Krish final

DESIGN AND IMPLEMENTATION OF PI CONTROLLER USING GENETIC ALGORITHM AND ANT COLONY OPTIMIZATION FOR A SPHERICAL TANK PROCESS

Mr. G. SAKTHIVELLecturer (selection grade)Department of Instrumentation EnggAnnamalai university chidambaram.ByA. KRISHNAMOORTHYM.E. (Process Control & Instrumentation Engg.) (2009-2011)

OBJECTIVES OF THE PROJECT WORKTo identify the model of the spherical tank process by black box modeling for various operating region.Low LevelMiddle LevelHigh LevelTo tune the PI controller by Ziegler- Nichols method.To optimize the designed PI controller using ACO (Ant Colony Optimization) Technique for various cost function like IAE, ITAE, ISE.To tune the PI controller by Genetic algorithm.

To compare the results of ACO tuned PI controller with Z-N tuned PI and GA tuned PI controller in terms of time domain specification and performance indices like ISE, MSE, ITAE, IAE. To obtain the results form both simulation and real time process for the corresponding models. To check to robustness of the above designed controller and test the ACO under white noise.

PI CONTROLLER It consist of proportional and integral action PID can be implemented as a stand alone controller (or) part of the controller e.g. DDC (or) DCS Various actions P-ACTION P = Kp* e I-ACTION I = ki e dt D-ACTION D = Kd d(e)/ dt whereKp = proportional gain KI = Integral gain

Closed loop Z-N tuned PI Controller

The transfer function of PI controller looks like following: U= Kp* e (t)+kie(t)Block diagram of PI controller Recommended PID Value Setting

TYPE OF CONTROLLERKpTiTdP0.5 Ku0PI0.45 KuPu/1.20PID0.6 KuPu/2Pu/8

OBJECTIVE FUNCTIONSThe following objective function we are using for both GA and ACO optimization. 1. Integral Absolute error

2. Integral square error 3. Integral time Multiplied by Absolute error

It is a type of machine learning technique

Mimics the biological process of evolution Genetic algorithms Software programs that learn in an evolutionary manner, similar to the way biological systems evolve

An efficient, domain-independent search heuristic for a broad spectrum of problem domains

Main theme: Survival of the fittes. Moving towards better and better solutions by letting only the fittest parents to create the future generations

Reproduction Multiple copies of the same string may be selected for reproduction and the fittest string should begin to dominate e.g. roulette wheel selectionDepiction of roulette wheel selection

CROSSOVER Once the selection process is completed, the crossover algorithm is initiated. The crossover operations swaps certain port of the two selected strings in a bid to capture the good parts of old chromosomes and create better new ones. Singe point Multi point Uniform

Single point crossover

Multi point crossover

Uniform crossover

MUTATION Mutation is the occasional random alternation of a value of a string position. Eg.

Ant Colony Optimization (ACO) is a paradigm for designing meta heuristic algorithms for combinatorial optimization problems.

Ants travel from node to node until end decision based on transition probability (called state transition)

Once all ants travel finished Solutions compared

Pheromone evaporation applied to all edges Pheromone increased along each edge of best/each ants path

Original ant system: at each iteration, the pheromone values are updated by all the ants that have build a solution in the iteration itself.

Daemon activities can be run (like local search)

Redo until termination criteria met

They have an advantage over simulated annealing and genetic algorithm approaches when the graph may change dynamically. The ant colony algorithm can be run continuously and can adapt to changes in real time.

Ants choose paths depending on pheromoneAfter collecting food, paths are marked After some time, the shortest path has the highest probability

When ants travel they mark their path with substance called pheromoneAttracts other ants

When an ant reaches a fork in its path the direction it follows is based on amount of pheromone it detectsDecision probabilistically made

This causes positive feedback situation (i.e. Choosing a path increases the probability it will be chosen)

While ( termination not satisfied )create antsFind solutionsTransition probability:

Pheromone updateDaemon activities {optional}

Quantity of pheromoneHeuristic distance, constants

While ( termination not satisfied )create antsFind solutionsPheromone update

Daemon activities {optional}Evaporation ratePheromone laid by each ant that uses edge (i,j)

RESULTS AND DISCUSION In this section the result of the implemented ACO (ant colony optimization) tuned PI Controller was obtained. The ACO designed PI controller is initialized with 10 Ants and 100 iterations then response is analyzed. From the ACO-PI controller Reponses it is compared with GA designed PI and ZN tuned PI controller. The various cost functions are plotted belowin the given figure with different tabulations.

