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Intelligent Position Control
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  IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 39, NO. 3, MAY/JUNE 2003 627 Implementation of anIntelligent-Position-Controller-BasedMatrix Formulation Using AdaptiveSelf-Tuning Tracking Control Ahmed Rubaai  , Member, IEEE   Abstract— This paper proposes an intelligent position controllerfor brushless motor drives and motion controls. The controller isbased on theory of the self-tuning tracking control. It integratesthe principles of fuzzy logic with learning functions of neuralnetworks into intelligent control architecture. A matrix formu-lation of a fuzzy-rule-based system is introduced. Consequently,a training-algorithm-based error function is also expressed ina matrix form. The resulting controller is significantly simplein structure and learning capability, and robust, and has hightracking performance (with respect to reference and measureddata). With the proposed controller the rotor position can traceany arbitrary selected trajectory without overshooting or over-stressing the hardware system. The entire system is designed andimplemented in thelaboratory usinga hardwaresetup. Theresultsof the laboratory testing are described in the paper. Compared tothe proportional-plus-integral controller, the proposed controlleryields a better dynamic performance with shorter settling time,without overshoot. Experimental results have shown that theproposed controller adaptively and robustly responds to a widerange of operating conditions.  Index Terms— Fuzzy logic control, high-performance motordrives, neural networks, neuro-fuzzy control, self-tuning control. I. I NTRODUCTION T HE requirement for high-performance drive systems invarious industry applications has produced great researcheffortintheapplicationofoptimalandadaptivecontrolmethods[1]–[3]. Using these control methods require exact mathemat- ical models such that, a high-performance controller can be de-signed and embedded. Nonetheless, the problem with these ap-proachesisthatpracticalmathematicalmodelsareoftencompli-cated,whichleadstodifficultcontrolalgorithmsthatmaynotbefeasible for practical implementations. Employing human lin-guistictermsandcommonsense,severalfuzzy-logic-basedcon-trollers have been developed to achieve high-accuracy tracking[4]–[6]. These fuzzy controllers have shown promise in dealing Paper MSDAD-A 03–01, presented at the 2001 Industry Applications So-ciety Annual Meeting, Chicago, IL, September 30–October 5, and approved forpublication in the IEEE T RANSACTIONS ON  I NDUSTRY  A PPLICATIONS  by the In-dustrial Automation and Control Committee of the IEEE Industry ApplicationsSociety. Manuscript submitted for review October 15, 2001 and released forpublication February 22, 2003.The author is with the Electrical and Computer Engineering De-partment, Howard University, Washington, DC 20059 USA (e-mail:rubaai@scs.howard.edu).Digital Object Identifier 10.1109/TIA.2003.811773 with nonlinear motor drive systems. Fuzzy logic control useshuman like linguistic terms in the form of   IF – THEN  rules to cap-ture the nonlinear system dynamics. Once in place, the fuzzyrules will not be able to adapt themselves to adequately capturethe dynamics of the system. To become adaptive, fuzzy logiccontrol must be able to learn to adjust its parameters in order tocapture the dynamics of the system. Artificial neural networks(ANNs)havealsofounduseinmotordrivesandmotioncontrols[7]–[13]. One of the major features of ANNs is their learning capability. Once trained, ANNs will be able to deal with thenonlinear terms of the controlled process. A drawback in usingan ANN for control is the choice in structural implementation,which is often difficult to decide how practical a structure is ac-tually required for the desired control. Besides, the implemen-tation is not at all intuitive and the hidden layers of the network are very much invisible to the designer.Recently, fuzzy logic adaptation has been explored. In fact,with the layer representation being explored by a number of authors [14]–[17], the possibility of systematic adaptation of a linguistic-rule-based system has become quite practical. Stillthese systems often rely on a simple second-order model of the system in order to adapt the inference mechanism. Otherfuzzy methods have focused on the derivation of coefficients,for which prior models were assumed [17]. Several adaptationstrategies of fuzzy logic control often involve offline training.Additionally, many implementations incorporated a multi-player approach to the control methodology that, althoughattractive, can become difficult to implement and update. Theneuro-fuzzy approach is a novel attempt by a number of authorsat implementing fuzzy reasoning while allowing for simplesystematic updates [18]–[21]. The neuro-fuzzy approach becomes very useful because it incorporates the intuitivenessof the fuzzy logic control while maintaining the trainability andadaptability of the neural network controller. Furthermore, forthe neuro-fuzzy implementation, most of the authors have useda model reference and neural network model to generate thetraining error for the online training algorithm.In this paper, both the fuzzy logic and neural networks areemployed together to design an intelligent controller for highperformance drives and motion controls. A position controllerwith learning ability is constructed and trained directly frominput and output data of the motor/converter/load dynamics.The controller is based on the adaptive self-tuning control, 0093-9994/03$17.00 © 2003 IEEE  628 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 39, NO. 3, MAY/JUNE 2003 Fig. 1. Schematic structure of the proposed control system. which does not require a pre-model formulation. The responseof the system is compared to the desired response selectedby the control system