Optimal Tuning of Brain Emotional Learning Based Intelligent Controller Using Clonal Selection Algorithm
Mohammad Jafari Department of Mechatronics Qazvin Branch, Islamic Azad University Qazvin, Iran [email protected]
Alireza Mohammad shahri Department of Electrical Engineering Iran University of Science and Technology Tehran, Iran [email protected]
Seyyed Hamid Elyas Department of Electrical Engineering Semnan University Semnan, Iran [email protected]
Abstract— In this paper, an optimal parameter assignment implemented on Field-Programmable Gate Arrays methodology for intelligent controller based on (FPGA), and applied to control a laboratory Overhead computational model of emotional learning in mammalian Traveling Crane [17]. Also, it was practically applied for brain is presented. Brain Emotional Learning Based speed control of a Digital Servo System via MATLAB Intelligent Controller (BELBIC) is an intelligent controller external mode [18]. based on emotional learning process in mammalian limbic system. The proposed controller has been applied to control Comparing Applying BELBIC to those plants to other a single link flexible joint manipulator. In this paper, the controllers, BELBIC shows very acceptable results. This CLONAL Selection Algorithm is utilized to obtain superior controller has two important inputs: Sensory Input (SI) and controller parameters in order to minimize Rise time, Primary Reward (Rew) and the flexibility in defining SI Settling time and Overshoot. and Rew makes BELBIC a popular controller in multi objective problems. Since BELBIC has ability of learning, Keywords-Intelligent Control; BELBIC; Optimal Tunning; it shows the response like Robust Adaptive methods. CLONAL Selection Algorithm One of the important parts of applying BELBIC to properly control a system is assigning the appropriate I. INTRODUCTION parameter for both Rew and SI. After Moren and Balkenius introduced a computational model of emotional learning in mammalian limbic system There are several methods for tuning the parameters of in 2000 [7], Lucas et al innovate a novel intelligent BELBIC such Particle-swarm-based Approach [6, 15], controller called Brain Emotional Learning Based Lyapunov Based Algorithm [13], Fuzzy Tuning [12] and Intelligent Controller (BELBIC) based on that cognitive trial and error method. model[1]. Since that, BELBIC was utilized in several For the first time in this paper an effective optimal applications and control problems such as Control of algorithm called CLONAL Selection Algorithm used to Intelligent Washing Machine [11], Emotional Control of obtain those parameters. In this article CLONAL-BELBIC Inverted Pendulum [8], Intelligent Controller applied to is applied to a single link flexible joint manipulator which neurofuzzy model of Micro-Heat Exchanger [5] and is a nonlinear system to examine the satisfactory results of Switched Reluctance Motor (SRM) Control [4]. proposed optimal parameter assignment. The result of Additionally, BELBIC has been successfully proposed controller is compared with Particle Swarm experimentally utilized in real-time by using a DSP-board Optimization (PSO) tuned BELBIC and a robust for a laboratory 1[hp] Interior Permanent Magnet controller. Synchronous Motor drive [16]. Furthermore, it was The rest of this paper is organized as follows. Section II describes CLONAL Selection algorithm. BELBIC Controller and the under control plant are presented in section III and IV respectively. Simulation results are provided in section V and finally some conclusions are presented in section VI.
II. CLONAL SELECTION ALGORITHM The CLONAL selection mechanism is a natural developmental process of the Immune systems. The body defend system depends on the performance of antibodies to recognize and eliminate foreign cells called antigens. The most important immune system cells are lymphocytes. Lymphocyte is divided into two main categories, B cells and T cells. These cells are used to identify the antigens. In the Immune system, after a successful identification of antigens, antibodies that have the ability to identify the antigens are proliferated in large scales. Furthermore, on the antibodies that have managed to identify the antigens, Figure 1. Graphical depiction of computational model of emotional mutations are done. This makes antibodies that can learning in amygdala[7] recognize the mutant antigens. This model is divided into two important parts: In mathematical models of the Immune system, each antibody as a candidate for solution is shown with a vector. The Amygdala Each vector component indicates one of the features of the antibody. In optimization problems, the objective function The Orbitofrontal Cortex (OFC) is a criterion to determine the excitability. Therefore, in The vector S shows stimuli inputs to the system. The CLONAL algorithm the objective function is used to output of each node in Amygdala (Ai) and OFC (Oi) determine the suitable particles. According to the above obtains by multiplying any input (Si) with the weights Vi description, the performance steps of the CLONAL and Wi respectively. algorithm are as follows [2, 10]: Generation of initial responses (N). Ai SiVi Determination of excitable cells. Oi SiWi Reselection of cells from initial set (M). Ath is another input to the Amygdala part which is the Proliferation of selected cells, proportional to maximum of stimuli inputs (S). their excitability.
