Research Article Neural Network Based Active Disturbance .
Hindawi Publishing CorporationShock and VibrationVolume 2016, Article ID 4921095, 9 h ArticleNeural Network Based Active Disturbance RejectionControl of a Novel Electrohydraulic Servo System forSimultaneously Balancing and Positioning byIsoactuation ConfigurationQiang Gao,1 Yuanlong Hou,1 Kang Li,1 Zhan Sun,2 Chao Wang,1 and Runmin Hou11School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210014, ChinaInstitute of North Automatic Control Technology, Taiyuan 030006, China2Correspondence should be addressed to Qiang Gao; gaoq0916@sina.comReceived 12 June 2015; Revised 1 September 2015; Accepted 2 September 2015Academic Editor: Mario TerzoCopyright 2016 Qiang Gao et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.To satisfy the lightweight requirements of large pipe weapons, a novel electrohydraulic servo (EHS) system where the hydrauliccylinder possesses three cavities is developed and investigated in the present study. In the EHS system, the balancing cavity of theEHS is especially designed for active compensation for the unbalancing force of the system, whereas the two driving cavities areemployed for positioning and disturbance rejection of the large pipe. Aiming at simultaneously balancing and positioning of theEHS system, a novel neural network based active disturbance rejection control (NNADRC) strategy is developed. In the NNADRC,the radial basis function (RBF) neural network is employed for online updating of parameters of the extended state observer (ESO).Thereby, the nonlinear behavior and external disturbance of the system can be accurately estimated and compensated in real time.The efficiency and superiority of the system are critically investigated by conducting numerical simulations, showing that muchhigher steady accuracy as well as system robustness is achieved when comparing with conventional ADRC control system. Itindicates that the NNADRC is a very promising technique for achieving fast, stable, smooth, and accurate control of the novelEHS system.1. IntroductionLarge pipe weapons, arms of heavy machineries, industrialrobotics, and space-borne manipulators possess a sort oflong and heavy linkages which have high ratio of lengthto diameter and time-varying unbalancing torque inducedby the misalignment between its gravity center and thecorresponding trunnion. The unbalancing torque servingas a sort of strong disturbance highly deteriorates controlperformances of the system [1, 2].Currently, there are two kinds of system balancingstrategies, namely, the external force based system balancing and the internal driving based system balancing. Theexternal methods mainly depended on adopting properbalance weights or adopting balance machinery, and thestatic unbalancing components can be well compensated.Practically, the unbalancing part including partial static anddynamic unbalancing components was treated as externaldisturbance and further compensated during active controlof the system. Regarding the large diameter of the pipe,the unbalancing components were heavy, highly challengingthe control system for positioning [3, 4]. Moreover, theextra machinery for balancing strongly increased weightsand costs of mechanical systems, being difficult to meet thelightweight requirements. With the internal driving basedsystem balancing methods, the most directly way was touse the driving forces for system balancing [5, 6]. Generally,the currently adopted method based on direct driving wasessentially a feedforward inverse compensation strategy, andit cannot achieve real-time balancing. It was obvious that not
2enough driving forces can be provided by the motor servosystem in terms of the heavy pipes. Another kind of adaptivebalancing method combining the hydraulic accumulator andbalancing machinery was recently developed in [7]. However,only partial unbalancing forces can be compensated duringthe process. Also, this method cannot be applied for activerejection of the unbalancing forces during the positioning.As discussed above, active compensation for the unbalancing components in pipe positioning is still an outstandingissue. In the present study, a novel electrohydraulic servo(EHS) system where the hydraulic cylinder possesses threecavities is developed. In the EHS system, the balancing cavityof the EHS is especially designed for active compensationfor the unbalancing force of the system, whereas the drivingcavity is employed for real-time positioning and disturbancerejection of the large pipe. By means of the hydraulic cylinderwith three cavities, simultaneous control and disturbancerejection can be achieved by using only one driving source,namely, isoactuation, greatly