Brain Emotional Learning Based Intelligent Controller and its Application on CSTR

AthulAjith & Mija S.J Electrical Engineering Department, NIT Calicut E-mail : [email protected], [email protected]

Abstract – In this paper, a bio-inspired intelligent controller computational model, the concept of BELBIC was first namely Brain Emotional Learning Based Intelligent introduced by Lucas et.al in [3]. Controller or BELBIC and its effectiveness as a controller for complex nonlinear dynamical systems is studied. The Further, BELBIC was applied on some intriguing product concentration control of Continuously Stirred Tank systems and results prove its effectiveness as a Reactor (CSTR) is an important control problem because of controller and it‟s capability to adapt to parameter its highly nonlinear dynamics. An attempt is made to verify variations and disturbances [4,5,6]. The efficiency of the suitability of BELBIC for this control problem using one BELBIC for complex industrial process was illustrated sensory signal for the controller. The transient response of in [7]. Real-time implementation of the BELBIC for the developed controller is then improved using BELBIC with interior permanent magnet synchronous motor (IPMSM) two sensory signals. Moreover, the performance of the drives was presented in [8]. Moreover, ability of such a developed controller is compared with that of a 2 DOF PID controller in signal processing has been amply controller. demonstrated in [9]. However, the infancy of this Keywords – BELBIC, Emotional Controller, CSTR, controller in terms of periods for which other control Intelligent Controller. strategies have been studied and implemented, classical and intelligent alike, leaves room for further I. INTRODUCTION implementation and analysis of BELBIC in terms of its performance, adaptability and efficiency. In recent years , application of intelligent and bio- inspired approaches such as Neural Networks, Particle Chemical reactors have been perhaps the most Swarm Optimisation (PSO), Genetic (GA) important unit of chemical power plant used for unit etc. have found wide spread acceptance among control operations. CSTR is of immense interest to control engineers. Good results have been regularly obtained for engineers even today and the reasons are manifold. Most even complexreal time systems through controllers importantly, it is a benchmark process control problem based on such approaches. The ability of this class of with complex nonlinear dynamics. The primary controllers to adapt to parameter variations and objective of the control mechanism developed for the disturbances is very much desirable. The latest entrant to CSTR would be to control the product concentration this class is the BELBIC- Brain Emotional Learning irrespective of disturbances. Many control strategies Based Intelligent Controller. BELBIC is a notion have already been used to control CSTR,conventional inspired from the way in which mammalian brain [10]-[12] and intelligent controllers [13]-[15] alike.The process and bring out . product concentration control of CSTR using BELBIC is expected to provide a comprehensive idea on generation is generally regarded as a low application of BELBIC for nonlinear systems and point level reaction in brain. However, researches have out its effectiveness and simplicity in comparison with pointed out that amygdala, a small structure in medial classical controllers. The performance of BELBIC for temporal lobe of the brain is largely responsible for the CSTR is compared with that of a classical 2DOF PID evaluation of emotional stimuli. The idea of emotional controller. learning was first presented by Moren&Balkenus in [1,2] as a neurologically inspired computational model The paper is organised as follows. Section IIis of amygdala and . Based on this devoted to shed more light on the concept of BELBIC.

