Artificial Neural Networks - Industrial and Control Engineering Applications 374 0 1000 2000 3000 4000 5000 0 500 1000 time, sec T D , °C Reference Ac tual T D 0 1000 2000 3000 4000 5000 -10 0 10 20 time, sec e , °C Fig. 12. Neural Network Predictive control response 0 1000 2000 3000 4000 5000 0 500 1000 time, sec T D , °C Reference Ac tual T D 0 1000 2000 3000 4000 5000 -5 0 5 time, sec e , °C Fig. 13. Piecewise Linearized Model Predictive control response 4.5 Discrete controller tuning online Control loop of this technique is connected in a way introduced briefly in section 3.3. Differential evolution is chosen as search technique. After some experiments, eligible parameters are chosen this way: NP = 30; CR = 0.85; F = 0.6; N = 20. Cost function is selected according to Eq. (19), where h 1 = 0.1, h 2 = 0.01. Control response is depicted in Fig. 14. There is no exact alternative in classical control theory to this technique. However, in a certain way it is close to predictive control, therefore it can be compared to Fig. 13. It is remarkable, that control response shown in Fig. 14 provides the most suitable performance of all experiments. But, on the other hand, it is highly computationally demanding technique. Artificial Neural Network – Possible Approach to Nonlinear System Control 375 0 1000 2000 3000 4000 5000 0 500 1000 time, sec T D , °C Reference Ac tual T D 0 1000 2000 3000 4000 5000 -1 0 1 2 time, sec e , °C Fig. 14. Discrete controller tuned online 5. Conclusion The aim of this work was to design a controller, which provides control performance with control error less than 10°C. Because of the nonlinearity of the plant, two groups of advanced control techniques were used. The first group is based on artificial neural networks usage while the second one combines their alternatives in modern control theory. Generally speaking, neural networks are recommended to use when plant is strongly nonlinear and/or stochastic. Although reactor furnace is indispensably nonlinear, it is evident that control techniques without neural networks can control the plant sufficiently and in some cases (especially predictive control and internal model control) even better. Thus, neural network usage is not strictly necessary here, although especially Discrete Controller Tuning Online brings extra good performance. 6. Acknowledgement This work was supported by the 6th Framework Programme of the European Community under contract No. NMP2-CT-2007-026515 "Bioproduction project - Sustainable Microbial and Biocatalytic Production of Advanced Functional Materials" and by the funds No. MSM 6046137306 and No. MSM 0021627505 of the Czech Ministry of Education. This support is very gratefully acknowledged. 7. References Baotic, M.; Christophensen, F.; Morari , M. (2006). Constrained Optimal Control of Hybrid Systems With a Linear Performance Index. IEEETrans. on Automatic Control, Vol.51, No 12., ISSN 1903-1919. Camacho, E.F.; Bordons, C. (2007). Model Predictive Control, Springer-Verlag, ISBN 1-85233- 694-3, London Artificial Neural Networks - Industrial and Control Engineering Applications 376 Coello, C. A. C.; Lamont, G. B. (2002). Evolutionary Algorithms for Solving Multi-Objective problems , Springer, ISBN 978-0-387-33254-3, Boston Dolezel, P.; Taufer, I. (2009a). PSD controller tuning using artificial intelligence techniques, Proceedings of the 17th International Conference on Process Control ’09, pp. 120-124, ISBN 978-80-227-3081-5, Strbske Pleso, june 2009, STU, Bratislava. Dolezel, P.; Mares, J. (2009b). Reactor Furnace Control using Artificial Neural Networks and Genetic Algoritm, Proceedings of the International Conference on Applied Electronics, pp. 99-102, ISBN 978-80-7043-781-0, Plzen, september 2009, ZCU, Plzen. Dwarapudi, S.; Gupta, P. K.; Rao, S. M. (2007). Prediction of iron ore pellet strength using artificial neural network model, ISIJ International, Vol. 47, No 1., ISSN 0915-1559. Economou, C.; Morari, M.; Palsson, B. (1986). Internal Model Control: extension to nonlinear system, Industrial & Engineering Chemistry Process Design and Development, Vol. 26, No 1, pp. 403-411, ISSN 0196-4305. Fletcher, R. (1987). Practical Methods of Optimization, Wiley, ISBN 978-0-471-91547-8, Chichester, UK. Lichota, J. ; Grabovski, M. (2010). Application of artificial neural network to boiler and turbine control, Rynek Energii, ISSN 1425-5960. Mares, J., Dusek, F., Dolezel, P.