Adaptation of PID Controller using AI Technique for Speed Control of Isolated Steam Turbine Mohamed .M. Ismail Faculty of Engineering – Helwan University Electrical power and machine department
[email protected] controller. Fuzzy, GA, PSO and ANFIS techniques will be used in this paper as adaptation techniques. The algorithm is tested on an experimental model to the Turbine Speed Control System. A comparison between the Adaptive Fuzzy Controller and other adaptation techniques are done. This paper is composed of six sections. Section II is a background of the steam turbine, section III is the modeling of the steam turbine and its governing system. Section IV, V, VI, VII, VIII specify the adaptation of PID controller using fuzzy logic, GA, PSO, BPSO and ANFIS respectively. Section IX is the simulation results. Finally, the conclusion is illustrated in section X . II. BACKGROUND In refineries, in chemical plants and other industries the steam turbine is a well known tool to drive compressors. These compressors are normally of centrifugal type. They consume much power due to the fact that very large volume flows are handled. The combination steam turbine-compressor is highly reliable. Hence the turbine-compressor play significant role in the operation of the plants. In the above set up, the high pressure steam (HPS) is usually used to drive the turbine. The turbine which is coupled to the compressor will then drive the compressor. The hydraulic governor which, acts as a control valve will be used to throttle the amount of steam that is going to the turbine section. The governor opening is being controlled by a PID which is in the electronic governor control panel. In this paper, it is proposed that the controller be tuned using the Genetic Algorithm technique. Using genetic algorithms to perform the tuning of the controller will result in the optimum controller being evaluated for the system every time. For this study, the model selected is of turbine speed control system.
Abstract—It is known that PID controller is employed in every facet of industrial automation. The application of PID controller span from small industry to high technology industry. Tuning the parameters of a PID controller is very important in PID control. Ziegler and Nichols proposed the well-known Ziegler-Nichols method to tune the coefficients of a PID controller. This tuning method is very simple, but cannot guarantee to be always effective. For this reason, this paper investigates the design of self tuning for a PID controller. For this study, the model selected is of isolated turbine speed control system. Isolated turbine system means that the turbine is not connected to the grid. The reason for this is that this model is often encountered in refineries in a form of steam turbine that uses hydraulic governor to control the speed of the turbine. The PID controller of the model will be designed using the adaptive fuzzy control method and the results analyzed. The same model will be redesigned using GA ,PSO and ANFIS methods. The results of design methods will be compared, analyzed and conclusion will be drawn out of the simulation made. Index Terms— PID controller, Fuzzy logic control, Self tuning controller, ANFIS, GA, PSO and steam turbine
I. INTRODUCTION Since many industrial processes are of a complex nature, it is difficult to develop a closed loop control model for this high level process. Also the human operator is often required to provide on line adjustment, which make the process performance greatly dependent on the experience of the individual operator. It would be extremely useful if some kind of systematic methodology can be developed for the process control model that is suited to kind of industrial process. There are some variables in continuous DCS (distributed control system) suffer from many unexpected disturbance during operation (noise, parameter variation, model uncertainties, etc.) so the human supervision (adjustment) is necessary and frequently. If the operator has a little experience the system may be damage or operated at lower efficiency [1, 4]. One of these systems is the control of turbine speed PI controller is the main controller used to control the process variable. Process is exposed to unexpected conditions and the controller fail to maintain the process variable in satisfied conditions and retune the controller is necessary. Adaptive controller is one of the succeed controller used in the process control in case of model uncertainties. But it may be difficult to the adaptive controller to articulate the accumulated knowledge to encompass all circumstance. Hence, it is essential to provide a tuning capability [2, 3]. The Speed control of turbine unit construction and operation will be described. Adaptive controller is suggested here to adapt normalized PID
c 978-1-4673-0484-9/12/$31.00 2012 IEEE
Figure 1 Turbine Speed Control
The reason for this is that this model is often encountered in refineries in a form of steam turbine that uses hydraulic governor to control the speed of the turbine as illustrated above in figure 1. The complexities of the electronic governor
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controller will not be taken into consideration in this dissertation. The electronic governor controller is a big subject by it and it is beyond the scope of this study. Nevertheless this study will focus on the model that makes up the steam turbine and the hydraulic governor to control the speed of the turbine. In the context of refineries, you can consider the steam turbine as the heart of the plant. This is due to the fact that in the refineries, there are lots of high capacities compressors running on steam turbine. Hence this makes the control and the tuning optimization of the steam turbine significant. III. MODELING OF THE STEAM TURBINE AND ITS GOVERNING SYSTEM A simplified construction of the steam turbine and its governing system is proposed in the figure 2 and 3
The identified model is approximated as a linear model that used in [4] , but exactly the closed loop is nonlinear due to the limitation in the control signal. IV. ADAPTATION OF PID CONTROLLER USING FUZZY LOGIC The fuzzy logic programming have been become widely used in industry. Extensive number of researches were developed using fuzzy logic technique [5-13]. This paper proposed two inputs-three outputs self tuning of a PID controller. The controller design used the error and change of error as inputs to the self tuning, and the gains (KP1, KI1, KD1) as outputs The controller proposed also contain a scaling gains inputs (Ke, K¨e) as shown in fig.5
Figure 5 Fuzzy self tuning proposed.