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The third section deals with system descriptionof From Fig 1.b, the action can be either inhibitory or CSTRsystem and application of BELBIC to CSTR. In excitatory. From mathematical view point, this converts section IV, an improved BELBIC is presented with the in to supplementing the final result either through objective of enhancing the transient response of the additions or subtraction respectively. It is seen that CSTR system. Finally, the results are discussed and orbitofrontal part takes care of the latter and amygdala conclusions are drawn in section V. produces signal which aids the final result. Likewise, a plastic connection identifies a connections without any II. BELBIC MODEL adjustable weights and a connection which can learn indicates The neurobiological structure of amygdala and orbitofrontal parts of mammalian brain is found to be There is one „A‟ node for every stimulus including responsible for most of the process associated with thalamic input in amygdala and one „0‟ node for each emotional learning. A mathematical model of this stimulus except for thalamic input in orbitofrontal structure acts as the base for BELBIC. The important cortex. Output of system is given by point to note is that BELBIC is more or less a functional model of the structure and doesn‟t necessarily represent (1) the entire physical structure. Where Ai represent the output of ‘A’ node for i’ th A. Mathematical Model stimulus signal. The model, similar to the original emotional Similarly, thalamic connection is calculated as processing architecture in mammalian brains is divided maximum overall stimulus Si. Unlike other inputs to the into two parts, Orbitofrontal and Amygdala. amygdala, the thalamic input is not projected into the Amygdaloidal part receives input from thalamus and orbitofrontal part and cannot be inhibited. cortical areas where as orbitofrontal part receives inputs from cortical areas and amygdala only [3]. The system (2) also receives an emotional reinforcing signal called reward. The general structure of BELBIC is as given in For each „A‟ node, there is a plastic connection weight Fig 1. „V‟ s. Any input is multiplied with this weight to become the output (Ai) from the node. The „0‟ nodes behave in a similar manner with a connection weight W applied to the input signal to create an output (0i).

(3)

The connection weight Vi is adjusted proportionally to the difference between reinforcing reward and the activation output of „A‟ nodes.

(4)

Wi isalso adjusted in a similar fashion

(5)

(a) Where ,  are constants and Ej is the apparent outputwhich is actual output minus the effect of thalamic input.

It is of great interest that the adjustment of Vi is monotonic in nature. Thus the connection weights of amygdala will never decrease. This is a major drift from the weight updating rules generally encountered. The (b) idea embraced here is that once the controller learns a Fig. 1: Structure of BELBIC model pattern, the same is not to be lost due to an opposing reward or the like. So whenever a result is inappropriate,

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International Journal of Advanced Electrical and Electronics Engineering, (IJAEEE) it is the task of orbitofrontal part to inhibit such an simple liquid phase reaction is considered output. This feature is unique to BELBIC structure. In here.Chemical species reacts to form species as fact, there is biological evidence that orbitofrontal shown in Fig 3. All the typical assumptions such as of cortex is found to inhibit the areas it is connected to as constant volume, perfect mixture, equal mass densities explained in [2]. of feed and product streams, uniform coolant The weight updating rule for orbitofrontal part is temperature negligent shaft work and heat losses etc. fairly straight forward and similar. As obvious, the are in order [16] and the primary objective is to control weight can both increase and decrease as needed to track the concentration of . the required inhibition. Thus the amygdaloidal part learns to predict and react to a given reinforcement and once a relation is learned, the subsystem can never unlearn the connection. On the other hand, the 0 nodescompare the expected and received reinforcing signal andinhibits the output of the model should there be a mismatch. The „  and‟terms are constants used to adjust the learning speed.Despite being constants, the values of  and  are very critical for optimal performance of controller. The aforementioned functional model was developed in Simulink® and is shown in the Fig 2.

Fig 3. CSTR

The controller will adjust the coolant temperature ( ), which is one of three plant inputs. The others are the concentration of the limiting reactant in the CSTR feed stream ( ) and the temperature of this stream ( ). The flow rate of the feed (input) and product (output) streams is kept constant ( ). The CSTR states are the temperature ( ) and Fig 2. BELBIC in Simulink concentration ( ) of the limiting reactant in the product stream and are assumedto be measurable and can be used for The most important consideration for BELBIC . applied to any system is the number of signals involved and signal conditioning. Every system will have The objective is to control the product independent set of input and output signals including concentration of CSTR from an initial condition of low controller outputs and various errors. Thus the input (~19%) conversion to a desired steady state at 80% signals to amygdala and orbitofrontal cortex of the conversion. The reaction is exothermic (liberates heat) controller are to be properly selected for the system. In and the CSTR temperature must be controlled to prevent fact only these signals need to be changed for various a thermal runaway. systems. The underlying structure of BELBIC can remain the same and hence provides great portability The mathematical model of CSTR is derived using and cost savings in terms of application for various mass balance and energy balance as in [13]. The model systems. of CSTR is given by III. BELBIC FOR CSTR A. CSTR (6) Continuous Stirred Tank Reactor System (CSTR) is a typical chemical reactor system with complex nonlinear dynamic characteristics. As the purpose is to (7) highlight the effectiveness and simplicity of BELBIC, a