Initialization of ParametersTo start up with GA, certain parameters need to be defined. Initializing value of the parameters for this project for is as follows: Population size-80Bit length of considered chromosome-6 Number of Generations-100Selection Method -Roulette wheel selectionCrossover type-Single point crossoverCrossover probability-0.8Mutation type-Uniform mutationMutation probability -0.05

Comparison of Performance index and time domain specification

KpKi%MpTptstrIAEISEMSEITAEZN0.73330.001842.93761320106315.71195.950.03929.22x104

ACO-ITAE0.44790.0008782.825041030209261.27196.240.03925.54x104ACO-IAE0.58250.001116.1412930143258.72181.850.03646.64x104ACO-ISE0.61620.001118.4398915135264.40180.380.03619.22x104

GA-ITAE0.52350.001216.1448849157256.64187.370.03754.72x104GA-IAE0.68860.001328.0370989108276.57181.560.03637.03x104GA-ISE0.66690.001736.3393114011295.01191.110.03827.56x104

ZN0.73330.001842.93761320106315.71195.950.03929.22x104ACO-ITAE0.44790.0008782.825041030209261.27196.240.03925.54x104GA-ITAE0.52350.001216.1448849157256.64187.370.03754.72x104

Step response for the closed loop system for the PI controller tuned with different methodsStep response for the closed loop system for the ACO -PI controller tuned with different cost function

Step response for the closed loop system for the GA- PI controller tuned with different cost function

Initial distribution of Kp, Ki for AC

Kp, Ki settled for ACO

Kp, Ki settled for GA

ACO ITAE setteled

Comparison of Performance index and time domain specification

KpKi%MptptstrIAEISEMSEITAEZN1.38460.003269.84251920105465.61279.930.05602.0565x105

ACO-ITAE0.96780.002038.4516940153371.14234.600.04691.1809x105ACO-IAE1.09780.001837.74611450130346.04220.200.04401.1059x105ACO-ISE1.13240.001940.54621430133349.93222.390.04451.1900x105

GA-ITAE1.15280.002552.34641440120388.66246.060.04921.3028x105GA-IAE1.18690.003365.14701750122454.97280.660.05611.8600x105GA-ISE1.24880.002960.84461400128420.10260.000.05211.5838x105

ZN1.38460.003269.84251920105465.61279.930.05602.0565x105ACO-ITAE0.96780.002038.4516940153371.14234.600.04691.1809x105GA-ITAE1.15280.002552.34641440120388.66246.060.04921.3028x105

Step response for the closed loop system for the PI controller tuned with different

Step response for the closed loop system for the ACO -PI controller tuned with different cost function

Step response for the closed loop system for the GA- PI controller tuned with different cost function

Initial distribution of Kp, Ki for AC

Kp, Ki settled for ACO

Kp, Ki settled for GA

ACO ITAE settled

zKpKi%MptptstrIAEISEMSEITAEZN2.29000.004663.74862140124499.58300.230.06002.3669x105

ACO-ITAE1.48520.002019.06161230210374.53245.520.04911.3270x105ACO-IAE1.69020.002528.85621590176375.28245.190.04901.2660x105ACO-ISE1.83000.003045.45101600158389.48251.790.05031.3200x105

GA-ITAE1.85860.002430.25251530160361.09238.410.04701.1800x105GA-IAE1.90720.003443.85281610150408.08261.230.05221.4300x105GA-ISE2.02370.003437.55361560140408.28258.890.05181.4750x105

ZN2.29000.004663.74862140124499.58300.230.06002.3669x105ACO-ITAE1.48520.002019.06161230210374.53245.520.04911.3270x105GA-ITAE1.85860.002430.25251530160361.09238.410.04701.1800x105

Step response for the closed loop system for the PI controller tuned with different methods

Step response for the closed loop system for the ACO -PI controller tuned with different cost function

Step response for the closed loop system for the GA- PI controller tuned with different cost function

Initial distribution of Kp, Ki for AC

Kp, Ki settled for ACO

Kp, Ki settled for GA

ACO ITAE settled

Robustness of the controller is defined as its ability to tolerate a certain amount of change in the process parameters without causing the feedback system to go unstableIn order to investigate the robustness of the proposed method in the model parameters were altered. henceGain constant K,Time const T,Delay time TdAre deviated by 15% of its nominal values. Therefore k is incremented by 15% T is incremented by 15% Td is reduced by 15% of

ACTUAL MODELSALTERED MODELS

ALTERED MODELSCase (i)Gain, K value is incremented by 15%.The value of is incremented by 15%.The value of td is decremented by 15%. Case (ii) Gain, K value is incremented by 10%.The value of is incremented by 10%.The value of td is decremented by 10%.

Case (iii)Gain, K value is incremented by 25%.and , td values no changes.Case (iv)Time constant is incremented by 25%.and k, td values no changes.Case (v)Time delay td is incremented by 25%.and k, values no changes.

