Tuning of 2-DOF PID Controller By Immune Algorithm

Transcription

1 Tuning of 2-DOF PD Controller By mmune Algorithm Dong Hwa Kim Dept. of nstrumentation and Control Eng., Hanbat National University, 16-1 San Duckmyong-Dong Yusong-Gu, Daejon City Seoul, Korea, Tel: , Fax: Abstract - This paper represents that auto tuning of 2-DOF PD Controller can be effectively performed by immune algorithms. A number of tuning approaches for PD controllers are considered in the context of intelligent tuning methods. However, in the case of 2-DOF PD Controller, quite a few tuning based on the classical approach such a trial and error has been suggested. Also, a general view is provided that they are the special cases of either the linear model or the single control system. On the other hand, since the immune network system possesses a self organizing and distributed memory, it is thus adaptive to its external environment and allows a PDP (parallel distributed processing) network to complete patterns against the environmental situation. Also. t can provide optimal solution. Simulation results reveal that immune algorithms based tuning are an effective approaches to search for optimal or near optimal control.. NTRODUCTON The Proportional-ntegral-Derivative (PD) controller has been widely used owing to its simplicity and robustness in chemical process, power plant, and electrical systems. ts popularity is also due to easy implementation in hardware and software. However, with only the P,, D parameters, it is very difficult to control a plant with complex dynamics, such as large dead time, inverse response, and highly nonlinear characteristics. That is, since the PD controller is usually poorly tuned, a higher of degree of experience and technology is required for the tuning in the actual plant [5]. There are many well known P and PD tuning formulas for stable processes. However, PD tuning formulas for unstable processes or complex plants are less common. Up to this time, many sophisticated tuning algorithms have been tried to improve the PD controller performance under such difficult conditions, since the control performance of the system depends on the P,, D parameter gains. n many cases, especially in the actual plant, they are manually tuned through a trial and error procedure, and the derivative action is switched off, since it is difficult to tune. Recently, automatic tuning hzzy, neural network, genetic algorithm, and their combined approaches has been suggested but all of them are required to overcome difficulty in generation of parameter tuning such as the membership function for controller. Therefore, some papers suggest that learning capability of neural networks and optimization techniques such as genetic algorithms play the important role for combined methods. [9-111 n spite of their individual philosophies and structural difference, all of these approaches share the same difficulty of fuzzy rule generation or tuning of weight function in the neural network, since fuzzy rules and weights in a mixed learning structure must be different according to the plant and the conditions in which they are operated. That is, it is required to have a systematic method for constructing appropriate auto-tuning method and rules. On the other hand, the artificial immune network always has a new parallel decentralized processing mechanism for various situations, since antibodies communicate to each other among different species of antibodiesm-cells through the stimulation and suppression chains among antibodies that form a large-scaled network. n addition to that, the structure of the network is not fixed, but varies continuously. That is, the artificial immune network flexibly self-organizes according to dynamic changes of external environment (meta-dynamics function). Also, mmune network can provides an optimal solution approach for nonlinear dynamic process like Genetic algorithm. This paper focuses on tuning of the 2-DOF PD Controller based on the immune network DOF PD COCTROLLER WTH A SEPARATED 2-DOF PARAMETER A 2-DOF PD controller with a separated 2-DOF parameter for the power generating plant is composed as in Fig. 1. The transfer function between the process value PV(s) and the settling value SV(s), and between the process value PV(s) and the manipulated value, MV(s) are given as the following equations, respectively: /02/$ EEE 675

