International Journal of Advanced Engineering Research and Science (IJAERS)
Vol-3, Issue-3 , March- 2016] ISSN: 2349-6495
Tuning of PID controller using Fuzzy Logic controller & Bacterial Foraging Optimization Algorithm Er. Kuljinder Singh Khaira1, Dr. Gursewak Singh Brar2 1
2
Research Scholar, Department of Electrical Engineering, BBSB Engineering College, Fatehgarh Sahib, Punjab, India Associate Professor & Head Department of Electrical Engineering BBSB Engineering College, Fatehgarh Sahib, Punjab, India
Abstract— Proportional integral derivative controller tuning is an area of interest for researchers in many disciplines of science and engineering. Work presented in this based on Fuzzy Logic Controller and Bacterial Foraging Optimization Techniques. The proposed techniques are applied to the problem of PID controller tuning and is compared. It is observed that Bacterial Foraging Optimization technique gives a better result. Keywords— PID, fuzzy logic controller, Bacterial Foraging, Control Actions.
There are four major characteristics of the closed-loop step response. These are Rise Time: the time it takes for the plant output y to rise beyond 90% of the desired level for the first time. Overshoot: how much the peak level is higher than the steady state, normalized against the steady state? Settling Time: the time it takes for the system to converge to its steady state. Steady-state Error: the difference between the steady-state output and the desired output. The effects of increasing each of the controller parameters KP, KI and KD can be summarized as:
I. INTRODUCTION A PID controller is a simple three-term controller. The letters P, I and D stand for, where P -Proportional, I – Integral, D – Derivative. The transfer function of the most basic form of PID controller is
Table 1 Show the effect of increasing each of the controller parameter. Rise Overshoot Settling S-S Error Response Time Time KP Decrease Increase NT Decrease KI Decrease Increase Increase Eliminate KD NT Decrease Decrease NT
C s =K +
+K s=
(1.1)
Where KP is Proportional gain, KI is Integral gain and KD is Derivative gain. R +
e -
U Controller C(s)
Plant Y G(s)
Fig.1:Shows basic block diagram of PID controller system It is assumed that controller is used in a closed-loop unity feedback system. The variable e denotes the tracking error, which is sent to the PID controller. The control signal u from the controller to the plant is equal to the proportional gain (KP) times the magnitude of the error plus the integral gain (KI ) times the integral of the error plus the derivative gain (KD) times the derivative of the error. =
+
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+
(1.2)
NT: No definite trend. Minor change. Typical steps for designing a PID controller are: Determine what characteristics of the system need to be improved. Use KP to decrease the rise time. Use KD to reduce the overshoot and settling time. Use KI to eliminate the steady-state error. II. FUZZY LOGIC BASED CONTROLLER Fuzzy controllers are very simple conceptually. They consist of an input stage, a processing stage, and an output stage. The input stage maps sensor or other inputs, such as switches, thumbwheels, and so on, to the appropriate membership functions and truth values. The processing stage invokes each appropriate rule and generates a result for each, then combines the results of the rules. Finally, the output stage converts the combined result back into a
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International Journal of Advanced Engineering Research and Science (IJAERS) specific control output value. The most common shape of membership functions is triangular, although trapezoidal and bell curves are also used, but the shape is generally less important than the number of curves and their placement. The processing stage is based on a collection of logic rules in the form of IF-THEN statements, where the IF part is called the ‘antecedent’ and the THEN part is called the ‘consequent’. Typical fuzzy control systems have dozens of rules. Taking an example rule for a thermostat: ‘If’ temperature is cold, ‘Then’ heater is high. III. PID Controller Using Fuzzy The structure of the fuzzy PID controller is presented in Fig. 2. In this case the derivation and integration is made at the input of the fuzzy bock, on the error e. The fuzzy block has three input variables xe, xie and xde. xe W e e’ x Ce + Ie ie’ xie ud
BF
Cie
de ’
De
Cu
xde
Cde r Fig.2: The block diagram of the fuzzy PID controller The transfer function of the PID controller is obtained considering a linearization of the fuzzy block BF around the origin, for xe=0, xie=0, xde=0 şi ud=0 with a relation of the following form: = + + (1.3) A relation, as the fuzzy block from the PID controller which has 3 input variables may described is: !"
;
,
=0 =
&' ()
,
* 0 (1.4)
Where = + + (1.5) The value K0 is the limit value in origin of the characteristics of the function: = lim() → !" ; , = 0 (1.6) Taking account of the correction made on the fuzzy block with the incremental coefficient cu, the characteristic of the fuzzy block corrected and linearized around the origin is given by the relation: u c1 K x3 x43 x53 (1.7) We are denoting: c61 c1 K (1.8) www.ijaers.com
Vol-3, Issue-3 , March- 2016] ISSN: 2349-6495
For the fuzzy controller RF-PID, with the fuzzy block BF linearized, the following input output relation in the z domain may be written: 8̃& :
7 8
=>? @=
A
7
7 ;
7
7
8̃& <8
8
=
=>?
(1.9)
With these observations the transfer function of the fuzzy ID controller becomes: BC" 7
& = =
8& D8̃
=
8
=>?
8
=>? @=
E
(1.10)
For the linear PID controller, the following relation for the transfer function is considered: BCF G
CF
D1
I G
?
JK L
E
(1.11)
IV.