Now the control action of the PID controller after self tuning can be describing as: Figure 2 Modeling of the steam turbine
Figure 3 hydraulic governing schemes
Using matlab simulink model, the simulink model of the speed governing system is indicated in the figure 4
U PID = K P 2 * e(t ) + K I 2 ³ edt + K d 2
de(t ) dt
(2)
Where KP2, KI2, and KD2 are the new gains of PID controller and are equals to: KP2=KP1 * KP, KI2=KI1 * KI, and KD2=KD1*KD. Where KP1, KI1, and KD1 are the gains outputs of fuzzy control, that are varying online with the output of the system under control. And KP, KI, and KD are the initial values of the conventional PID. The membership functions for the inputs and outputs for the fuzzy controller are shown in figures 6 and 7
Figure 6 Member ships function of inputs (e, ¨e).
Figure 4 Simulink model of the speed governing system
To obtain the mathematical model of the process i.e. to identify the process parameters, the process is looked as a black box; a step input is applied to the process to obtain the open loop time response. From the time response, the transfer function of the open loop system can be approximated in the form of a third order transfer function: KK g 1 Gs = ≈ s (T g s + 1)( T t s + 1) S ( S + 1)( S + 5 ) (1)
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Figure 7 Member ships functions of outputs (KP1, KI1, and KD1).
Tables (1), (2), and (3) show the control rules that used for fuzzy self tuning of PID controller.
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V. ADAPTATION OF PID CONTROLLER USING GENETIC ALGORITHM
Genetic Algorithms (GA.s) are a stochastic global search method [14-16] that mimics the process of natural evolution. It is one of the methods used for optimization. John Holland formally introduced this method in the United States in the 1970 at the University of Michigan. The continuing performance improvement of computational systems has made them attractive for some types of optimization. The genetic algorithm starts with no knowledge of the correct solution and depends entirely on responses from its environment and evolution operators such as reproduction, crossover and mutation to arrive at the best solution. By starting at several independent points and searching in parallel, the algorithm avoids local minima and converging to sub optimal solutions. In this way, GAs have been shown to be capable of locating high performance areas in complex domains without experiencing the difficulties associated with high dimensionality, as may occur with gradient decent techniques or methods that rely on derivative information [17,18].The summary of the process will be described below:
is scattered , the stopping rules is the no of generation is 100 , and the stall time limit is 200 sec., VI. ADAPTATION OF PID CONTROLLER USING PSO Optimization techniques using analogy of swarming principle have been adopted to solve a variety of engineering problems in the past decade. Swarm Intelligence (SI) is an innovative distributed intelligent paradigm for solving optimization problems that originally took its inspiration from the biological examples by swarming, In the earlier PSO algorithms, each particle of the swarm is accelerated by its best previous position and towards the best particle in the entire swarm. Here, the underlying assumption is that each particle in the swarm remembers the best position already visited and also it is informed about the best particle position. After letting the particles to search adequate number of times in the solution space independently for the best possible positions, they are attracted to the basin containing the best particle by establishing proper communication among them about the th
search environment [19], [20] and [21]. Let the i particle of the swarm is represented by the D–dimensional vector
x i = (x i 1 , x i 2 ,..., x iD ) and the best particle in the swarm, i.e. the particle with the smallest function value, is denoted by the index g. The best previous position (the position giving the best function value) of the i recorded and represented as
pi
the position change (velocity)
th
particle is
= ( p i 1 , p i 2 , ..., p iD )
, and
v i = (v i 1 , v i 2 ,..., v iD )
of
th
the i particle is. The particles are manipulated according to the equations
v id = w .v id + c1.r1.( p id - x id ) + c 2 .r2 .( p gd - x id )
(4)
x id = x id + v id
(5) where d = 1, 2, . . . , D; i = 1, 2, . . . , N and N is the size of population; w is the inertia weight; c 1 a n d c 2 are two
r and r
2 are two random values in the positive constants; 1 range {0,1}. The first equation is used to calculate
i th particle’s new velocity by taking into consideration three terms: the particle’s previous velocity, the distance between the particle’s best previous and current position, and, finally, the distance between swarm’s best experience (the position of Figure 8 Genetic Algorithm Process Flow chart
In this paper, we are defining the parameters to be used in the GA optimization as followings: sys_overshoot=max(yout)-1 alpha=10;beta=10, The fitness function ( to be minimized ) is defined as F=(de/dt) beta+sys_overshoot*alpha . The yout in this research is the turbine speed , e is the speed error and alpha and beta are constants the no of variables is three (Kp , KI ,KD) , the population type is double vector , population size is 20 , the initial range of variable is (0.2– 10) For the reproduction , the elite count is 2 and the crossover friction is 0.8 , the mutation function is Gaussian , the crossover function
the best particle in the swarm) and i
th
particle’s current
position. Then, following the second equation, the i flies toward a new position.