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International Journal of Advanced Electrical and Electronics Engineering, (IJAEEE) where is the volume of CSTR, is the density of - mixture, is the heat capacity of - mixture, is the volumetric flow rate, is the heat of reaction for  , „ ‟ is the rate constant and rate of reaction , is the molar concentration of , is the overall heat transfer coefficient, „ ‟ is the wall area of CSTR, are the feed and coolant temperature respectively.

B. BELBIC design The most important aspect of the aforementioned controller is the signals associated with it. Initially, BELBIC with one sensory signal was used for the control. This would seem apt here because there is only one control variable and the objective is to control only product concentration. A weighted error signal is used Fig 5. 2 DOF PID for CSTR as the sensory signal and a combination of weighted reference and error signal is used as the reward signal. B. Performance evaluation of BELBIC Thus the reward and sensory signals were selected as The controllers are applied to the system in order to have a comparison of their performance.Both simulations were completed within 1 sec on a dual core 2.1 GHz system with 4 GB of memory. where represents numerical weights, is the concentration error signal and is the reference concentration. The simulation model of this BELBIC for CSTR is shown in Fig 4.

Fig 4. BELBIC for CSTR c. 2 DOF PID Fig 5. (a) Concentration and (b) Temperature of CSTR under Since the controller is relatively new and we have BELBIC and 2DOF PID set out to analyse the efficiency, a comparison is inevitable. A 2DOF PID is used to fill in the slot. The The reactor temperature and concentration of the default tuning available in Simulink® is used. The ® reactant plotted against time are shown in Fig 6. As Simulink model is shown in Fig 5. obvious from the figure, BELBIC was able to achieve steady state faster and more accurately. A qualitative analysis is due. However, there is much scope of improvement in response, particularly in terms of the number of oscillations.

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IV. IMPROVED BELBIC FOR CSTR 10 BELBIC 1 A. Design of Improved BELBIC 8 Even though there is only one control variable, CSTR Improved BELBIC is basically a dual output system with temperature 6 being the second variable. The proposition of reducing the variation of temperature is taken in to account and 4 to analyse how much one more sensory signal can Concentration (kmol/m^3) contribute to the system performance, another BELBIC 2 model with two sensory signals was developed.

0 5 10 15 20 25 30 The mathematical description of sensory and Time (s) reward signals used for this two signal model of controller is more or less the same as that provided for Fig 8.(a) the previous BELBIC model for with one sensory 380 signal. The second sensory signal is constituted as the 360 weighted function of reactor temperature with idea of BELBIC 1 providing stability to the same. The Simulink® model is 340 as shown in the Fig 7. 320 300

280 Temperature(K) Improved BELBIC

260

240

220 0 5 10 15 20 25 30 Time (S) Fig 8. (b) Fig 8. Performance of CSTR using improved BELBIC in terms of (a) concentration and (b) temperature

Moreover, in order to assess the performance of BELBIC under noise, a Gaussian white noise is introduced as a measurement noise. The response of CSTR under such a scenario to BELBIC and improved B. Performance Evaluation BELBIC is as shown in the Fig 9. 10

The response of the CSTR to the improved BELBIC BELBIC 1 9 is compared with that of the BELBIC with one sensory 8

Improved BELBIC signal is shown in Fig 8. 7 As obvious, BELBIC with two sensory signals is 6 able to give a far smoother control and especially very 5 4 less variation in temperature. From a reaction point of 3 view, the result is much desirable Concentration(kmol/m^3) 2