2 (3) where, 1 F(s) = pts filter transfer function, P(,) = KP[ 1 ++) : P controller transfer function, D(s) = - KpT,s : D controller transfer function, 1 + qt,s ~ : plant Z' ~ transfer function. n equation (l), the numerator has a similar function as that of the conventional PD controller. That is, if we tune the proportional gain K~ with a greater value, the affect of disturbance G, against plant output is smaller. However, in equation (2) and (3), the process value PV(s) and the plant G@) depend on the two degrees parameter a, p, y, and the proportional gain is also affected by the parameter a, y given for two degrees of function. n the long run, since the disturbance can be reduced by gains K ~ T,,, y, and the process value PV and the plant G,(s) are effectively controlled by the two degrees parameter a, p, y, the 2-DOF PD controller with a separated 2-DOF parameter can have two degrees of function completely CHARACTERSTC OF MMUNE NETWORK ALGORTHMS The artificial immune network system implements a learning technique inspired by the human immune system which is a remarkable natural defense mechanism that learns about foreign substances, However, the immune system has not attracted the same kind of interest from the computing field as the neural operation of the brain or the evolutionary forces used in learning classifier systems [6]. Other areas of the characteristic relating to the immune system for engineering field are summarized below: The learning rule of the immune system is a distributed system with no central controller, since the immune system is distributed and consists of an enormous number and diversity of cells throughout our bodies. 0 The immune system has a naturally occurring event-response system which can quickly adapt to changing situations and shares the property with the central nervous system that a definite recognition can made be made with a fuzzy stimulus. The immune system possesses a self organizing and distributed memory Therefore, it is thus adaptive to its external environment and allows a PDP (parallel distributed processing) network to complete patterns against the environmental situation @ Disturbance input Fig. 1. The structure of 2-DOF PD Controller for power plant system. 0 The correct fimctioning of the immune system is to be insensitive to the fine details of the network connections, since a significant part of the immune system repertoire is generate by somatic mutation processes. n particular, immune system can play an important role to maintain own system dynamically changing environments. Therefore, immune system would be expected to provide a new paradigm suitable for dynamic problem dealing with unknown environments their rather than static system. V. DYNAMC OF MMUNE ALGORTHM FOR TUNNG OF 2-DOF PD CONTROLLER A. mmune Algorithm Here, the objective function can be written as the followings: i=l 6; : objective function z: the number of process for obtaining an optimal gain, respectively 1 (4) /02/$ EEE 676

3 mmune Afinity Algorithm calculation oval Fig.3. The structure of controller. nteraction between agents given by: Fig.2. Proposed mechanism for selection of P,, D, a, P, and Y. L, : optimal level in process for selection of an optimal gain L:*J~'' : target optimal value in process in process for selection of an optimal gain 6 : penalty constant fn : penalty hnction P: the number of route for selection of an optimal gain Ri : gain level in route i Zi,. : subsidiary hnction LF : limit speed in gain This algorithm is implemented by the following procedures. [step 13 nitionalization and Recognition of antigen: The immune system recognizes the invasion of an antigen, which corresponds to input data or disturbances in the optimization problem. [step 21 Product of antibody from memory cell: The immune system produces the antibodies which were effective to kill the antigen in the past, from memory cells. This is implemented by recalling a past successhl solution. [step 31 Calculation of affinity between antibodies: The affinities q k obtained by equation (4) and the affinity ok using equation (5) is calculated for searching the optimal solution. [step 41 Differentiation of lymphocyte: The B-lymphocyte cell, the antibody which matched the antigen, is dispersed to the memory cells in order to respond to the next invasion quickly. This dispersed corresponds to strong the solution in a database. [step 51 Stimulation and suppression of antibody: The expected value q, of the stimulation of the antibody is where 6, is the concentration of the antibodies. The concentration is calculated by affinity based on phenotype but not genotype because of the reduction of computing time. So, ak is represented by: sum of antibodies with same aff;nity as me Ok = ' (6) sum of antibodies Using by equation (7), a immune system can control the concentration and the variety of antibodies in the lymphocyte population. f antibody obtains a higher affinity against an antigen, the antibody stimulates. However, an excessive higher concentration of an antibody is suppressed. Through this function, an immune system can maintain the diversity of searching directions and a local minimum. [step 61 Stimulation of antibody: To capture to the unknown antigen, new lymphocytes are produced in the bone marrow in place of the antibody eliminated in step 5. This procedure can generate a diversity of antibodies by a genetic reproduction operator such as mutation or crossover. These genetic operators are expected to be more efficient than generation of antibodies. mmune algorithms (A) are optimization techniques based on the principles of natural evolution. A operates on the population of potential solutions to a problem. A notion of fitness is used in A like GA to measure the goodness of a candidate solution (chromosome). A operators of selection, crossover, and mutation are repeatedly applied to the population to increase the fitness of chromosomes. The success of employing A to solve a given optimization problem greatly depends on correctly choosing the fitness function. Fitness function must positive values and must be maximized. 1) Mapping solution space into immune search space, binary strings. Constructing fuzzy fitness function F using /02/$ EEE 677