th
particle
VII.BACTERIAL PARTICLE SWARM OPTIMIZATION (BPSO) is a modified method for the classical optimization method of PSO algorithm the velocity updating and position updating rules of particles are reinforced by two bacterial behaviors, i.e. reproduction and elimination-dispersal. Reproduction is applied to speed up the convergence rate, and
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elimination-dispersal provides diversity to overcome premature problem and escape from local optima. Particle swarm may lead to a stagnation phenomenon. If a particle's current position coincides with gbest, the particle will not move if its inertia weight and previous velocity are very close to zero. Once other particles have gathered around gbest, they will stop moving if their previous velocities are very close to zero. The whole swarm may not move further more and this stagnation could induce a premature convergence. In fact, the current gbest is the best position searched so far, which may not be the global optima. Therefore, particles fail to find the best position in search space. In order to solve this problem, researchers have proposed some strategies, e:g., adding a new parameter and an Additional equation, introducing a breeding and subpopulation strategy, and incorporating the mutation process used in GA into PSO [22] to solve the premature problem appears in the PSO optimization algorithm . BPSO reserves searching behavior of PSO and is reinforced by two bacterial behaviors. The pseudo code of evolution strategy in BPSO is listed in Algorithm 2. The bacterial behaviors are applied to particles after a number of Nud update behaviors. Reproduction behavior is performed if rd1 locates in the range of [0; Pre); and elimination-dispersal behavior is per- formed if rd1 locates in the range of [Pre; 1]. Therefore, Pre determines which bacterial behaviors would be applied to the optimization. In case of elimination-dispersal behavior is performed, the probability Pd is offered to determine which particles and how many particles will be selected to disperse. A random number rd2 is generated for each particle. Whether a particle will be dispersed or remained depends on the comparison result between rd2 and Pd. It can be concluded that, for each particle, the probability of reproduction behavior to be performed is Pre and the probability of eliminationdispersal behavior is Ped * Pd. , the algorithm of BPSO will be performed as followings : for 1 to Nbc do for 1 to Nud do Update velocity according to Eq.(7); Update velocity according to Eq.(8); Evaluate ¯tness value of each particle; Update pbest and gbest; end for Generate a random number rd1 in the range of [0; 1]; If rd1 < Pre then Sort particles in desc ending order according to fittness value; Select ¯rst Ni=2 particles as group1; Select second Ni=2 particles as group2; for 1 to Ni=2 do Eliminate particle in group1; Reproduce particle in group2; end for else for 1 to Ni do Generate a random number rd2 in the range of [0, 1];
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if rd2 < Pd then Initialize position of particle randomly in search space; Initialize velocity of particle randomly in velocity range; else Remain position and velocity of particle; end if end for end if end for VIII. Neuro Fuzzy Controller (ANFIS) An adaptive neuro -Fuzzy Inference System (ANFIS) is a cross between an Artificial Neural Network (ANN) and a fuzzy inference system (FIS). An artificial neural network is designed to simulate the characteristics of the human brain and consists of a collection of artificial neurons. An adaptive network is a multi-layer feed-forward network in which each node (neuron) performs a particular function on incoming signals. The form of the node functions may vary from node to node. In an adaptive network, there are two types of nodes, adaptive and fixed. The function and the grouping of the neurons are dependent on the overall function of the network. Based on the ability of an ANFIS to learn from training data, it is possible to create an ANFIS structure from an extremely limited mathematical representation of the system. In sequel, the ANFIS architecture can identify the near-optimal membership functions of FLC for achieving desired inputoutput mappings. The network applies a combination of the least squares method and the back propagation gradient descent method for training FIS membership function parameters to emulate a given training data set. The system converges when the training and checking errors are within an acceptable bound. The ANFIS system generated by the fuzzy toolbox available in MATLAB allows for the generation of a standard Sugeno style fuzzy inference system or a fuzzy inference system based on sub-clustering of the data. The main purpose of using ANFIS controller in this paper is for tuning the PID parameter based on GA and PSO optimization techniques . There are two ANFIS controller structure one is based on PID tuning using GA and the other is based on PSO will be shown in Figures (12) and (13) respectively. The fuzzy logic PID parameters are turned using neural network method which is well known in MATLAB program as ANFIS structure. The parameters are selected such that, optimization method is hybrid, the membership function is gbellmf , the membership function output is linear , error tolerance was chosen to be 0. 01 , the no of epochs are 1000 , grid partitions , the inputs of the grid partitions are the number MFS are 3 , MF type is gbellmf , the outputs is MF type defined to be constant .