1

0 0 5 10 15 20 25 30 Time (S) (a)

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380 robustness of the controller under noise conditions have 360 also been established in this paper. This serves as an BELBIC 1

340 encouragement to apply BELBIC on more complex and real time system 320

300 The structure of BELBIC remains the same for any

280 Temperature (K) Temperature Improved BELBIC system and this in fact is the biggest advantage 260 associated with BELBIC. For any given system, the

240 control engineer has to generate only corresponding

220 sensory signals and reward which boils down to simple 0 5 10 15 20 25 30 Time (S) signal generation. (b) The only concern here would be the lack of proper Fig 9. Performance of BELBIC under noise in terms guidelines to generate sensory and reward signals. The of (a) Concentration and (b) Temperature proper selection of the same is of utmost importance. However, given the relative low time period the The importance of introducing a second sensory controller has been researched up on, there is much signal is obvious from the figure. Even though there is more scope for research and improvement in all facets only one control variable, the BELBIC with two sensory for BELBIC. signals was able to outperform the earlier BELBIC with VI. REFERENCES one sensory signal in a significant manner without any change in reward. This perhaps can be attributed to the [1] J. Moren, “Emotion and Learning – A Computational idea of controller getting more information about the Model of the Amygdala”, PhD dissertation, Lund system in the form of a second sensory signal. University, Lund, Sweden, 2002 [2] J. Moren, C. Balkenius, "A Computational Model of A qualitative analysis of all the three controllers is Emotional Learning in the Amygdala", Cybernetics given in the Table 1. and Systems, Vol. 32, No. 6, 2000, pp. 611- 636. TABLE I [3] C. Lucas, D. Shahmirzadi, N. Sheikholeslami, Performance of Various Controllers "Introducing BELBIC: Brain EmotionalLearning Based Intelligent Controller", International Journal of Intelligent Automation and Soft Computing, Vol. 10, NO.1, 2004, pp. 11- 22. [4] C. Lucas, R. Mohammadi and B. N. Araabi, "Intelligent modeling and control of washing machine using LLNF modeling and modified BELBIC", Asian Journal of Control, Vol. 8, No. 4, (2006), pp. 393-40 [5] H. Rouhani, M. Jalili, B. N. Araabi, W. Eppler and C. Lucas, "Brain emotional learning based intelligent controller applied to neuro-fuzzy modelof micro-heat exchanger", Expert Systems with Applications, Vol. 32, (2007),pp. 911-924 The final difference between BELBIC and a [6] S. Jafarzadeh, R. Mirheidari, M. R. J. Motlagh and M. classical 2DOF PID is rather overwhelming for any Barkhordari, "Intelligent Autopilot Control Design for criteria of performance measure. Coupled with this a 2-DOF Helicopter Model", International Journal of efficient performance, the simplicity of BELBIC Computers, Communications & Control, Vol. 3, structure makes it a rather suitable candidate for various (2008), pp. 337-342 control applications. [7] Hassen T. Dorrah, Ahmed M. El-Garhy, Mohamed E. El-Shimy, “PSO-BELBIC scheme for two coupled V. CONCLUSION distillation column process”, Journal of Advanced The concept of emotional controller namelyBrain Research, 2011- 2, pp 73-83 Emotional Leaning Based Intelligent Controller or BELBIC is applied for concentration control of CSTR. [8] Milasi, R. M., Lucas, C., Arrabi, B. N., Radwan, T. S., & Rahman, M. A. “Implementation of emotional In order to enhance the transient performance, BELBIC controller for interior permanent magnet synchronous with 2 sensory signals is also designed. The BELBIC motor drive”. IEEE Transactions On Industry showed better performance compared to the Applications, Vol. 44, No. 5, October 2008 conventional 2 DOF PID controller. The efficiency and

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