Robustness check with various cost functions for various model

CASE 1 Model 1 Model 2 Model 3 Kp Ki %Mp tp Ts tr Kp Ki %Mp tp Ts tr Kp Ki %Mp tp Ts tr ZN 0.7333 0.0018 33.5 347 1000 105 1.3846 0.0032 53.8 390 1230 105 2.29 0.0046 49.6 448 1390 123 ACO 0.4479 0.00087 1.96 484 380 201 0.9678 0.0020 30.8 504 1225 157 1.4852 0.0020 28.6 618 1310 195 GA 0.5235 0.0012 11.7 439 729 162 1.1528 0.0025 39.5 437 1230 128 1.8586 0.0024 33.9 509 1350 155

CASE 2 Model 1 Model 2 Model 3 Kp Ki %Mp tp Ts tr Kp Ki %Mp tp Ts tr Kp Ki %Mp tp Ts tr ZN 0.7333 0.0018 36.9 356 1040 105 1.3846 0.0032 59.4 402 1260 105 2.29 0.0046 52.9 464 1440 125 ACO 0.4479 0.00087 2.16 520 552 215 0.9678 0.0020 32.9 506 1140 155 1.4852 0.0020 30 628 1290 197 GA 0.5235 0.0012 13.4 433 668 157 1.1528 0.0025 43.8 545 1330 127 1.8586 0.0024 36.2 524 950 157

CASE 3 Model 1 Model 2 Model 3 Kp Ki %Mp tp Ts tr Kp Ki %Mp tp Ts tr Kp Ki %Mp tp Ts tr ZN 0.7333 0.0018 65.7 348 2050 84 1.3846 0.0032 93.9 391 3560 85.7 2.29 0.0046 85.2 450 3400 102 ACO 0.4479 0.00087 14.7 423 935 150 0.9678 0.0020 53.2 451 1410 121 1.4852 0.0020 46.8 546 1650 153 GA 0.5235 0.0012 30.8 393 1100 120 1.1528 0.0025 70.7 416 1900 102 1.8586 0.0024 60.4 485 1800 125

CASE 4 Model 1 Model 2 Model 3 Kp Ki %Mp tp Ts tr Kp Ki %Mp tp Ts tr Kp Ki %Mp tp Ts tr ZN 0.7333 0.0018 36.7 401 1170 118 1.3846 0.0032 55.6 478 1500 128 2.29 0.0046 49.3 554 1680 153 ACO 0.4479 0.00087 2.42 587 667 244 0.9678 0.0020 33.1 624 1290 192 1.4852 0.0020 31.4 773 1050 242 GA 0.5235 0.0012 13.4 499 809 181 1.1528 0.0025 42 539 1110 156 1.8586 0.0024 34.8 638 1240 194

CASE 5 Model 1 Model 2 Model 3 Kp Ki %Mp tp Ts tr Kp Ki %Mp tp Ts tr Kp Ki %Mp tp Ts tr ZN 0.7333 0.0018 20.5 326 648 109 1.3846 0.0032 40.8 370 1140 107 2.29 0.0046 35.2 428 1270 129 ACO 0.4479 0.00087 0 0 985 272 0.9678 0.0020 22.2 508 1310 166 1.4852 0.0020 20.4 641 1440 213 GA 0.5235 0.0012 3.19 450 550 182 1.1528 0.0025 29.3 424 1170 133 1.8586 0.0024 22.9 505 1034 186

Robustness Investigation for model 1(Case1)

Robustness Investigation for model 2(Case1)

Robustness Investigation for model 3(Case1)

The following results shows different PI-tuned methods are implemented from real time process for above said models.

Comparison of Performance index and time domain specification

%MptsISEZN0.23.58.5274 x108GA0.1635.3635x 106ACO0.122.57.3456x 105

Step response for the closed loop system for the PI controller tuned with deferent methods

In order to test the PI tuning with ant algorithm in the presence of noise, ACO- ITAE is usedThe above system is tested for three different variances 2=0.0025 2=0.025, 2=0.25Ant algorithm was run 5 times with 10 ants and 100 iterations due to the probabilistic nature of AA and noise.

White noise for variance-0.0025

White noise for variance-0.025White noise for variance-0.00025

In phase 2 of this project work, the conventional PI controller was tuned by Z-N tuning method and compared with proposed GA and ACO methods.

Then it is implemented to the first order with dead time process. Then simulation studies are carried out to analyze the performance of the spherical tank process and Robustness of above mentioned controller for the different set points.

It is also implemented in real time for the real time results of GA, ACO, ZN same set points. The result of both simulation and real time process were compared.

From the output response obtained using ACO tuned PI controller gives less over shoot, fastest settling time, fastest rise time then the other techniques.

Time domain specification and performance indices were tabulated for the above said models.

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Sigurd Skogestasd, Simple analytic rules for model reduction ad PID controller tuning, Journal of process control, 13,2003, pp.291-309.

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Thank you

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