Mutation of proliferate cells, proportional to Ath maxSi their excitability.
Selecting M number of the cells with most The Vi and Wi can be obtained from: excitability (N-M).
Randomly selection of P number of the cells Vi Si max0, Re w A j and replacement instead of omitted cells. j Wi Si Aj O j Re w III. BELBIC CONTROLLER j j Moren et al developed a computational model of those The weights V cannot decrease, because once an parts of limbic system thought responsible for processing emotional reaction is learned, this should be permanent. It emotions. Fig.1 plots a graphical depiction of the is the task of OFC part to inhibit this reaction when it is emotional learning in amygdala. inappropriate [7]. According to the Moren model, BELBIC was introduced by Lucas et al [1]. x1 x2 mgl K x sinx x x 2 I 1 I 1 3
x3 x4 B K 1 x4 x4 x1 x3 u(t) J J J Figure 2. Typical feedback control block diagram[1] Where
Fig.2 demonstrates a typical feedback control block x1 link position diagram consisting BELBIC Controller. x2 link angular velocity Emotional Signal (Primary Reward) and Sensory Input blocks could be defined as follows: x3 rotor position
x4 rotor angular velocity
Re w f e,u,r I link inertia SI gy,e J rotor inertia
Where K the constant of elastic joint y plant output m link mass r reference input l link length e error g gravity constant u control effort B viscosity BELBIC parameters are divided into two separate u(t) control input groups: the first learning rates in Amygdala and OFC The system parameters are chosen from [14] that list in ( and ) and the second coefficients which appear in Table I. Sensory Input and Primary Reward signal formulation.
In this paper all parameters have been chosen by TABLE I. SYSTEM PARAMETERS CLONAL Selection algorithm in order to achieve the optimal answers. Symbols Values Units mgl 5 [N m]
IV. SINGLE LINK FLEXIBLE JOINT MANIPULATOR I 1 [Kg m2] J 0.3 [Kg m2] B 0.1 [Kg m2/sec] K 100 [N m]
V. SIMULATION RESULTS This section presents numerical simulations of single Figure 3. Model of Single Link Flexible Joint Manipulator[3] link flexible joint manipulator. The drawback of utilization of BELBIC is that its gains often tuned using trial and Fig.3 illustrated a single link flexible joint manipulator. error rather than a specific approach. So this paper The dynamics of this system can be described by [3]. introduced a modified version of BELBIC which employs an optimal method called CLONAL Selection algorithm. The proposed CLONAL-BELBIC controller is used to Iq1 mglsinq1 Kq1 q2 0 control this system and finally the results would be Jq Bq Kq q u 2 2 1 2 compared with the robust control approach (RCA) in [9] and PSO-BELBIC. Equation (6) shows the state-space representation of system which is driven from (5). The following function used as Primary Reward signal for both CLONAL-BELBIC and PSO-BELBIC control scheme.
de Re w K e K e dt K p i d dt As mentioned in previous section all the parameters are adjusted by CLONAL Selection algorithm and the optimum values are given in Table II. It should be noticed that PSO algorithm is also used to tune the BELBIC parameter to show the effectiveness of proposed method.
TABLE II. THE BEST PARAMETERS OF THE BELBIC OPTIMIZED BY PSO AND CLONAL ALGORITHMS
CLONAL PSO Parameters Values Values
Kp 20.5358 11.2268 Figure 6. Step response of link position (x1) with PSO-BELBIC Ki 923.6764 724.7461
Kd 653.6999 526.2764 Figs 4-6 prove that the performance of CLONAL- 0.3832 0.4698 BELBIC is much better than PSO-BELBIC and the RCA. 0.4584 0.6449 VI. DISCUSSION AND CONCLUSION
In spite of slower response, both CLONAL-BELBIC Fig.4 shows step response of link position (x1) and PSO-BELBIC Controllers show very small Overshoot controlled by RCA. In spite of fast response, the Overshoot and Settling Time than RCA Controller. Also the result of is high. CLONAL tuned controller shows the better result comparing with PSO one. Although this paper used simple Primary Reward signal it shows the usefulness of proposed controller over the RCA. Simulation result for single link flexible joint manipulator demonstrates the effectiveness of CLONAL- BELBIC. The main contribution of this paper is to use CLONAL Selection algorithm to adjust BELBIC parameters and employs the proposed controller to control the complex system of single link flexible joint manipulator.
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