reducing weights of weaponswith heavy pipes. However, there are certain extremelycomplicated segments with strong nonlinearities in guncontrol systems, including time-varying parameters inducedby varying working conditions, random external appliedloads, and complex friction forces between the cannonand trunnion. All these nonlinear behaviors add difficultiesin achieving high control performances (both static anddynamic), blocking improvements of working performancesof the gun control system. In terms of nonlinear control,considerable work has been done based on certain types ofadaptive control strategies, such as fuzzy control, adaptivesliding mode robust control, and adaptive equivalent disturbance compensation control [4β7]. All these nonlinearcontrol methods can significantly improve the uncertaintiesof the control system in terms of its tolerance and robustness,but only at the expense of the positioning accuracy andresponse speed.The recently developed active disturbance rejection control (ADRC) is an efficient nonlinear digital control strategywhich regards the unmodeled part and external disturbanceas overall disturbance of the controlled system [8β10]. TheADRC mainly consists of a tracking differentiator (TD), anextended state observer (ESO), and a nonlinear state errorfeedback (NLSEF) control law. In this ADRC approach, theprocesses with higher orders, uncertainties, and unmodeleddynamics are viewed as lower-ordered systems with generaldisturbances; meanwhile, the general disturbances are estimated by ESO and are actively compensated [11β20]. Thereare a large number of adjustable parameters in the ADRC,and choosing proper parameters can contribute to excellentperformances of the control system. To optimally get the system parameters, the global optimization strategy based offline tune methods [11, 12] and the artificial intelligent basedonline tune methods [13β16] were developed. Generally, theoff-line tune methods are highly dependent on identifiedphysical model of the controlled system, and the obtainedparameters cannot adapt to variable working conditions. Theonline updating method can adjust control parameters to getoptimal control performance in real time. In [13], the fuzzycontrol scheme was introduced in the ADRC to estimate theShock and Vibrationstates and accordingly update the compensation factors ofthe ESO. In [14], the diagonal recurrent neural network wasintroduced to realize online tuning of the NLSEF. In termsof parameters of the NLSEF, the compensation gains in ESOhighly affect estimation performance of the control system,especially the estimation accuracy of overall disturbances.Thereby, the backpropagation neural network (BPNN) wasadopted in [15] to tune the gains in ESO. However, the BPNNsuffers easily trapping in local minimum and slow convergentspeed.Motivated by this, the radial biases function (RBF) neuralnetwork is introduced in an improved ADRC to solve thepractical issue in control of the newly developed EHS systemwith three hydraulic cavities for simultaneous balancing andpositioning, constructing the novel neural network basedactive disturbance rejection control (NNADRC) strategy.Four adjustable compensation gains in the ESO are onlineupdated by adopting the RBF neural network.2. The Isoactuation ElectrohydraulicServo System2.1. System Configuration and Working Principle. Figure 1illustrates the schematic of the isoactuation EHS systemfor simultaneous balancing and positioning. As shown inFigure 1, the EHS system mainly consists of a positioningcontroller, a variable capacity pump, a proportional servovalve, a rotary transformer, a RDC modular, a balancingcontroller, a constant displacement pump, a proportionalpressure-reducing valve, a pressure sensor, and an actuationhydraulic cylinder. The actuation hydraulic cylinder has threecavities, namely, the upper, lower, and balancing cavity. Acombination of the upper and lower cavities is adopted forsystem actuation.In practice, the balancing controller compares and calculates the deviation between the measured and desiredpressure in the balancing cavity. The control signal forthe proportional pressure-reducing valve is obtained basedon the deviation to accurately control the pressure in thebalancing cavity, accordingly cancelling the load and weighttorque on the system. As for the positioning, the deviationbetween the measured and desired positions of the pipeis similarly calculated, and accordingly a control signal isgenerated for the proportional servo valve to control the flowrate and direction of the hydraulic fluid for the upper andlower cavities. Thereby, position of the pipe can be accuratelycontrolled by adopting the feedback control strategy.2.2. Modelling the EHS System. Assume the state variables areππ₯ [π₯1 π₯2 π₯3 ] with π₯1 π, π₯2 π,Μ and π₯3 π;Μ thestate space equation for the isoactuation EHS system can bedetermined byπ₯1Μ π₯2 ,π₯2Μ π₯3 ,π₯3Μ π (π₯) ππ’1 π (π‘) ,(1)
