To smplfy the process of computer calculaton t s consdered that g(x=gs constant. Thus, n ths case the controller s: { 1 u=α g [ ˆ f ( x θ f + y (n m + k T e ]} + (1 α u (x θ D (22 Smlarly to the ndrect and drect models, and after some manpulaton, the followng adaptaton laws are obtaned [13]: θ f = γ f e T p n ξ f (x (23 θ D =γ D ge T p n ξ D (x (24 4. Software Archtecture Ths secton presents the developed fuzzy control software archtecture. It mplements the methods presented n Sectons (2 and (3. The archtecture s based on the followng four dstnct modules. Mathematcal Fuzzy Lbrary: Ths module mplements a complete set of mathematcal fuzzy logc concepts and methods, ncludng the fuzzy logc/control theory and the adaptve fuzzy control technques. The software s organzed as a herarchcal structure, permttng to append and remove methods, wthout modfcaton of other resources. Graphcal User Interface (GUI: Ths module s mplemented wth the objectve of permtng the desgn and specfcaton of a fuzzy system or controller by the user n an easy and ntutve approach. The use of common graphcal resources (such as buttons, menus, comboboxes, etc are preferred over textual programmng technques. When the user fnshes the system specfcaton, a fle specfyng the knowledge base s generated. Ths type of fle wll be denoted by fuzzy fle. Fuzzy Controller: Ths module generates and mplements the controller usng the knowledge base recorded n fuzzy fles. The objectve of ths module s to communcate wth the feld devces and to control the process by the rules of the fuzzy controller. The user can

6 nteract wth ths module by turnng on/off the control loop, or by loadng the fuzzy fle. Industral communcaton: Ths module of the software archtecture permts communcaton on real-tme ndustral control plants wth control devces from dfferent manufacturers. The communcaton s performed wth OPC (OLE (Object Lnkng and Embeddng for Process Control standard. Through the OLE nterface, the fuzzy control software s able to get data from sensors and send control actuaton commands to feld devces dstrbuted over a ndustral plant. The organzaton of the system usng these modules has the advantage of permtng the development of mprovements on the modules separately, usng experts from dfferent areas. Another advantage s to permt a dstrbuted approach, n the sense that the system where the controller s desgned may not be the same as the system where the control s processed Mathematcal Fuzzy Lbrary Archtecture The man problem when developng an applcaton concernng Fuzzy methods s the exstence of a varety of dfferent fuzzy concepts and methods. For example, Secton 2 presents the defnton of Fuzzy varable, and shows that a fuzzy rule can ntegrate dfferent fuzzy sets. In other areas of fuzzy theory, varous optons are also present. To attan a generc fuzzy system n software, t s mandatory to support multple optons on the fuzzy components. The mathematcal fuzzy lbrary mplements background concepts and methods that used on controllers. The global software archtecture s capable of mplementng a largely generc fuzzy system. Object-orented programmng technques were ntensvely used on the development of the lbrary, wth specal focus on the concepts of dervaton and polymorphsm of classes. The objectve s to have some base nterfaces, one per fuzzy component, where the procedures are only declared. The mplementaton of declared procedures s done n derved objects. Ths permts the development of varous methods and varants for the same component, wthout changng the structure of the software. The global structure s presented n Fg. 4. The lbrary uses polymorphsm technques whch allows values of dfferent data types to be handled usng a unform nterface. Both data types and functons can exhbt polymorphsm (parametrc polymorphsm. The presented archtecture permts ndependent research and extenson of the varous fuzzy components wth low mpact on the overall system. The extensblty s an mportant property of ths lbrary. 6 Fgure 4: Lbrary global archtecture Graphcal User Interface The software archtecture ncludes a graphcal user nterface (GUI for the complete specfcaton of fuzzy controllers wth common wdgets and actons. Fgure 5 presents a screenshot of the GUI. The fuzzy compo- Fgure 5: Fuzzy GUI. nents can be selected and organzed from the components avalable on the Fuzzy lbrary to specfy a complete fuzzy controller. Ths approach does not requre

