Hybrid Direct Neural Network Controller With Linear Feedback Compensator Dr.Sadhana K. Chidrawar1, Dr. Balasaheb M. Patre2 1 Dean , Matoshree Engineering, Nanded (MS) 431 602 E-mail: sadhana_kc@rediff.com 2 Professor S.G.G.S. Institute of Engineering and Technology, Nanded (MS) 431 606 E-mail: bmpatre@yahoo.com Abstract In this paper Hybrid Direct Neural Controller (HDNC) with They also develop a hybrid intelligent system combining Linear Feedback Compensator (LFBC) has been developed. neuro fuzzy logic and fractal dimension for the problem of Proper initialization of neural network weights is a critical time series prediction. (Xianzhong and Shin 1993) presented problem. This paper presents two different neural network a novel method using direct adaptive controller and a configurations with unity and random weight initialization coordinator using neural network. The developments in while using it as a direct controller and linear feedback neural network based control systems for real time control compensator. The performances of these controller applications are still in early stage. There is still necessity of configurations are demonstrated on the two different carrying out lot of work to reach a stage of perfection, the applications i.e. Continues Stirred Tank Reactor as nonlinear stage after which, the ANN based networks may be freely and DC Motor as linear. In this work a direct neural control used for all types of process control applications in the strategy with linear feedback compensator is used to control industry. This paper presents a work carried out to develop a the process. Error back propagation algorithm based on hybrid direct neural controller that may find wider gradient algorithm is used to minimize the error between the applications in different types of industrial control plant output and desired output signal. The Direct Neural environments. Controller (DNC) and Hybrid Direct Neural Controller The specific contribution in this paper is respect (HDNC) are compared in terms of the Integral Square Error to (i) The development of a direct Neural Network (ISE) and Integral Absolute Error (IAE). Addition of a Controller for studying the effect of initialization of unity linear feedback compensator helps to improve both the and random weights in neural network control structure. (ii) transient as well as steady state response of the system The development of a Hybrid Direct Neural Controller. The HDNC has been developed by modifying a Direct Neural Controller (DNC) by adding a Linear Feedback Introduction Compensator (LFBC) in parallel with the neural network controllers. The comparison of both the controllers i.e. DNC There are many industrial applications where the and HDNC in terms of the Integral Square Error (ISE) and direct and coordination control strategies are required. Integral Absolute Error (IAE). The test results are highly Different types of controller are in use to provide appropriate encouraging and establish the superiority of HDNC over the control inputs to process plants to obtain desired outputs by other controller being used in the process industry for linear changing its parameters. Neural network has been applied as well as nonlinear systems. successfully in the identification and control of dynamical systems (Wang et al.2005). (Yuan et al. 2006) give the methodology of design of a conventional model reference ANN Techniques adaptive control system extended to design a direct neural control for a class of nonlinear system. (Peng and Huang 2006) has given a novel hybrid forward algorithm (FA) for Fully connected neural network used in this work, the construction of radial basis neural network with tunable consists of an input layer with six neurons, one hidden layer nodes. (Huang and Lee 2002) develop a decentralize neural with seven neurons and a single neuron in output layer as network controller for a class of large scale nonlinear high shown in Fig. 1. To reflect the status of the controlled order interconnections. He also proves that this NN system, the inputs of the neural network controller are controller can achieve for large scale systems. (Castilo and chosen as the desired system outputs, actual output and the Melin 2002) has describe a new method for estimation of the output errors: YD(k), YD(k-1), Y(k), Y(k-1), e(k), e(k-1) . fractal dimension of a geometry fuzzy logic technique. Fig. 1. Neural Network Architecture ANN Method For Direct Control A control system with DNC is shown in Fig. 2 Error Back Propagation Algorithm (Nahas, Henson and Seborg 1992) based on gradient algorithm is used to Fig.3. Direct neural controller with linear feedback compensator minimize the error between plant output and the desired Addition of a LFBC helps to improve both the output signal. Without a specific pre-training stage the transient as well as steady state response of the system. The weights of the neural network are adjusted online to hybrid combination of neural network and LFBC helps to minimize the error. eliminate the need of auto tuning of constants K1, K2 and K3 as required in conventional PID and Adaptive controllers. Once the values of constants are selected properly at one operating point, then these help to produce good results throughout the operating region of the systems. The hybrid combination of the neural network and the linear feedback compensator helps to compensate the limitation of