Shock and Vibration3UppercavityBQuantitative pumpπOProportionalrelief ontrollerPressuresensorResolverProportionalservo valveRDCmodulePositioningcontrollerFigure 1: Schematic of the isoactuation EHS system.whereπ (π₯) 2.3. Controlling Principle of the EHS Systemπ½π πΆπ‘ πΊπ½ππ₯ π (π·π2 πΆπ‘ π΅π 0 πΊ) π₯2 ,π½π0 1 π½π0π½π π½ππ(π½πΆπ‘ 0 π΅π ) π₯3 ,π½π0π½ππ π (π‘) π½ππ·πΎπΎ,π½π0 π π 1(2)π½π πΆπ‘1π πΜ ,π½π0 πΏ π½ πΏ π (π‘) Const,where π denotes the actual position of the pipe, π’1 denotes theoutput signal of the positioning controller, π½π is the effectivebulk modulus of elasticity, πΆπ‘ is the overall leakage coefficient,πΊ represents the load elastic stiffness, π½ is the rotationalinertia, π0 is the volume of a cavity, π·π is the equivalentsurface total displacement, π΅π is the viscoelastic dampingcoefficient, πΎ1 represents the current-flow rate amplificationratio, πΎπ is the gain of the servo amplifier, and ππΏ representsthe external loads. Practically, the overall leakage coefficient,the viscoelastic damping coefficient, the equivalent surfacetotal displacement, and the external loads vary with respectto working conditions, showing strong nonlinear behavior ofthe working system.2.3.1. Principle of Balancing Control. In (1), the external loadππΏ denotes a combination of unbalancing torque, externaldisturbance torque, and launch impact torque. To compensate for these external disturbances, a novel active actuationconfiguration based on a hydraulic cylinder with three cavities is proposed for simultaneous positioning and balancing.The basic principle can be summarized as follows: the weighttorque varies with respect to the rotation position π, whichcan be expressed by ππΊ(π). With a specified arm of force π(π)and the acting area π΄, the required pressure ππΊ(π ) providedby the balancing cavity can be accordingly determined.To actively balance the weight torque, the pressure in thebalancing cavity is controlled by means of the proportionalpressure-reducing valve. Thereby, the required torque forbalancing the weight torque can be achieved.Since the working frequency of the proportionalpressure-reducing valve is much higher than the naturalfrequency of its actuation, it can be simply regarded as aproportional element. Thus, the relationship between thecontrol signal π2 (π ) and output flow rate π1 (π ) of the valvecan be expressed byπ1 (π ) πΎ2 πΎπ1 π2 (π ) ,(3)where πΎ2 is the voltage-displacement coefficient and πΎπ1 isthe flow rate gain for the valve.
4Shock and VibrationThe theoretical pressure in the balancing cavity can bedetermined byππ (π ) 1[π (π ) ππΏ1 (π ) π1 (π )](π1 /π½π ) π πΆπΏ1 π 111π π (π )[ππ 1 (π ) π΄π (π)(π1 /π½π ) π πΆπΏ1(4)With the TD process, it is employed for transient process and command signal generation. Fast tracking withoutovershoots as well as suspension of rapid fluctuations of thecontrol signal when the presetting parameters are suddenlychanged can be achieved by employing the TD. The definitionof the TD process can be expressed byV1 (π 1) V1 (π) βV2 (π) ,V2 (π 1) V2 (π) βV3 (π) , πΎ2 πΎπ1 π2 (π )] ,where ππ 1 (π ) and ππΏ1 (π ) denote the flow rate of the constantdisplacement pump and the flow rate into the balancingcavity, π1 is the volume between the output end of the pump,the input end of the valve, and the balancing cavity, and πΆπΏ1is the leakage coefficient of the balancing cavity.2.3.2. Principle of Positioning Control. The feedback controlscheme is employed for the positioning. Since there arecertain nonlinear components and unbalanced torque in thesystem, the ESO is further employed for the estimation ofthese unbalanced components; the control signal is thenobtained by following the nonlinear state error feedback control law with consideration of the disturbance compensation.3. Design of the Controllers3.1. Balancing Controller. The typical PID controller isadopted for the balancing of the gun control system. Assumethat the desired and practical pressures in the balancing cavityare ππΊ(π‘) and πππ (π‘), respectively; the command signal for thebalancing system can be determined byπ‘πππ (π‘)0ππ‘π’2 (π‘) ππ [ππ ππ (π‘) ππ ππ (π‘) ππ‘ ππ],(5)ππ (π‘) ππΊ (π‘) πππ (π‘) ,where ππ denotes the maximum output voltage for thecontrol and ππ , ππ , and ππ are proportional, integral, anddifferential coefficients of the PID controller.3.2. The Improved ADRC Controller. To better track thetrajectory of the control system, an improved ADRC control strategy is developed. To suppress the inherent