Figure 12 PID tuning using ANFIS based on GA optimization technique
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100 90 speed reference steam turbine output s peed
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Figure 13 PID tuning using ANFIS based on PSO optimization technique
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Figure 17 Speed control using ANFIS training based on GA optimization algorithm for PID parameters tuning 160 speed reference steam turbine output speed
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IX. SIMULATION RESULTS The simulations have performed using MATLAB simulink program for tuning of the PID controller that is used for speed control of the steam turbine governed system with an approximate transfer function in equation (1) . The simulation is done first by using adaptive fuzzy controller for PID tuning , next we will use optimization techniques using GA and PSO , then the performance of the PSO will be improved using BPSO and finally the tuning is performed using ANFIS based on GA and PSO for adaptation of the fuzzy rules . The input speed reference used will be step and the turbine speed output response will be indicated using figures (14) to (22). A complete comparison between the output speed responses for the different AI techniques is indicated in figures (23) and (24).
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Figure 18 Speed control using PSO optimization algorithm for parameters tuning
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Figure 19 Speed control using PSO optimization algorithm for parameters tuning
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Figure 14 Speed control using fuzzy PID tuning algorithm
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Figure 20 Speed control using ANFIS training based on PSO optimization algorithm for PID parameters tuning
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Figure 15 Speed control using fuzzy PID tuning algorithm
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Figure 16 Speed control using GA optimization algorithm for PID parameters tuning
Figure 21 Speed control using parameters tuning
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Figure 22 Speed control using ANFIS training based on BPSO optimization algorithm for PID parameters tuning 160 speed reference output speed using fuzzy output speed using GA output speed using PSO output speed using BPSO
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Figure 23 comparisons between the system response using different classical AI techniques with the reference speed 250 speed reference output speed using ANFIS based on GA output speed using ANFIS based on PSO output speed using ANFIS based on BPSO
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Figure 24 comparisons between the system response using ANFIS based on different AI techniques with the reference speed
The speed reference used in simulation will be 100 r .p .m, Figure 18 indicate the speed response of the steam turbine by using the adaptive PID based on the fuzzy controller with membership functions included in figure 6 and 7. Amplification is done for the transient period of figure 14 is indicated in figure 15. Figure 16 specify the system response by using GA for tuning of PID controller. Figure 17 identify the system response base on ANFIS trained by GA algorithm. Similarly figure 18 and 20 but by using PSO algorithm. An amplification of the transient response occurred in 18 is indicated in figure 19. An improvement in the PSO algorithm is performed by BPSO which is pointed out in figures 21 and 22.From the above figure we can point out that the fuzzy PID tuning have the best performance for the turbine speed governed system in comparison between fuzzy and other AI techniques in the percentage overshoot and settling time .GA have better performance than PSO in this simulation but the BPSO have improved the performance of PSO and become better in the response than GA . Figure (23) give complete comparisons between the fuzzy, GA, PSO and BPSO in the system output speed. By training of the fuzzy rules using ANFIS, figure (24) signify that the tanning of the fuzzy rules based on BPSO have the best performance than the other methods.