4 fuzzy measure of distance d, objective function given by Equation (4). 2) Creating initial population (set of chromosomes) randomly, i.e. a population of fuzzy weights of fuzzy neural networks which are randomly specified. 3) Evaluating each chromosomes in the population in terms of fitness value using Eq. (8). 4) f termination conditions are met go to step 8. 5) Generating new population using selection operator. This operator randomly selects chromosomes from the current population with the probabilities proportional to the values of fitness of the chromosomes. 6) Creating new chromosomes by mating randomly selected (with some specified probability called probability of crossover, Pc chromosomes. The resulting offspring replaces the original parent chromosomes in the population. 7) Mutating some randomly selected (with some specified probability called probability of mutation, chromosomes. Return to step 3. B. Performance Criteria For Tuning Generally there are many kinds of decisions for the control performance of control system. This paper is used as follows: 1) Minimum time- Weighted ntegral of Squared Errors TWS = ft'e'dt, 0 k = 0,1,2,..., m. (7) 2) Combined Performance ndex using Overshoot ( ov ) and Rise Time(T,) PF = k,ov -- k,t, (8) where in Equation (7) and (S), k, k,, k, are experimental parameters in order to emphasize our requirement about OV or T,. V. SMULATONS AND DSCUSSONS n this paper the plant transfer function shown in Fig. 1 is used for simulation. Fig. 2 is selection mechanism of immune network mechanism for the 2-DOF PD Controller of the transfer function of the combined power plant. Tables 1-2 represent variation of each parameter in immune cells and Figs show response of control system in the power plant controlled by variation of parameter in immune cell. Fig. 4 is the result of simulation by initial value range of immune network, Range (0-20; 0-10; 0-10; 0-1; 0-2; 1-2). Fig. 5 shows and Fig. 6 illustrates response to range of initial parameter value in cell (0-20; 0-20; 0-1 0; 0-1 ; 0-1 ; 1-2) and cell (0-20; 0-20; 0-20; 0-1; 0-2; 1-2), respectively. Fig. 6 has the most stable response as it represents response when the value of cell is (0-20; 0-20; 0-10; 0-1; 0-1; 1-2). Fig shows response of uncontrolled system after train by immune algorithms on each initial range (e.x.; 0-10; 0-10; 0-10; 0-1; 0-2; 1-2), respectively. V. CONCLUSONS There are many well known P and PD tuning formulas for stable processes. However, PD tuning formulas for unstable processes or complex plants are less common. Up to this time, many sophisticated tuning algorithms have been tried to improve the 2-DOF PD Controller performance under such difficult conditions, since the control performance of the system depends on the P,, D parameter gains. n many cases, especially in the actual plant, they are manually tuned through a trial and error procedure, and the derivative action is switched off, since it is difficult to tune. A number of the combined intelligent techniques have been studying in the viewpoint of tuning of control systems. However, there are still many problems must be improved in parameter tuning for learning On the other hand, the artificial immune system (AS) implements a learning technique inspired by the human immune system which is a remarkable natural defense mechanism that learns about foreign substances, However, the immune system has not attracted the same kind of interest from the computing field as the neural operation of the brain or the evolutionary forces used in learning classifier systems. Also, the immune system possesses a self organizing and distributed memory. Therefore, it is thus adaptive to its external environment and allows a PDP (parallel distributed processing) network to complete patterns against the environmental situation. n this paper, method to acquire intelligent tuning of 2-DOF PD Controller for optimal control has been described using immune algorithms. The simulation studies have been performed using the immune based parameter tuning for intelligent control Table 1 Variation of uarameter range in immune cell. Table /02/$ EEE 678