individual controllers. The actual controlling signals u(k) is the sum of output of neural controller and LFBC and is expressed as follows: u (k ) un ( k ) u f ( k ) (1) Where u n ( k ) is the output of the neural network controller and u f ( k ) is the output of the linear feedback compensator (LFBC). Linear feedback compensator is a three term Fig. 2. Direct Neural Control System controller and expressed as YD (k) is the desired process output, Y(k) is the actual process k output, u(k) is the output of the neural network and e(k) is u f (k ) K1e(k ) K 2 e(k ) K 3 e(k ) (2) the network error output. i 0 Where, e(k ) YD (k ) Y (k ) and DNC With Linear Feedback Compensator In order to overcome problems associated with direct neural controller architecture a linear feedback compensator e(k ) e(k ) e(k 1) (LFBC) is placed in parallel with the neural controller. The application arrangement of the proposed hybrid scheme is And K1, K2 and K3 are the constants. The limitation of using shown in fig 3. LFBC with ANN configuration is in the initial selection of values of the fixed constant K1, K2 and K3 to get the best performance. The constants K1, K2 and K3 are the basic design parameters of LFBC. The values of these constants can be obtained by trial and error procedure by observing the effect of these constants on the performance of the system. Result To evaluate the applicability of the controller, the performance of the controller has been studied on a simulated system. Effect of Neural Network Weights Initialization for Non linear Application Example 1 In this section neural controller is applied to a highly nonlinear CSTR system given in (Mitra and Pal 1996). A schematic of the CSTR system is shown in Fig. 4. A single irreversible, exothermic reaction A→B is assumed to occur in the reactor. Fig. 5. Set point Tracking Performance of CSTR using DNC when Initial Weights of Network are 1 Fig. 4. Continuous Stirred Tank Reactor Here objective is to control the effluent concentration by manipulating coolant flow rate in the jacket. Following differential equations given in Equation (3) describes the behavior of this CSTR: E Fig. 6. Set point tracking performance of CSTR using dCA q DNC when initial weights of network are Random (CAf CA ) k0CAe RT dt V In Fig. 6, the set point tracking behavior of neural E hA dT q H k0CA RT c Cpc qc c Cpc controller with random weights in the range of 0 to 1 is Tf T e qc (1 e ) Tcf T shown. In order to complement the visual indications of dt V Cp CpV performance for the simulation runs was made using ISE (3) (integral of square errors) and IAE (integral of absolute error) criteria, which demonstrate the tracking ability of the Where, CAf is feed concentration, CA is product system. Table I gives the ISE and IAE values for both the concentration. TF, T and Tc are feed, product and coolant neural configurations. temperature respectively. q and qc are feed and coolant flow Table I rate. Here temperature T is controlled by manipulating Comparison Of Performance Of CSTR Process using DNC When coolant flow rate qc. Initially operating conditions are set to: Initial Neural Weights Are 1 And Random q=100 lit/min, CAF=1mol/lit, TF=350 K, TCF=350 K, V=100 lit, hA=7x105 cal/min K, k0=7.2x1010 /min, T=440.2 K, Set point All Initial Network All Initial Network E/R=9.95x103 K, -∆H=2x105 cal/mol, ρ, ρc=1000 gm/lit, CP, Weights are 1 Weights are Random CPC=1 cal/gmK, qc=103.41lit/min, CA=8.36x10-2 mol/lit ISE IAE ISE ISE In Fig. 5, the set point tracking behavior of neural 0.0700 0.0050 0.8538 0.0046 0.8800 controller with unity weights initialization is shown. 0.0836 0.0002 0.1850 0.2695 8.8873 0.0850 0.0075 1.0442 0.0071 1.0562 0.1000 0.0077 0.9988 0.0073 0.9363 In Fig. 7, the set point tracking behavior of neural controller Effect of Neural Network Weights Initialization with LFBC for unity weights initialization is shown and in for linear Application Fig. 8, the set point tracking behavior of neural controller with LFBC for random weights in the range of 0 to 1 is Example 2 shown. DNC with linear feedback componsator for Concentration Control of Nonlinear CSTR Process In this section the neural controller is applied to a linear 0.115 system. Here a DC motor is considered as a linear system 0.11 from (Dorf and Bishop, 1998). A simple model of a DC motor driving an inertial load shows the angular rate of the 0.105 load, ω(t), as the output and applied voltage, Vapp, as the Concentration (mol/lit) 0.1 input. The ultimate goal of this example is to control the angular rate by varying the applied voltage. Fig. 9 shows a 0.095 simple model of the DC motor driving an inertial load J. 0.09 0.085 0.08 0.075 0 500 1000 1500 2000 2500 Time (ms) Fig. 7. Set point tracking performance of CSTR using Direct Neural Controller with LFBC when initial weights of network are 1 DNC with linear feedback componsator for Concentration Control of Nonlinear CSTR Process 0.12 Fig. 9. DC motor driving inertial load 0.11 In this model, the dynamics of the motor itself are 0.1 idealized for instance, the magnetic field is assumed to be constant. The resistance of the circuit is denoted by R and Concentration (mol/lit) 0.09 the self-inductance of the armature by L. The important 0.08 thing here is that with this simple model and basic laws of 0.07 physics, it is possible to develop differential equations that describe the behavior of this electromechanical