(2010a) Nelinearni a linearizovany model reaktorové pece. In Proceedings of Conference ARTEP’10", 24 26. 2 2010.Technicka univerzita Kosice, 2010. Pp. 27-1 – 27-14. ISBN 978-80-553-0347-5. Mares, J., Dusek, F., Dolezel, P.(2010b). Prediktivni rizeni reaktorove pece. In Proceedings of XXXVth Seminary ASR’10 „Instruments and Control" , VSB- Technical University Ostrava, 2010. Pp. 269 – 279. ISBN 978-80-248-2191-7. Montague, G.; Morris, J. (1994). Neural network contributions in biotechnology, Trends in biotechnology, Vol. 12, No 8., ISSN 0167-7799. Nguyen, H.; Prasad, N.; Walker, C. (2003). A First Course in Fuzzy and Neural Control, Chapman & Hall/CRC, ISBN 1-58488-244-1, Boca Raton. Norgaard, M.; Ravn, O.; Poulsen, N. (2000). A Neural Networks for Modelling and Control of Dynamic Systems , Springer-Verlag, ISBN 978-1-85233-227-3, London. Rivera, D.; Morari, M.; Skogestad, S. (1986). Internal Model Control: PID Controller Design, Industrial & Engineering Chemistry Process Design and Development, Vol. 25, No 1., pp. 252-265, ISSN 0196-4305. Teixeira, A.; Alves, C.; Alves, P. M. (2005). Hybrid metabolic flux analysis/artificial neural network modelling of bioprocesses, Proceedings of the 5th International Conference on Hybrid Intelligent Systems , ISBN 0-7695-2457-5, Rio de Janeiro. 18 Direct Neural Network Control via Inverse Modelling: Application on Induction Motors Haider A. F. Almurib 1 , Ahmad A. Mat Isa 2 and Hayder M.A.A. Al-Assadi 2 1 Department of Electrical & Electronic Engineering, The University of Nottingham Malaysia Campus Semenyih, 43500 2 Faculty of Mechanical Engineering, University Technology MARA (UiTM) Shah Alam, 40450 Malaysia 1. Introduction Applications of Artificial Neural Networks (ANNs) attract the attention of many scientists from all over the world. They have many advantages over traditional algorithmic methods. Some of these advantages are, but not limited to; ease of training and generalization, simplicity of their architecture, possibility of approximating nonlinear functions, insensitivity to the distortion of the network and inexact input data (Wlas et al., 2005). As for their applications to Induction Motors (IMs), several research articles have been published on system identification (Karanayil et al., 2003; Ma & Na, 2000; Toqeer & Bayindir, 2000; Sjöberg et al. 1995; Yabuta & Yamada, 1991), on control (Kulawski & Brys, 2000; Kung et al., 1995; Henneberger & Otto, 1995), on breakdown detection (Raison, 2000), and on estimation of their state variables (Simoes & Bose, 1995; Orłowska-Kowalska & Kowalski, 1996). The strong identification capabilities of artificial neural networks can be extended and utilized to design simple yet good performance nonlinear controllers. This chapter contemplates this property of ANNs and illustrates the identification and control design processes in general and then for a given system as a case study. To demonstrate its capabilities and performance, induction motors which are highly nonlinear systems are considered here. The induction machine, especially the squirrel-cage induction motor, enjoys several inherent advantages like simplicity, ruggedness, efficiency and low cost, reliability and compactness that makes it the preferred choice of the industry (Vas, 1990; Mehrotra et al., 1996; Wishart & Harley, 1995; Merabet et al., 2006; Sharma, 2007). On the other hand, advances in power switching devices and digital signal processors have significantly matured voltage-source inverters (VSIs) with the associated pulse width modulation (PWM) techniques to drive these machines (Ebrahim at el., 2010). However, IMs comprise a theoretically challenging problem in control, since they are nonlinear multivariable time-varying systems, highly coupled, nonlinear dynamic plants, and in addition, many of their parameters