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BELBIC for MRAS with Highly Non-Linear Process Alexandria Engineering Journal (2015) 54, 7–16 HOSTED BY Alexandria University Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com BELBIC for MRAS with highly non-linear process Ahmed M. El-Garhy a,*, Mohamed E. El-Shimy b a Department of Electronics, Communications and Computers, Faculty of Engineering, Helwan University, Helwan, Egypt b Department of Computers and Systems, Faculty of Engineering, Minia University, Minia, Egypt Received 20 July 2011; revised 12 August 2014; accepted 14 December 2014 Available online 20 January 2015 KEYWORDS Abstract Model Reference Adaptive Systems (MRASs) use mostly the traditional MIT rule based Model Reference Adaptive controllers to drive the difference (error) between the model reference signal and actual output one System (MRAS); to zero value. MIT rule based controllers are slow and cause large error values in case of highly non- MIT rule based controllers; linear process. In this paper, we propose the Brain Emotional Learning Based Intelligent Controller Brain Emotional Learning (BELBIC) to replace the MIT rule based one. BELBIC benefits Brain Emotional Learning modeled Based Intelligent Controller algorithm in mammalians brain to seek the proper control signal that eliminates the error. In spite (BELBIC); of some overshoots in MRAS with BELBIC, simulation of the proposed BELBIC for MRAS with System dynamics its large number of adjustable gains achieves remarkable fast response. ª 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction evaluation is based on emotional cues, which evaluate the impact of the external stimuli on the ability of the system both The design of intelligent systems has received considerable to function effectively in the short term and to maintain its attentions in recent years. Control techniques based on Artifi- long term prospects for survival [10]. Emotional learning is cial Neural Networks [1], Fuzzy Control [2] and Genetic Algo- one of the learning strategies based on emotional evaluations. rithms [3] are among them. Emotional Learning is a In mammalian brains, this learning process occurs in the brain psychologically motivated algorithm which is a family of intel- Limbic System [11]. ligent algorithms [4]. Moren and Balkenius [12,13] presented a neurologically Recently, biologically motivated intelligent computing has inspired computational model of the amygdala and the Orbito- been successfully employed for solving different types of prob- frontal Cortex in the Limbic System. Based on this model, a lems [5–9]. The greatest different of an intelligent system from control algorithm called Brain Emotional Learning Based a traditional one is the capability of learning. A common attri- Intelligent Controller (BELBIC) has been suggested [14]. There bute of the learning process is the adaptation of the system are two approaches of applying the Brain Emotional Learning parameters to better tackle the changing environment. An model into control systems, direct approach and indirect evaluation mechanism is necessary that any learning algorithm approach. The former uses BELBIC as the controller block, assesses the operating condition of the system. One type of while the latter utilizes BELBIC to tune the controller parameters. In [10], the model was adapted for applications in control * Corresponding author. Tel.: +20 1001408908. systems and the applicability of the model is verified by simu- E-mail address: [email protected] (A.M. El-Garhy). lating it in controlling different systems with increasing com- Peer review under responsibility of Faculty of Engineering, Alexandria plexity. The results of designing a BELBIC and a PID University. http://dx.doi.org/10.1016/j.aej.2014.12.001 1110-0168 ª 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 8 A.M. El-Garhy, M.E. El-Shimy Nomenclature h adjustable parameter for MIT rule based control- A amygdala output ler Ath thalamus output e difference between the reference and actual output O orbitofrontal cortex output l adaptation rate for MIT rule based controller V weight of the amygdala connection 0 l combined parameter of l and both actual and ref- Vth weight of the thalamus connection erence model parameters W weight of the Orbitofrontal cortex connection m step number S sensory input y actual output of the model Re w emotional cue signal yr reference output of the model a, ath learning rate in the amygdala u controller output b learning rate in the Orbitofrontal cortex a1,a2,...,a5,b4,b5, ...,b7 coefficients of the highly non-lin- Kp,Ki,Kd controller gains of the PID controller ear diesel engine process j jth input of the sensory