BACTERIAL FORAGING OPTIMIZATION ALGORITHM Bacterial Foraging Optimization Algorithm (BFOA) is an nature inspired optimization algorithms. Application of group foraging strategy of a swarm of E.coli bacteria in multi-optimal function optimization is the key idea of this new algorithm. Bacteria search for nutrients is a manner to maximize energy obtained per unit time. Individual bacterium also communicates with others by sending signals. A bacterium takes foraging decisions after considering two previous factors. The process, in which a bacterium moves by taking small steps while searching for nutrients, is called chemo taxis. The key idea of BFOA is mimicking chemo tactic movement of virtual bacteria in the problem search space. p : Dimension of the search space, S : Total number of bacteria in the population, Nc : The number of chemo tactic steps, Ns : The swimming length. Nre : The number of reproduction steps, Ned : The number of elimination-dispersal events, Ped : Elimination-dispersal probability, C(i): The size of the step taken in the random direction specified by the tumble. Foraging theory is based on the assumption that animals search for and obtain nutrients in a way that maximizes their energy intake E per unit time T spent foraging. Hence, they try to maximize a function like E/T (or they maximize their long-term average rate of energy intake). Maximization of such a function provides nutrient sources to survive and additional time for other important activities (e.g., fighting, fleeing, mating, reproducing, sleeping, or shelter building). Shelter building and mate finding activities sometimes bear similarities to foraging. Clearly, foraging is very different for different species. Herbivores Page | 114
International Journal of Advanced Engineering Research and Science (IJAERS) generally find food easily but must eat a lot of it. Carnivores generally find it difficult to locate ate food but do not have to eat as much since their food is of high energy value. The â&#x20AC;&#x153;environmentâ&#x20AC;? establishes the pattern of nutrients that are available (e.g., via what other organisms are nutrients available, geological constraints such as rivers and mountains ountains and weather patterns) and it places constraints on obtaining that food (e.g., small portions of food may be separated by large distances). During foraging there can be risks due to predators, the prey may be mobile so it must be chased and the physiological siological characteristics of the forager constrain its capabilities and ultimate success. V. IMPLEMENTATION OF PROPOSED WORK The performance is significantly imprecise and the efficiency is minimized due to nonlinearity in the process plant. The fuzzy PID controllers are the normal extension of their conventional version, which conserve their linear structure of PID controller. The fuzzy PID controllers implemented using fuzzy logic control principle in order to attain a new controller that possesses systematic formulas very similar to digital controllers. Fuzzy PID controllers has variable control gains in their linear structure. structure These inconsistent gains are nonlinear function of the errors and variable rate of error signals. The main part of these variable gains in improving the control performance is that they are self- tuned gains and can adjust to rapid changes of the errors and rate of change of error based by time delay effects, uncertainties and non linearities of the underlying process. Effort has been made to realize globally minimal error squared error integral criterion in the step response of a process which is flowed with PID controller by tuning the Ki integral gain, Kp proportional gain and Kd differential gain values. Generally, the option of the controller coefficients is realized by approximate methods, which will not guarantee globally optimal way out for control contro applications. The values of Kd, Kp and Ki derived through the Fuzzy Logic Control and Bacterial Forging Optimization methods and the closed loop PID controller flowed with the process is tuned for values Kp, Ki and Kd. Results achieved by using proposed methods are presented in table 2.
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Vol-3, Issue-3 , March- 2016] ISSN: 2349-6495
Fig.3: Sows the Simulink model for PID controller using Fuzzy Logic Controller
Fig.4: Show the graphical output for PID Controller using Fuzzy Logic Controller
Fig.5: Sows the Simulink model for PID controller using BFOA
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International Journal of Advanced Engineering Research and Science (IJAERS)
[4]
[5]
Fig.6: Show the graphical output for PID Controller by using BFOA
Table 2. Show the comparison of both the techniques proposed for PID Controller tuning Bacterial Foraging Fuzzy Logic Parameter Opimiztion Controller Algorithim Rise Time
1.1
5.1000
Settling Time
2.4
4.6000
Peak
1.1
.0667
[6]
[7]
Vol-3, Issue-3 , March- 2016] ISSN: 2349-6495
Natural Computation (Volume:4 ), Page(s) : 282 – 286, Aug. 2007. Zhang Yangzhou & Li Jingjiao, “Fractional-order PID controller tuning based on genetic algorithm”, International Conference on Business Management and Electronic Information (BMEI), Volume:3, Page(s): 764 – 767, May 2011. Jiuq Han, Peng Wan & ; Xin Yang, ” Tuning of PID controller based on Fruit Fly Optimization Algorithm”, International Conference on Mechatronics and Automation (ICMA), Page(s): 409 – 413, Aug. 2012. Selamat, N.A., Wahab, N.A. & Sahlan, S., ”Particle Swarm Optimization for multivariable PID controller tuning”, IEEE 9th International Colloquium on Signal Processing and its Applications (CSPA), Page(s): 170 – 175, March 2013. Chen Shihe, Zhong Qing, Zhang Xi & Xue Yali, “Parameter Analysis of DDE-Based PID Controller Tuning Method”, Fourth Global Congress on Intelligent Systems (GCIS), Page(s): 167 – 171, Dec. 2013.
VI. Conclusion According to the analysis done on the basis of results obtained, we have landed to a conclusion that for the design of a PID controller for the low damping plant Bacterial Foraging Optimization technique gives a better result than Fuzzy Logic Controller techniques. It has been observed that as the number of iterations went on increasing the performance of the system also went on improving. REFERENCES [1] Ding-Li Yu, Chang, T.K. & Ding-Wen Yu, “Fault tolerant control of multivariable processes using autotuning PID controller”, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, (Volume:35 Issue: 1 ), Page(s): 32 – 43, Feb. 2005. [2] O'Dwyer, “Performance Improvement using Simple PID Controller Tuning Formulae”, The 3rd IET International Conference on Power Electronics, Machines and Drives Page(s): 276 – 280,April 2006. [3] Tan Guanzheng, Bin Jiang & Liming Yang, “A Novel Immune Genetic Algorithm-Based PID Controller Design and Its Application to CIP-I Intelligent Leg” , (ICNC 2007) Third International Conference on
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