vary with time and operating condition (Mehrotra et al., 1996a; 1996b; Merabet et al., 2006). Artificial Neural Networks - Industrial and Control Engineering Applications 378 2. System identification This chapter will carry out the system identification of an induction motor using the artificial neural network and precisely the Back Propagation Algorithm. The procedure used to identify the system is as described in Fig.1. Data Collection (Experimental Work) Selecting the Model Structure Fitting the Model to the Data Validating the Model Accepting the Model ? Yes No Model structure is not good Data is not good Insert Filtration Factor if Necessary Fig. 1. System identification loop Now, the system identification problem would be as follows: We have observed inputs, u(t), and outputs, y(t), from the plant under consideration (induction motor): ( ) ( ) ( ) 1, 2, , t uuu ut =⎡ ⎤ ⎣ ⎦ " (1) ( ) ( ) ( ) 1, 2, , t y yy yt =⎡ ⎤ ⎣ ⎦ " (2) where t u is the input signal to the plant (input to the frequency inverter) and t y is the output signal (measured by the tacho-meter representing the motor’s speed). We are looking for a relationship between past 11 , tt uy −− ⎡ ⎤ ⎣ ⎦ and future output, y(t): ( ) ( ) ˆ |, y tgt θ ϕθ =⎡ ⎤ ⎣⎦ (3) where ˆ y denotes the model output which approximates the actual output () y t , g is a nonlinear mapping that represents the model, ( ) t ϕ is the regression vector given by () ( ) 11 , tt tuy ϕϕ −− = (4) Direct Neural Network Control via Inverse Modelling: Application on Induction Motors 379 and its components are referred to as regressors. Here, θ is a finite dimensional parameter vector, which is the weights of the network in our case (Bavarian, 1988; Ljung & Sjöberg, 1992; Sjöberg et al. 1995). The objective in model fitting is to construct a suitable identification model (Fig. 2) which when subjected to the same input ( ) ut to the plant, produces an output () ˆ y t which approximates () y t . However, in practice, it is not possible to obtain a perfect model. The solution then is to select θ in Eq. (3) so as to make the calculated values of ( ) ˆ | yt θ fit to the measured outputs ( ) y t as close as possible. The fit criterion will be based on the least square method given by ( ) min , N Vt θ θϕ ⎡ ⎤ ⎣ ⎦ (5) where () () ( ) 2 1 1 ˆ ,| N N t Vt ytyt N θϕ θ = ⎡ ⎤= ⎡ − ⎤ ⎣ ⎦⎣ ⎦ ∑ (6) Hence, the error ε is given by ( ) ( ) ( ) ˆ | tytyt ε θ =− (7) This is illustrated in Fig. 2. + - Plant Plant P M () ty () ty ˆ () t ε () tu Fig. 2. Forward plant modelling 3. Artificial Neural Networks Strong non-linearities and model uncertainty still pose a major problem for control engineering. Adaptive control techniques can provide solutions in some situations however in the presence of strongly non-linear behaviour of the system traditional adaptive control algorithms do not yield satisfactory performance. Their inherent limitations lie in the linearization based approach. A linear model being a good approximation of the non-linear plant for a given operation point cannot catch up with a fast change of the state of the plant and poor performance is observed until new local linear approximation is built. Artificial neural networks offer the advantage of performance improvement through learning using parallel and distributed processing. These networks are implemented using massive connections among processing units with variable strengths, and they are attractive for applications in system identification and control. Artificial Neural Networks - Industrial and Control Engineering Applications 380 3.1 The network architecture Figure 3 shows a typical two-layer artificial neural network. It consists of two layers of simple processing units (termed neurons). The outputs computed by unit j of the hidden-layer and unit k of the output-layer are given by: ( ) 1, 2, , jhj xfH j h== (8) ( ) 1, 2, , kok yf Ik m== (9) respectively, where h f and o f are the bounded and differentiable activation functions. Thus, the output unit k will result in the following: kkjjii ji yf wf vu ⎡ ⎤ ⎛⎞ = ⎢ ⎥ ⎜⎟ ⎝⎠ ⎢ ⎥ ⎣ ⎦ ∑∑ (10) where k y here is the vector representing the