designer in advance. In the approachreported in this paper, adaptation of the fuzzy controllerinvolves rule output weight adjustment-based error signal. Thederivation of the training signal is a point of distinction of thiswork from previous publications that employ a predeterminedmodel. This paper employs somewhat different approach.In this approach, the training error is derived from the statevariables of the drive system, which are already available asopposed to using a predefined mathematical model. Onlinetraining is accomplished by updating the increment in theoutput matrix of the neural network. The training algorithm isbased on the supervised gradient decent method using a deltaadaptation law. The analysis, design, and experimental resultsof the resulting controller are presented in the paper.II. P ROPOSED  I NTELLIGENT  (N EURAL -F UZZY ) P OSITION C ONTROLLER In this section, both fuzzy logic principles and learning func-tions of neural networks are employed together to design an in-telligent-controller-based self-tuning tracking control. The in-tegration of both paradigms allows the merging of a currentintelligent control strategy, which is developed in the domainof neural networks, together with the representation of qualita-tive and cognitive rules in fuzzy logic control. The fuzzy ap-proach establishes a structural control framework to express theinput–output relationship of the neural network, and the neuralnetwork can introduce the most important features of compu-tation power and learning capability into the fuzzy controller.The schematic structure of the overall control system is showninFig.1.Itconsistsof:1)neuralfuzzycontroller(NFC);2)errormechanism; and 3) motor/converter/load. The NFC is a multi-player neural-network-based fuzzy controller. The error mech-anism is generated using an error function. To obtain the errorfunction, both the position error and the rate of change in theerror arenormalized usingabipolar activation function,therebymapping both of them to the unit interval. Then, the error func-tion is backpropagated using the Widrow–Hoff learning algo-rithm.The implementation of the proposed control system mainlycomprises two phases: the learning phase and the operationphase. In the learning phase, the purpose is to tune the outputof the NFC to achieve good control performance. In theoperation phase, the trained NFC is directly used to controlthe motor/converter/load dynamics. It should be noted that theproposed controller is of the incremental type. Therefore, theprevious output is added to the current output of theFLC . This provides the control signal which isthe input to the motor. Thus, . Fur-thermore, a voltage limiter is also included to limit the motorvoltage command to its nominal value. In this application, thelimit is set between 24 and 24 V.  A. Topology of the NFC  The proposed NFC is a multiplayer neural-network-basedfuzzy logic controller (FLC). The network architecture is built,such that the designer recognizes the internal nodes as theyrelate to the components of fuzzy controller. The system has atotal of five layers. The architecture of the network is shown inFig. 2. The signal propagation and the basic function of eachlayer is introduced in the following.  Layer 1—Input Layer:  Each node in this layer is an inputnode,whichcorrespondstooneinputvariable.Thesenodesonlybypass input signals to the next layer. The input variables arethe position error and change in position  RUBAAI: INTELLIGENT-POSITION-CONTROLLER-BASED MATRIX FORMULATION 629 Fig. 2. Topology of the NFC. error , respectively. The fuzzy setsproposed for the input variables are positive large (PL), positivesmall (PS), zero (ZE), negative large (NL), and negative small(NS)where is the th input to the node of layer 1, namely, theerror and the change in the error  Layer 2—Membership Layer:  Each node in this layer acts asa linguistic label of one of the input variables in layer 1, i.e., themembership value specified the degree to which an input valuebelongs to a fuzzy set is determined in this layer. The Gaussianactivationfunctionisutilizedtorepresent themembershipfunc-tions. The weights between the input and membership level areassumed to be unitywhere and are, respectively, the mean and the standarddeviation of the Gaussian function in the term of theinput linguistic variable to the node of layer 2.  Layer 3—Rule Layer:  Each nodein layer 3 multiplies thein-comingsignalandoutputstheresultoftheproduct.Thesenodesperform the connective  AND  function. Consequently, each nodeof thislayer is a rule node that represents one fuzzycontrol rule.Each node takes two inputs, one from nodes 1–5, and the otherfrom nodes 6–10 of layer 2. Nodes 1–5 define the membershipvalues for theposition error andnodes 6–10 definethe member-ship values for the change in position error. Accordingly, thereare 25 nodes in layer 3 to form a fuzzy rule base for two inputvariables, with five linguistic variables each. The input/outputlinks of layer 3 define the preconditions and the outcome of therule nodes, respectively. The outcome is the strength applied tothe evaluation of the effect defined for each particular rule. Foreach rule node, there are two fixed links from the input termnodeswhere represents the input to thenodeof layer 3, andis also assumed to be unity.  Layer 4—Sigmoidal Layer:  Layer 4 implements the sig-moidal activation function. This level is essential in ensuringthe system’s stability and allowing a smooth control action.Without the limiting performed by this layer, large fluctuationsin the control signal may occur. Therefore, layer 4 acts uponthe output of layer 3 multiplied by the connecting weights.These link weights, represents the output action of the rulenodes evaluated by layer 3where the link weight is the output action of the th outputassociate with the th rule, and is the learning rate.
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