7 ÎÐÓØÝ ÖÔÑ» textual programmng technques, and thus tends to decreases programmng errors. The system specfed by the user can be recorded n a fle ( fuzzy fle, usng ether a custom language or the standard FCL language [18], and subsequently mported by the Fuzzy controller module that mplements the desgned controller. 5. Expermental Setup The expermental system conssts of two coupled DC motors (Fg. 6, where the frst motor acts as an actuator, whle the second motor s used to generate nonlneartes and/or a tme-varyng load. The system exhbts nose, parastc electro-magnetc effects, frcton and other phenomena commonly encountered n practcal applcatons, that make the control task more dffcult. The man am s to perform constant velocty control whle the load of the DC motor s changed. The only measured varable n for the fuzzy controller n ths experment s the motor speed. Ths smplfes the process and makes more easy the specfcaton of fuzzy rules by human operators. The velocty unts are rpm/10 (rotatons per 100 mllseconds. The generator has an electrcal load composed of a varable number of leds connected n parallel. When the number of connected leds decreases, the electrcal load to the generator s decreased, and consequently the mechancal load that the generator apples to the motor also decreases. Thus, by changng the number of connected leds t s possble to change the mechancal load to the motor, and consequently change ts model. speed. Thus, the encoder resoluton s 26 pulses per revoluton (PPR whch s poor and leads low resoluton velocty measures, whch n turn makes the control task more dffcult. The control software (Secton 4 runs on a PC that communcates by OPC to a PLC (Mcrologx 1200 expanded wth an analog I/O module for sgnal condtonng. The PLC provdes the voltage command sgnal to the DC motor through the sgnal condtonng crcut. Ths crcut also nterfaces the encoder to the PLC. The samplng perod s 100 ms. 6. Expermental results In all experments, the objectve s to control the system output at a constant value of y m = 13 [RPM/10]. The chosen control parameters were k 1 = 2, P=[5], and the adjustable parameters are ntalzed wth the centers of the consequent fuzzy sets of the rules (typcally obtaned from human knowledge. Tunng of controllers constant parametersγ f,γ g, andγ D, s easly performed manually. In Fg. 7 t can be observed that when a constant voltage s appled to the motor (wthout any control and the motor load s changed, then the motor velocty changes (by about 30% n ths example. It can also be observed that, due to the low encoder resoluton, the velocty s not perfectly constant. ¾ ÌÑ Fgure 7: Velocty of the DC motor for constant nput voltage and load changes. Fgure 6: The expermetal scheme Hardware overvew The hardware conssts of two DC motors (Transmotec, SD3039 whose command sgnal s the voltage wth range [ 12, 12] [V]. Both DC motors have a rated speed of 258 rpm and have coupled a magnetc Hall effect encoder wth 13 magnetc poles to measure motor Indrect Adaptve control To desgn an ndrect adaptve fuzzy controller (Sec. 3.1, some plant plant knowledge s requred. Ths entals the defnton of the fuzzy models (rules and membershp functons of f ˆ(x and ĝ(x that respectvely approxmate f (x and g(x of (3. The fuzzy models were extracted from human nspecton of the DC motor model (25: ẋ (t= K Vk T JR x (t+ K T JR υ a (t (25