network output. It has been formally shown (Lippman, 1987; Fukuda & Shibata, 1992) that Artificial Neural Networks with at least one hidden layer with a sufficient number of neurons are able to approximate a wide class continuous non-linear functions to within an arbitrarily small error margin. Hidden layer j Input layer i Output layer k v ji w kj ∑ ∑ Hidden unit’s neuron Output unit’s neuron Biase Biase i u k y j x k y Fig. 3. A two layer artificial neural network 3.2 The training agorithm In developing a training algorithm for this network, we want a method that specifies how to reduce the total system error for all patterns through an adjustment of the weights. This chapter uses the Back-Propagation training algorithm which is an iterative gradient algorithm designed to minimize the mean square error between the actual output of a feed-forward network and the desired output (Lippman, 1987; Weber et al., 1991; Fukuda & Shibata, 1992). Direct Neural Network Control via Inverse Modelling: Application on Induction Motors 381 The back-propagation training is carried out as follows: the hidden layer weights are adjusted using the errors from the subsequent layer. Thus, the errors computed at the output layer are used to adjust the weights between the last hidden layer and the output layer. Likewise, an error value computed from the last hidden layer output is used to adjust the weights in the next to the last hidden layer and so on until the weight connections to the first hidden layer are adjusted. In this way, errors are propagated backwards layer by layer with corrections being made to the corresponding layer weights in an iterative manner. The process is repeated a number of times for each pattern in the training set until the criterion minimization is reached. This is illustrated in Fig. 4. Therefore, we first calculate the predicted error at each time step s (we refer to s here to introduce the discrete time factor). Then, an equivalent error is calculated for each neuron in the network. For example the equivalent error δ k of the neuron k in the output layer is given by (taking into account that the derivative of the output layer’s activation function is unity because it is a linear activation function): ( ) ( ) ( ) ( ) ˆ kkkk ss y s y s δε ==− (11) The equivalent error δ j of neuron j in the hidden layer is given by: () () ( ) () () j j kk j k j df H s ssw dH s δδ = ∑ (12) Weights connecting the hidden and output layers are adjusted according to: ( ) ( ) ( ) () () () ( ) 1 1 kj kj kj kj k j kj ws ws ws ws sxs ws αδ β =−+Δ Δ =+Δ− (13) where: α and β are the learning rate and the momentum parameters respectively. Weights connecting the input and hidden layer are adjusted according to: ( ) ( ) ( ) () () () ( ) 1 1 ji ji ji ji j i ji vs vs vs vs sus vs αδ β =−+Δ Δ =+Δ− (14) y d u v ji w kj k i j δ δ ∑ Desired Output Network Output Fig. 4. Back-propagation algorithm In summary, the training algorithm is as follow: the output layer error is calculated first using Eq. (11) and then backpropagated through the network using Eq. (12) to calculate the Artificial Neural Networks - Industrial and Control Engineering Applications 382 equivalent errors of the hidden neurons. The network weights are then adjusted using Eq. (13) and Eq. (14). 3.3 Model validation In order to check if the identified model agrees with the real process behavior, model validation is necessary. This is imperative as to taken into account the limitations of any identification method and its final goal of model application. This includes a check to determine if the priori assumptions of the identification method used are true and to compare the input-output behaviour of the model and the plant (Ljung & Guo, 1997). To validate the model, a new input will be applied to the model under validation tests. The new outputs will be compared with the real time outputs and validation statistics is calculated. These statistics will decide whether the model is valid or not. To carry out the validation task, we use the following statistics for the model residuals: The maximal absolute value of the residuals ( ) 1 max NtN M t ε ε ≤≤ = (15) Mean, Variance and Mean Square of the residuals () 1 1 N N t mt N ε ε = = ∑ (16) () 2 1 1 N NN t Vtm N εε ε = ⎡ ⎤ =− ⎣ ⎦ ∑ (17) () () 2 2 1 1 N NNN t StmV N ε εε ε = ==+ ∑ (18) In particular we stress that the model errors must be separated from any disturbances that can occur in the modelling. As this can correlates the model residuals and the past inputs. This plays a crucial role. Thus, it is very useful to consider two sources of model residuals or model errors ε . The first error originates from the input ( ) ut while the other one originates from the identified model itself. If these two sources of error are additive and the one that originates from the input is linear, we can write ( ) ( ) ( ) ( ) t q ut vt ε =Δ + (19) Equation (19) is referred to as the separation of the model residuals and the disturbances. Here, v(t) would not change, if we changed the input u(t). To check the part of the residuals that might originate from the input, the following statistics are frequently used: If past inputs are ( ) ( ) ( ) ( ) ,1,, 1 T tutut utM φ = ⎡− −+⎤ ⎣ ⎦ " and () () 1 1 N T N t Rtt N φφ = = ∑ , then the scalar measure of the correlation between past inputs ( ) t φ and the residuals ( ) t ε is given by: 1MT NuNu rRr ε ε ξ − = (20) Direct Neural Network Control via Inverse Modelling: Application on Induction Motors 383 where () ( ) 0, , 1 T uu u rr rM εε ε =⎡ − ⎤ ⎣⎦ " with () () ( ) 1 1 N u t rtut N ε τ ετ = =− ∑ . The obtained model should pass the validation tests of a given data set. Then we can say that our model is unfalsified. Here, we shall examine our model when the validation test is based on some of the statistics given previously in Eqs. (15-20). Let us first assume that the model validation criterion be a positive constant 0 μ > for the maximal absolute value of the residuals N M ε stated in Eq. (15) ( ) ( ) , is not validated iff N gt M ε ϕ θθμ ⎡ ⎤≤ ⎣⎦ (21) The problem of determining which models satisfy the inequality of Eq. (21) is the same problem that deals with set membership identification (Ninness & Goodwin, 1994). Typically this set is quite complicated and it is customary to outerbound it either by an ellipsoid or a hypercube. Therefore, it is agreed that a reasonable candidate model for the true dynamics should make the sample correlation between residuals ( ) ( ) ( ) ˆ ,| tytyt ε θθ =− and past inputs ( ) ( ) 1, ,ut ut m−−" small within certain criterion. One possible validation criterion is to require this correlation to be small in comparison with the Mean Square of the Model Residuals N S ε stated in Eq. (18). This is given by: ( ) ( ) ( ) , is not validated iff M NN gt S ε ϕ θξθγθ ⎡⎤ ≤ ⎣⎦ (22) where γ is a subjective threshold that will be selected according to the application. 4. The neurocontroller Conceptually, the most fundamental neural network based controllers are probably those using the inverse of the plant as the controller. The simplest concept is called direct inverse control, which is used in this chapter. Before considering the actual control system, an inverse model must be trained. There are tow ways of training the model; generalized training and the specialized training. This chapter uses the generalized training method. Figure 5 shows the off-line diagram of the inverse plant modelling. Plant Plant P C ( ) ε t ( ) yt ( )  ut ( ) ut ( ) rt Fig. 5. Inverse plant modelling Given the input-output data set which will be referred to as N Z over the period of time 1 tN≤≤ ( ) ( ) ( ) ( ) { } 1, 1, , , N Zuy uNyN= (23) [...]