system. In 0.06 this example, the relationships between electric potential and mechanical force are Faraday's law of induction and 0.05 Ampere’s law for the force on a conductor moving through a 0.04 magnetic field. A set of two differential equations given in 0.03 0 500 1000 1500 2000 2500 Equation (4) describes the behavior of the motor. The first Time (ms) for the induced current, and the second for the angular rate, Fig. 8. Set point tracking performance of CSTR using Direct di R Kb 1 i(t ) (t ) Vapp Neural Controller with LFBC when initial weights of network are dt L L L Random d KF Km Table II gives the ISE and IAE values for both the neural (t ) i(t ) configurations. dt J J (4) Table II Here objective is to control angular velocity ω by Comparison Of Performance Of CSTR Process, Using DNC With manipulating applied voltage, Vapp. Initially operating LFBC When Initial Neural Weights Are 1 And Random conditions are set to: R=2Ω, L=0.5H, Km=0.015 (Torque Set point All Initial Network All Initial Network Constant), Kb=0.015 (emf Constant), KF=0.2Nms, J=0.02 Weights are 1 Weights are Random Kg.m2/sec2. In Fig. 10, the set point tracking behavior of neural ISE IAE ISE ISE controller with unity weights initialization is shown and in 0.08 1.9740 0.0817 1.1895 0.0398 Fig. 11, the set point tracking behavior of neural controller 0.09 1.9730 0.0816 1.1894 0.0397 with random weights in the range of 0 to 1 is shown. 0.10 1.9720 0.0815 1.1893 0.0396 0.11 1.4694 0.953 2.3870 0.0465 controller with random weights in the range of 0 to 1 is shown. DNC with LFBC for Output Angular Rate Control of Linear DC MOTOR 0.9 0.8 0.7 Angular Rate (rad/sec) 0.6 0.5 0.4 0.3 0.2 0.1 . Fig. 10. Set point tracking performance of DC Motor using DNC 0 0 500 1000 1500 2000 2500 when initial weights of network are 1 Time (ms) Fig.12. Set point tracking performance of DC Motor using Direct Neural Controller with LFBC when initial weights of network are 1 DNC with LFBC for Output Angular Rate Control of Linear DC MOTOR 0.9 0.8 Angular Rate (rad/sec) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Fig. 11. Set point tracking performance of DC Motor using DNC 0 0 500 1000 1500 2000 2500 when initial weights of network are Random Time (ms) Fig. 13. Set point tracking performance of DC Motor using Direct Table III gives the ISE and IAE values for both the neural Neural Controller with LFBC when initial weights of network are configurations in DC Motor application. Random Table IV gives the ISE and IAE values for both the Table III Comparison Of Performance Of DC Motor Using DNC When neural configurations in DC Motor application. Initial Neural Weights Are 1 And Random Table IV Set point All Initial Network All Initial Network Comparison Of Performance Of DC Motor Using DNC With Weights are 1 Weights are Random LFBC When Initial Neural Weights Are 1 And Random ISE IAE ISE ISE Set point All Initial Network All Initial Network 0.4 0.648 7.926 0.676 8.208 Weights are 1 Weights are Random 0.6 8.437 27.356 18.490 44.684 0.7 2.049 15.303 2.159 16.108 ISE IAE ISE ISE 0.9 1.365 19.294 1.426 20.049 0.4 0.0016 0.9941 0.0017 0.9958 0.6 0.0019 1.1598 0.0019 0.1618 In Fig. 12, the set point tracking behavior of neural 0.7 0.0033 1.9883 0.0033 1.9917 controller with LFBC for unity weights initialization is 0.9 0.0019 1.1598 0.0019 1.1618 shown. In Fig. 13, the set point tracking behavior of neural Conclusion In this paper, a Hybrid Direct Neural Control configuration Huang S .N, Lee T.H., 2002. A decentralize control of has been proposed. A Linear Feedback Compensator is used interconnected systems using neural network,IEEE to improve the performance of the Direct Neural Controller. transaction on neural network, vol.13,issue 6, pp.1554-1557. The DNC and proposed HDNC have been tested on a nonlinear application of CSTR and a linear application of Castilo O.,Melin P,2002. Hybrid intelligent systems for DC Motor. The performance of these two controllers was time series prediction using neural networks, fuzzy logic and tested when neural networks are initialized with all unity fractal theory, IEEE transaction on neural network, parameters and random parameters. It is found that neural vol.13,issue 6, pp.1395-1408. network with unity weight initialization is always better choice for any linear or nonlinear applications in DNC Xianzhong cui, Kang G. Shin, 1993. Direct control and configuration while random weight initialization is better coordination using neural network, IEEE transaction on choice for nonlinear application using HDNC configuration. systems, man and cybernatics, Vol.23, No.3, pp 686-697. The unity or random weight initialization for linear application in HDNC configuration gives similar results. It is found that for all set point changes, neural controller with LFBC yields a fast response with little overshoots. In contrast with the direct neural controller has sluggish behavior for every set point. The test results of hybrid direct neural controller with linear feedback compensator are highly encouraging and establish the superiority of HDNC over the other controller being used in the process industry for linear as well as nonlinear systems. References Nahas, E.P., Henson M.A. and Seborg D. E. 1992. Nonlinear internal model control strategy for neural network models, Computers Chemical Engineering, vol.16, pp. 1039-1057. 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