5 l l " bmpsua ton 190 1,P m o ~ w." ,.,.,_.$,... i"".., ~,. ".....~...,.. "... " " r W t Fig. 4. Plant response to range of initial value. (Rang~O-20; 0-10; 0-10; 0-1; 0-2; 1-2) 8 " :! i 2 -,! i - C Q r i C Fig. 8. Plant response to range of initial value. (Range=O-20; 0-20; 0-20; 0-1; 0-2; 1-2) *.* ' 2 ~ r. h*, Fig. 5. Plant response to range of initial value. (Range=O-20; 0-20, 0-20; 0-1; 0-2; 1-2) Fig. 9. Plant response to range of initial value. (Range=O-30; 0-20; 0-30; 0-1; 0-2; 1-2) Fig. 6. Plant response to range of initial value. (Range=O-20; 0-20; 0-10; 0-1; 0-1; 1-2) w ww Fig. 10. Plant response to range of initial value. (Range=O-O; 0-10; 0-10; 0-1; 0-2; 1-2) -6.1, Fig. 7. Plant response to range of initial value. (Rang-0-20; 0-20; 0-10; 0-1; 0-2; 1-2) Fig Plant response to range of initial value. (Range=O-O; 0-20; 0-10; 0-1; 0-2; 1-2) /02/$ EEE 679

6 Fig. 12. Plant response to range of initial value. (Range=O-20; 0-20; 0-20; 0-5; 0-2; 1-2),.., ,,.. structure and have revealed that the 2-DOF PD controller tuned by immune algorithms effectively regulate a plant with a time delay. To resolve this problem, this paper has introduced cost function. t is believed that the same method can be also applied successfully to other type of control structures. Using genetic algorithms to explore pattern recognition in the immune system, Evolutionary computation, vol. 1, pp , [ll] F. J. Valera, A. Coutinho, B. Dupire and N. N. Vaz., Cognitive networks: mmune, neural, and Otherwise, Theoretical mmunology, vol.2, pp , [12] J. Stewart, The immune system: Emergent self-assertion in an autonomous network, n Proceedings of ECAL-93, pp , [ 131 Dong Hwa Kim, ntelligent tuning of a PD controller for multivariable process using mmune network model based on fuzzy set, FUZZY-EEE2001, Dec. 3, 2001, Australlia. [ 141 Dong Hwa Kim, ntelligent tuning of a PD Controller using immune algorithm, KEE, vol. 14, no., pp. 1-8, References Assilian and E.H. Mamdani, An experiment in linguistic synthesis with fuzzy logic controllers, nt. J. Man-Machine Studies, vol. 7, pp. 1-13, A. Homaifar and E. Mccormick, Simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms, EEE Trans. Fuzzy Systems 3 pp , R. Ketata, D. De Geest and A. Titli, Fuzzy controller: design, evaluation, parallel and hierarchical combination with a PD controller, Fuzzy Sets and Systems vol. 71 pp , J. D. Farmer, N. H. Packard and A. S. Perelson, The immune system, adaptation, and machine learning, Physica. D 22, pp , J. Stewart, The mmune System: Emergent self-assertion in an autonomous network, n Proceedings of ECAL-93, pp , Kaz, uyuki Mori and Makoto Tsukiyama, mmune algorithm with searching diversity and its application to resource allocation problem, Trans. JEE, vol. 113-C, no. 10, 93. Dong Hwa Kim, Tuning of a PD controller using a artificial immune network model and fuzzy set July 28, FSA200 1, Vancouver. X. M. Qi, Genetic algorithms based fuzzy controller for high order systems, Fuzzy Sets and Systems, vol. 91, pp , C. Berek and C. Milstein, The Dynamics Nature of the antibody repertoire, mmunology Review, vol. 105, no. 5, [lo] S. Forrest, B. Javomik, R. E. Smith and A. S. Perelson, /02/$ EEE 680