input r reference input T sampling time Kr1,...,Kr4,Ky1, ...,Ky5 MIT rule based controller gains Ks1,Ks2 gains of the sensory input block E output of the BELBIC controller showed that the responses of the BELBIC were developed at the Instrumentation Laboratory (now the Draper faster when compared with the PID responses. Laboratory) at MIT. To present the MIT rule, we consider a In real time control and decision systems, Emotional closed-loop system in which the controller has just one Learning is a powerful methodology due to its simplicity, adjustable parameter h, then the MIT controller is designed low computational complexity and fast training where the such that gradient based methods and evolutionary algorithms are hard dh @e to be applied because of their high computational complexity ¼le ð1Þ [15–20]. dt @h Lately, many engineering systems are proposed by BELBIC where e = reference output – actual output = yr À y, l: such as power system [21], active queue management [22], adaptation rate. washing machine [23], aerospace launch vehicle [24], interior If Eq. (1) is digitized then we get permanent magnet synchronous motor system [25], micro-heat exchanger [26], flight simulation servo system [27], delayed sys- de hðm þ 1Þ¼hðmÞl0eðmÞ ð2Þ tems [28], two coupled distillation column system [29] and dh other uncertain nonlinear systems [30]. l0 is a combined parameter of l and both actual and reference 1.1. MRAS with MIT rule based controller model parameters. Eq. (2) is known as updating equation. Fig. 1 illustrates MRAS with MIT controller. The model-reference adaptive system (MRAS) [31] is an important adaptive control system. It may be regarded as an adaptive servo system in which the desired performance is 1.2. MRAS with BELBIC expressed in terms of a reference model, which gives the desired response to a command signal. Generally speaking, direct and indirect adaptive control In the MRAS the desired behavior of the system is specified schemes represent two distinct methods for the design of adap- by the model, and the parameters of the controller are adjusted tive controllers. To use emotional computations to design based on the error, which is the difference between the outputs adaptive controllers, we will easily end up with Direct Adap- of the closed-loop system and the reference model. The MIT tive Control (DAC) and Indirect Adaptive Control (IAC) rule [32] is the original approach to model-reference adaptive schemes. In the DAC, the parameters of the controller are control. The name is derived from the fact that it was directly adjusted to minimize the error, while in the IAC Figure 1 MRAS with MIT rule based controller. BELBIC for MRAS 9 Figure 2 Graphical depiction of BELBIC computational model. Figure 3 Architecture of MRAS with BELBIC. scheme, parameters of the plant under study are adjusted The amygdala part receives input from the thalamus and based on these estimates. The first scheme is used in this paper. from cortical areas, while the orbital part receives inputs BELBIC is divided into two parts, very roughly corre- from the cortical areas and amygdala only. The system also sponding to amygdala and orbitofrontal cortex, respectively. receives reinforcing (Rew) signal. There is one A node for 10 A.M. El-Garhy, M.E. El-Shimy Table 1 Coefficients of the non-linear diesel engine process. Coefficients a1 a2 a3 a4 a5 b4 b5 b6 b7 Reference model À1.7732 0.7077 0.2112 À0.2244 0.0916 0.0071 À0.0009 0.0006 0.0022 OC1 À1.6952 0.6663 0.2459 À0.3750 0.1709 0.0104 0.0035 0.0011 0.0025 OC2 À1.7490 0.7618 0.1367 À0.2331 0.0990 0.0096 0.0051 0.0002 0.0017 OC3 À1.7972 0.7693 0.1586 À0.1655 0.0507 0.0089 0.0023 0.0002 À0.0007 OC4 À1.8665 1.0419 À0.1164 À0.1049 0.0643 0.0091 0.0044 0.00009 0.0022 every stimulus S (including one for the thalamic stimulus). The coefficients of the process characterize the behavior of There is also one O node for each of the stimuli (except for the engine at nominal speed 1000 rpm. The relationship the thalamic node). There is one output node in common between the engine speed (rpm) and the tacho-generator out- for all outputs of the model, called E. The E node simply put voltage representing the speed is sums the outputs from the A nodes, and then subtracts the Engine SpeedðrpmÞ¼168 ðTacho OutputÞvolt þ 510 ð4Þ inhibitory outputs from the O nodes. The result is the out- put from the model. The E0 node sums the outputs from A except Ath and then subtracts from inhibitory outputs from 2.1. Traditional MIT rule based controller for the case study the O nodes. Fig. 2 depicts the computational model of BELBIC [33]. Fig. 3 demonstrates the architecture of From Eq.
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