chatterphenomenon, a novel nonlinear function nfal( ) featuringsmooth switching behavior is employed to replace the conventionally adopted nonlinear function fal( ) which is a keycomponent of the ADRC controller. Besides, the radial biasesfunction (RBF) neural network is adopted to online updatethe compensation gains of the ESO in the ADRC.3.2.1. Configuration of the Control System. Schematic of theADRC is illustrated in Figure 2; it mainly consists of a TD, anESO, and a NLSEF control law. In this ADRC approach, theprocesses with higher orders, uncertainties, and unmodeleddynamics are viewed as lower-ordered systems with generaldisturbances which are further estimated by ESO and areactively compensated.V3 (π 1) V3 (π) βππ π‘,(6)ππ π‘ π (π (π (V1 ππ ) 3V2 ) 3V3 ) ,where ππ (π‘) denotes the desired trajectory of the controlsystem, π and β determine the speed and the step length,respectively, and V1 (π‘), V2 (π‘), and V3 (π‘) track ππ (π‘), ππΜ (π‘), andππΜ (π‘), respectively.With the ESO, the change rate and total disturbance ofthe error can be real-time estimated using ESO from thecontrol variables and the position errors of the input signal.Thereby, dynamic compensation for the disturbances canbe conducted properly using estimated total disturbances.By introducing the novel nonlinear function nfal( ), theimproved third-order discrete ESO can be configured asfollows:π (π) π§1 (π) π (π) ,π§1 (π 1) π§1 (π) β [π§2 (π) π½01 π (π)] ,π§2 (π 1) π§2 (π) β [π§3 (π) π½02 nfal (π (π) , π1 , π1 , πΎ1 )] ,π§3 (π 1)(7) π§3 (π) β [π§4 (π) π½03 nfal (π (π) , π1 , π2 , πΎ1 ) π0 π’ (π)] ,π§4 (π 1) π§4 (π) βπ½04 nfal (π (π) , π1 , π3 , πΎ1 ) ,where π½01 , π½02 , π½03 , and π½04 are adjustable compensationgains, and π1 , π2 , π3 , πΏ1 , and π0 are design parameters. π§1 (π‘),π§2 (π‘), π§3 (π‘), and π§4 (π‘) are the estimate outputs of the ESOΜ π(π‘),Μ and the estimatedprocess, respectively, tacking π(π‘), π(π‘),total disturbance.The nonlinear function nfal( ) can be expressed bynfal (π (π) , π, π, πΎ) π arc tanπ (π (π) πΎ) π0,π/2 π0(8)π0 arc tan (π (0 πΎ)) ,where V determines the shape of the operator, π determinesthe range of the operator, and πΎ determines the center of theoperator.Essentially, the NLSEF controller is a nonlinear PDcontroller; nonlinear combination of the error componentsderiving from the outputs of the TD and the state estimation
Shock and Vibration5TLe (t) 1 e (t) 2 (t) 2 3 (t)e3 (t) 1 (t)πd (t)TDNLSEFu0 (t) u1 (t)π(t)Plant 1/b0b0z4 (t)z1 (t)z2 (t)ESOz3 (t)Figure 2: Schematics of ADRC. 1 (t)πd (t)TDe (t) 1 e (t)2 e3 (t) 3 (t) 2 (t)NLSEFu0 (t) u1 (t)π(t)Plant 1/b0b0TLz4 (t)z1 (t)z2 (t)z3 (t)π½01π½02π½03π½04ESORBFNNFigure 3: The diagram of ADRC based on RBF neural network.from the ESO is properly designed to construct the commandsignal π’π (π‘). The third-order discrete governing law of theNLSEF can be determined byπ1 (π 1) V1 (π 1) π§1 (π 1) ,π2 (π 1) V2 (π 1) π§2 (π 1) ,π3 (π 1) V3 (π 1) π§3 (π 1) ,π’0 (π 1) π½1 nfal (π1 (π 1) , π0 , π4 , πΎ0 )(9) π½2 nfal (π2 (π 1) , π0 , π5 , πΎ0 ) π½3 nfal (π3 (π 1) , π0 , π6 , πΎ0 ) ,where π½1 , π½2 , and π½3 represent the control gains, respectively,and π4 , π5 , π6 , and πΏ0 are the parameters for the design process.By combining the estimated disturbance through theESO, the actual control variables applied to the actuator ofthe control system can be obtained as follows:π’1 (π 1) [π’0 (π 1) π§4 (π 1)],π0(10)where b0 is the compensation factor.3.2.2. Adaptive Updating of the ESO. Overall, there are fourimportant parameters in the ESO that govern the controlaccuracy and system robustness of the whole control system,namely, π½01 , π½02 , π½03 , and π½04 . To achieve optimal controlduring the whole working process, an online updating of thefour parameters based on RBFNN is developed in the presentstudy. The configuration of the adaptive control system isillustrated in Figure 3. As shown in Figure 3, a three-layerRBFNN is adopted where π1 (π‘), π2 (π‘), π3 (π‘), and π(π‘) areserving as the input nodes, while π½01 , π½02 , π½03 , and π½04 areserving as the output nodes. The number of node in hiddenlayer is chosen as 6.The goal of adaptive adjustment of the control parametersis to seek for a control signal that can minimize the differencebetween the process output and the desired output. The performance criterion employed in this paper for the parameterupdating is defined byπΈ (π) 112[π (π) π (π)] π2 (π) .2 π2(11)The output of each hidden node in the RBFNN can beobtained as follows: 2 π πΆπ ππ (π) exp ( ),2ππ2(12)where π [π1 , π2 , π3 , π]π denotes the input vector of theNN, πΆπ [ππ1 , ππ2 , ππ3 , ππ4 ]π denotes the center vector of the πthhidden node, and ππ is the width of the radial basis functionof this node.