... Industry Applications, Vol 31(3), pp 612- 619 394 Artificial Neural Networks - Industrial and Control Engineering Applications Wlas M.; Krzeminski, Z.; Guzinski, J.; Abu-Rub, H.; Toliyat, H.A (2005) ArtificialNeural-Network-Based Sensorless Nonlinear Control of Induction Motors, IEEE Transection of Energy conversion, Vol 20, 3 (Sept 2005), pp 520-528 Yabuta T & Yamada T (1991) Learning Control Using Neural. .. widely for system identification and control applications Shim D H et al [28] described time-domain system identification approaches to design the control system for RUAVs 398 Artificial Neural Networks - Industrial and Control Engineering Applications 3 System identification and control The main idea of system identification is often to get a model that can be used for controller design System identification... reference control, the controller is a neural network that is trained to control a plant so that it follows a reference model The neural network plant model is used to assist in the controller training The neural model reference control architecture uses two neural networks: a controller network and a plant model network, as shown in the Fig 6 The plant model is identified first, and then the controller... the three control architectures mention above, system identification stage is identical but control design stage is different For model predictive control, the plant model is used to predict future behavior of the plant, and an optimization algorithm is used to select the control input that optimizes future performance 400 Artificial Neural Networks - Industrial and Control Engineering Applications. .. activation function and one output layer with a linear 388 Artificial Neural Networks - Industrial and Control Engineering Applications activation function) The network weights are initially randomised around the values -0.5 and +0.5 before the training The back-propagation training showed good results when using a network structure with two layer feed forward architecture neuron and 3000 samples as... signals and overcame the applied load torque disturbance demonstrating the strong capabilities of artificial neural networks in nonlinear control applications 7 References Bavarian B (1988) Introduction to Neural Networks for Intelligent Control, IEEE Control Systems Magazine, Vol 8, No 2, pp 3-7 Ebrahim Osama S., Mohamed A Badr, Ali S Elgendy, and Praveen K Jain,(2010) ANNBased Optimal Energy Control. .. Networks - Industrial and Control Engineering Applications 4 Design of control system The key challenge to deploy the designed control system of UAV is the potential risk and cost So, to minimize the cost and the potential risk, we have to test and simulate the control system rigorously to get high degree of precision of safeness Design, testing and simulation are the iterative process and this can be accomplished... Predictive Control • NARMA-L2 (Feedback Linearization) Control • Model Reference Control There are typically two steps involved when using neural networks for control systems: • System identification • Control design In the system identification stage, we develop a neural network model of the plant that we want to control The flow of control system design with system identification is shown in Fig 5 In the control. .. Flow of Control System Design with System Identification d Reference Model + NN Plant Model Command Input r y^ + - NN Controller - Plant u Control Input Control Error + ec Model Error + eI Plant Output y Fig 6 Neural Network MRC architecture For NARMA-L2 control, the controller is simply a rearrangement of the plant model We used model reference control to simulate the nonlinear identification and control. .. flight data from Eq 23-24 for design and simulation 408 Artificial Neural Networks - Industrial and Control Engineering Applications A= 0 0 −9.8 0 0 0 0 0 ⎤ −9.8 ⎡ −0.78501 ⎢ ⎥ 0 0 0 0 −0.065145 0 −56.659 −0.79784 −0.0045036 1344.1 ⎥ ⎢ ⎢ 0.35 712 0 0 0 92.468 −0.063629 0 0 0 56.515 ⎥ ⎢ ⎥ 0 0 1 0 0 0 0 0 0 0 ⎥ ⎢ ⎢ 0 0 0 0 0 0 0 −1 −11.842 −7.1176 ⎥ (23) ⎢ ⎥ 0 0 0 0 0 0. 1124 5 0 0 9.8 9.8 ⎥ ⎢ ⎢ 0.46624 0 . reference signal Artificial Neural Networks - Industrial and Control Engineering Applications 390 are illustrated in Figs. 11 and 12 respectively. It can be seen from Fig. 12 that the speed. function and one output layer with a linear Artificial Neural Networks - Industrial and Control Engineering Applications 388 activation function). The network weights are initially randomised. calculated first using Eq. (11) and then backpropagated through the network using Eq. (12) to calculate the Artificial Neural Networks - Industrial and Control Engineering Applications 382 equivalent