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X. CONCLUSION From the simulation results, the responses had showed to us that the designed PID with Adaptive Fuzzy Controller has much faster response than using the other AI methods. The Adaptive Fuzzy designed PID is much better in terms of the rise time and the settling time. BPSO have better response than the classical PSO and the GA optimization techniques. The training of the fuzzy membership functions using ANFIS has better performance in BPSO than other AI algorithms. In this paper, some of the new adaptation algorithms are applied for selecting the optimum PID gains such that BPSO and ANFIS. REFERENCES [1] Astrom, K., T. Hagglund: PID Controllers; Theory, Design and Tuning, Instrument Society of America, Research Triangle Park, 1995. [2] M. A. El-Geliel: Supervisory Fuzzy Logic Controller used for Process Loop Control in DCS System, CCA03 Conference, Istanbul, Turkey, June 23/25, 2003. [3] Kal Johan Astroum and Bjorn Wittenmark: Adaptive control, AddisonWesley, 1995 [4] saifudin bin mohamed ibrahim , “the pid controller design using genetic algorithm “ , University of Southern Queensland Research Project, October, 2005 [5] J. M. Mendel: Fuzzy Logic Systems for Engineering: A tutorial, Proc. IEEE, vol. 83, pp. 345-377, 1995. [6] L. X. Wang: Adaptive Fuzzy System & Control design & Stability Analysis, Prentice-Hall, 1994. [7] H.X.Li and S.K.Tso, "Quantitative design and analysis of Fuzzy Proportional-Integral-Derivative Control- a Step Towards Autotuning", International journal of system science, Vol.31, No.5, 2000, pp.545-553. [8] Thana Pattaradej, Guanrong Chen and Pitikhate Sooraksa, "Design and Implementation of Fuzzy P2ID Control of a bicycle robot", Integrated computer-aided engineering, Vol.9, No.4,2002. [9] Weiming Tang, Guanrong Chen and Rongde Lu,”A Modified Fuzzy PI Controller for a Flexible-jonit Robot Arm With Uncertainties”, Fuzzy Setd and System, 118 (2001) 109-119. [10] Leronid Reznik, Omar Ghanayem, anna bourmistrov, "PID Pulse Fuzzy Controller Structures as a Design for Industrial Application", Engineering application of artificial intelligence, Vol.13,No.4,2002,pp.419-430. [11] Keven M.Passino and Stephen Yurkovich, "Fuzzy Control", Addison Wesley longnan, Inc., 1998. [12] G.R.Chen and T.T.Pham, "Introduction to fuzzy sets, fuzzy logic, fuzzy control system", CRC.Press,Boac Raton,FL,USA,2000. [13] Michall Petrov, Ivan Ganchev and Ivan dragotinov, “Design Aspects of Fuzzy PID Control”, International conference on soft computing, Mendel “99”, Brno,czech republic, 9-12, jun.1999, pp.277-282. [14] Johan Andersson “Applications of a Multi-objective Genetic Algorithm to Engineering Design Problems”, Springer Berlin,ISBN 0302-9743 [15] Colin R. Reeves, Jonathan E. Rowe, ”Genetic algorithm Principles and perspective, A Guide to GA theory”, Kluwer Academic PublishersISBN 14020-7240-6, 2002 [16] R. Bandyobadhyay, U.K. Chakraborty, “Autotuning a PID Controller : A Fuzzy-Genetic approach ”, Journal of System Architecture 47 (2001) 663-673 [17] Goldberg, David E. .Genetic Algorithms in Search, Optimization and Machine Learning.Addison-Wesley Pub. Co. 1989. [18] Q.Wang, P.Spronck & Figure 10 Genetic Algorithm Process Flow chart ering Problems,. Proceedings of the Second Conference on Machine Learning and Cybernetics, 2003. [19] M.O. Tokhi and M.S. Alam " Particle Swarm Optimization Algorithms and Their Application to Controller Design for Flexible Structure system". [20] Nadia Nedjah,” Swarm Intelligent Systems”, Studies in Computational Intelligence, Springer, vol 26 [21] K.E. Parsopoulos and M.N. Vrahatis. Recent approaches to global optimization problems through particle swarm optimization. Natural Computing 1: 235 – 306, 2002. [22] JI Zhen ,WANGYiwei ,CHUYing and WUQinghua “Bacterial Particle Swarm Optimization “Chinese Journal of Electronics Vol.18, No.2, Apr. 2009
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