8 ÎÐÓØÝ ÖÔÑ» ÎÓÐØ Î º º º ¹ ¹¾ ¹ ¾ x Ò¹ÐÖ Ò¹ ÑÐÐ ÁÒ ÒÒØ Ô¹ ÑÐÐ Ô¹ÐÖ º º º ÁÒ ÒÒØÜ ¹ ¹¾ ¹ ¾ x º º º ¹ ¹¾ ¹ ¾ ex = ym x Ò¹Ò Ò¹ Ò¹ÐÖÖ ÁÒ ÒÒØ Ô¹ÐÖÖ Ô¹ Ô¹Ò º º º ¹ ¹ ¹ ¹¾ ¾ f(x Ò¹ Ø Ò¹ ÐÓÛ ØÐÐ Ô¹ ÐÓÛ Ô¹ Ø º º º ØÐÐÜ ¾ ¾ g(x º º º ¹ ¹ va Ò¹ÐÑØ Ò¹ Ø Ò¹Ö ØÐÐ Ô¹Ö Ô¹ Ø Ô¹ÐÑØ (a (b (c Fgure 8: (a, (b, (c, represent the fuzzy membershp functons of rules (9, (10 (ndrect control, and (18 (drect control, respectvely. Upper plots: fuzzy membershp functons of the antecedent parts of the rules. Lower plots: ntal fuzzy membershp functons of the consequent parts of the rules. where x(t s the motor velocty,υ a (t s the command voltage, R s the armature resstance, J s the overall moment of nerta, and K V and K T are postve constants. In other systems the fuzzy model can be formulated from human analyss of plant operaton. Let x= [ ] T x 1 = [x] T. From (3 and (25 t can be seen that f (x= K V k T JR x, (26 g(x= K T JR. (27 The fuzzy system ˆ f (x was defned by 5 fuzzy IF- THEN rules. Snce g(x does not depend of motor velocty and s constant, then only one rule s used to mplement ts approxmator ĝ(x. Fgs. 8a, and 8b llustrate the fuzzy membershp functons of the antecedent (upper plots and ntal consequent (lower plots parts of rules (9, and (10, respectvely. The gans on adaptaton laws (16 and (17 have been chosen asγ f = 0.4 andγ g = Fgure 9 presents the results of adaptve ndrect fuzzy control. Mechancal load changes n the motor (thus also motor model changes have been ntroduced approxmately at nstants 29 [s], 47 [s], 60 [s], and 79 [s] Drect Adaptve control To desgn a drect adaptve fuzzy controller some control knowledge s requred (Sec In ths experment, the velocty error s the only antecedent varable used n (18. The control knowledge was characterzed by 7 fuzzy rules that were desgned takng nto account that the voltage range of motor s [ 12, 12] [V]. Fg. 8c llustrates the fuzzy membershp functons of the antecedent (upper plots and ntal consequent (lower 8 θf ¾ ¹ ¾ ÌÑ ¹ ¾ ÌÑ θg ¾ ¾ ¾ ÌÑ ¾ ¾ ÌÑ Fgure 9: Results of ndrect adaptve fuzzy motor control. Frst lne: motor velocty and appled voltage. Second lne: temporal evoluton of the adjustable parameters of f ˆ(x and ĝ(x, respectvely. plots parts of rules (18. The gan on adaptaton law (21 was chosen asγ D = 0.1. Fgure 10 presents the results of adaptve drect fuzzy control. Mechancal motor load changes have been ntroduced approxmately at nstants 25 [s], 44 [s], 54 [s], and 75 [s] Combned Adaptve control For the combned adaptve control, the same knowledge (fuzzy rules and membershp functons as n Secs. 6.1 and 6.2 has been used, wth g (x=15 beng constant. The gans of adaptaton laws (23 and (24 have been chosen asγ f = 0.1 andγ g = 0.4. Fgure 11 presents the results of combned adaptve fuzzy control. Mechancal motor load changes have been ntroduced approxmately at nstants 19 [s], 35 [s], 44 [s], and 60 [s].

9 ÎÐÓØÝ ÖÔÑ» ÎÐÓØÝ ÖÔÑ» θd ÎÓÐØ Î ÎÓÐØ Î ¾ ¹ ¾ ÌÑ ¹ ¹ ¾ ÌÑ ¾ ¾ ¾ ÌÑ Fgure 10: Results of drect adaptve fuzzy motor control. Frst lne: motor velocty and appled voltage. Second lne: temporal evoluton of the controller adjustable parameters. θd ¾ ¾ ¹ ¾ ÌÑ ¹ ¾ ÌÑ θf ¾ ¾ ¾ ÌÑ ¹ ¹ ¾ ÌÑ Fgure 11: Results of combned model wth followng sequence. Frst lne: motor velocty and voltage appled. Second lne: temporal evoluton of the adjustable parameters of the controller and of f ˆ(x, respectvely. a smlar response wth an adaptaton mechansm workng adequately. The temporal evoluton of the adjustable parameters of the controller s also shown n Fgs. 9, 10 and 11. Snce t s not guaranteed that the controller fuzzy rules (that represent knowledge about the plant and/or the control have good ntal qualty, the fuzzy rules are adapted ntally (ntal sample tmes. Therefore, t s concluded that t s possble to control the system even f the ntal knowledge about the plant and/or control s not of good qualty. When the load of the DC motor s changed, then the rules are agan adjusted takng nto account the correspondng changes n the system model. Note that some parameters reman constant durng the tests. These parameters belong to rules that do not have effect for the specfc values that the relevant process varables take