6Shock and Vibration0.46Position tracking control voltage (V)0.35Position tracking error (rad)0.30.250.20.150.10.050420 2 4 0.05 0.1012345Time (s)6789 6100NNADRC tracking signal errorADRC tracking signal error12347891078910NNADRC control voltageADRC control voltage(a)(b)120800700Position tracking torque error (Nm)100Square wave disturbance/z456Time (s)8060402006005004003002001000 100 200123456Time (s)78910 2000123456Time (s)DisturbanceNNADRC z4ADRC z4(c)(d)Figure 4: Step response of the control system: (a) errors of position signal with square wave disturbance, (b) position tracking control voltage,(c) square wave disturbance and the estimated z4 , and (d) torque errors of position tracking.Thus, output of the RBFNN can be determined byThe update law for the weights of the RBFNN yields thefollowing:πππ (π)
e recently developed active disturbance rejection con-trol (ADRC) is an e cient nonlinear digital control strategy which regards the unmodeled part and external disturbance as overall disturbance of the controlled system [ ] . e ADRC mainly consists of a tracking di erentiator (TD), an extended state observer (ESO), and a nonlinear state error
Amendments to the Louisiana Constitution of 1974 Article I Article II Article III Article IV Article V Article VI Article VII Article VIII Article IX Article X Article XI Article XII Article XIII Article XIV Article I: Declaration of Rights Election Ballot # Author Bill/Act # Amendment Sec. Votes for % For Votes Against %
neural networks and substantial trials of experiments to design e ective neural network structures. Thus we believe that the design of neural network structure needs a uni ed guidance. This paper serves as a preliminary trial towards this goal. 1.1. Related Work There has been extensive work on the neural network structure design. Generic algorithm (Scha er et al.,1992;Lam et al.,2003) based .
A growing success of Artificial Neural Networks in the research field of Autonomous Driving, such as the ALVINN (Autonomous Land Vehicle in a Neural . From CMU, the ALVINN [6] (autonomous land vehicle in a neural . fluidity of neural networks permits 3.2.a portion of the neural network to be transplanted through Transfer Learning [12], and .
Different neural network structures can be constructed by using different types of neurons and by connecting them differently. B. Concept of a Neural Network Model Let n and m represent the number of input and output neurons of a neural network. Let x be an n-vector containing the external inputs to the neural network, y be an m-vector
An artificial neuron network (ANN) is a computational model based on the structure and functions of biological neural net-works. Information that flows through the network affects the structure of the ANN because a neural network changes - or learns, in a sense - based on that input and output. Pre pro-cessing Fig. 2 Neural network
Neural Network Programming with Java Unleash the power of neural networks by implementing professional Java code FΓ‘bio M. Soares Alan M.F. Souza BIRMINGHAM - MUMBAI . Building a neural network for weather prediction 109 Empirical design of neural networks 112 Choosing training and test datasets 112
neural networks. Figure 1 Neural Network as Function Approximator In the next section we will present the multilayer perceptron neural network, and will demonstrate how it can be used as a function approximator. 2. Multilayer Perceptron Architecture 2.1 Neuron Model The multilayer perceptron neural network is built up of simple components.
application of neural networks is to test the trained neural network. Testing the artificial neural network is very important in order to make sure the trained network can generalize well and produce desired outputs when new data is presented to it. There are several techniques used to test the performance of a trained network, a few of which are