durng the presented experments. It s concluded that all controllers can control the system even when changes to the characterstcs of the system are appled. In general, the presented adaptve fuzzy control methodologes can cope wth changes n the system load, as well as n the other parameters of the plant. The load can be of any type, such as electrcal, mechancal, chemcal, etc. A change n plant parameters nfluences/leads the presented control methods to auto-adapt to adequately control the plant n the new stuaton, resultng n an mprovement of closed loop system performance n the new stuaton. The results also show the performance of the presented software archtecture for controllng systems usng OPC-based real-tme ndustral command and control structures Analyss of Results and Dscusson From the results shown n Fgs. 9, 10 and 11, t can be seen that, n all tested controllers, the controller s able to adequately (attan and control the system output at the desred value of 13 [rpm/10]. In terms of ntal response of the controller, t can be seen that the ndrect model presents a smoother response than drect model. However, the ndrect model has a hgher overshoot. On the other hand, the combned model, whch has knowledge both about the plant and the control, has an ntal response whch s smoother and wth small(er overshoot. When the load of the DC motor s changed the velocty s temporarly affected by around 4 [rpm/10] (about 30 % of the reference sgnal. Even wth these plant changes, n average all controllers elmnate ths dsturbance n 12 samplng tmes. All algorthms have shown 9 7. Concluson In ths paper, ndrect, drect and combned adaptve fuzzy control schemes have been studed and compared. The controllers are able to use ntal knowledge (e.g. human knowledge about the plant (ndrect and combned methods and/or the control (drect and combned methods provdng an ntal fuzzy control soluton. Afterwards, the operaton of the system teratvely adjusts the controller parameters to attan better control solutons and to adapt to changes n plant parameters. An expermental benchmark consstng of two coupled DC motors have been used for comparson studes. The expermental setup exhbts nose, parastc electro-magnetc effects, frcton and other phenomena commonly encountered n practcal applcatons. Load/model changes were ntroduced n DC motor. The expermental results ndcate that all tested

10 controllers have good performance even n response to changes n the DC motor load/model. It s concluded that the best adaptve controller s the combned model. However, f the knowledge about the plant s unknown, the drect adaptve controller often can be used snce t shows also good results, and typcally n such cases t s easer to provde control knowledge than to provde plant knowledge. The results also show the performance of the presented software archtecture for controllng systems usng OPC-based real-tme ndustral command and control structures. Acknowledgement Ths work was supported by Mas Centro Operaconal Program, fnanced by European Regonal Development Fund (ERDF, and Agênca de Inovação (AdI under Project SInCACI/3120/2009. [12] M. Hojat, S. Gazor, Hybrd adaptve fuzzy dentfcaton and control of nonlnear systems, IEEE Trans. Fuzzy Systems 10 (2 ( [13] C.-H. Wang, H.-L. Lu, T.-C. Ln, Combned drect/ndrect adaptve fuzzy-neural control wth state observer & supervsory controller for unknown nonlnear dynamc systems, n: IEEE Internatonal Conference on Fuzzy Systems, 2001, pp [14] L.-X. Wang, A Course n Fuzzy Systems and Control, Prentce- Hall, Inc., Upper Saddle Rver, NJ, USA, [15] L.-X. Wang, J. Mendel, Fuzzy bass functons, unversal approxmaton, and orthogonal least-squares learnng, IEEE Transactons on Neural Networks 3 (5 ( [16] J.-J. Slotne, W. L, Appled Nonlnear Control, Prentce-Hall, Englewood Clffs, NJ, USA, [17] L.-X. Wang, Fuzzy systems are unversal approxmators, n: Proceedngs of the IEEE Internatonal Conference on Fuzzy Systems, 1992, pp [18] Programmable controllers part 7: Fuzzy control programmng, Internatonal standard CEI/IEC :2000, IEC- Internatonal Electrotechncal Commsson, Geneva, Swtzerland (2000. References [1] E. H. Mamdan, Applcaton of fuzzy algorthms for smple dynamc plant, Proceedngs of the IEEE 121 ( [2] E. H. Mamdan, S. Asslan, An experment n lngustc synthess wth a fuzzy logc controller, Internatonal Journal of Man- Machne Studes 7 (1 ( [3] M. Ramírez, R. Haber, V. Peña, I. Rodríguez, Fuzzy control of a multple hearth furnace, Computers n Industry 54 (1 ( [4] R. E. Haber, J. R. Alque, A. Alque, J. Hernández, R. Urbe- Etxebarra, Embedded fuzzy-control system for machnng processes results of a case study, Computers n Industry 50 (3 ( [5] C. M. Lm, Implementaton and expermental study of a fuzzy logc controller for dc motors, Computers n Industry 26 (1 ( [6] S. K. Honga, Y. Nam, Stable fuzzy control system desgn wth pole-placement constrant: an lm approach, Computers n Industry 51 (1 ( [7] G. Acosta, E. Todorovch, Genetc algorthms and fuzzy control: a practcal synergsm for ndustral applcatons, Computers n Industry 52 (2 ( [8] R.-E. Precup, S. Pretl, G. Faur, P predctve fuzzy controllers for electrcal drve speed control: Methods and software for stable development, Computers n Industry 52 (3 ( [9] L.-X. Wang, Stable adaptve fuzzy controllers wth applcaton to nverted pendulum trackng, IEEE Transactons on Systems, Man, and Cybernetcs, Part B: Cybernetcs 26 (5 ( [10] L.-X. Wang, Stable adaptve fuzzy control of nonlnear cystems, n: Proceedngs of the 31st IEEE Conference on Decson and Control, 1992, pp [11] L.-X. Wang, Adaptve Fuzzy Systems and Control: Desgn and Stablty Analyss, Prentce-Hall, Inc., Upper Saddle Rver, NJ, USA, Jérôme Mendes was born n Compegne, France, Snce 1990 he s lvng n Portugal. He receved the B.Sc. and M.Sc. degrees n Electrcal and Computer Engneerng (Automaton branch from the Unversty of Combra n 2008 and 2009, respectvely. He s currently pursung hs Ph.D. degree n Electrcal and Computer Engneerng at the Unversty of Combra. Snce 2009, he s a Researcher at the Portuguese Insttute for Systems and Robotcs (ISR. Hs research nterests nclude genetc algorthms, predctve control, adaptve control and fuzzy control for ndustral processes. Ru Araújo receved hs B.Sc. degree ( Lcencatura n Electrcal Engneerng, the M.Sc. degree n Systems and Automaton, and the Ph.D degree n Electrcal Engneerng from the Unversty of Combra n 1991, 1994, and 2000 respectvely. He joned the Department of Electrcal and Computer Engneerng of the Unversty of Combra where he s currently an Assstant Professor. He s a foundng member of the Portuguese Insttute for Systems and Robotcs (ISR-Combra, where he s now a researcher. Hs research nterests nclude computatonal ntellgence, ntellgent control, learnng systems, fuzzy systems, neural networks, control, embedded systems, real-tme systems, soft sensors, ndustral systems, sensor-based moble robot navgaton, and n general archtectures and systems for controllng robot manpulators, and for controllng moble robots.

11 Pedro Sousa receved hs B.Sc. degree ( Lcencatura n ElectrcalandComputer Engneerng, fromthe Unversty of Combra n He s currently a researcher at Acontrol, Portugal. Hs research nterests nclude ntellgent control, soft sensors, embedded systems, real-tme systems, control, and ndustral systems. Flpe Apóstolo receved hs M.Sc. degree n Electrcal and Computer Engneerng, from the Unversty of Combra n He s currently a researcher at Acontrol, Portugal. Hs research nterests nclude fuzzy control, ntellgent control, control, and ndustral systems. ndustral systems. Luís Alves receved hs B.Sc. degree from Polytechnc Insttute of Tomar, n 2006, and the M.Sc. degree from the Unversty of Combra, n 2008, both n Electrcal and Computer Engneerng. He s currently a researcher at the Department of Electrcal and Computer Engneerng, Faculty of Scences and Technology, Unversty of Combra. Hs research nterests nclude embedded systems, real-tme systems, control, and 11