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This paper delineates a conventional buck converter controlled by optimized PID controller where Genetic Algorithm (GA) is employed with a view to enhancing the performance by analyzing the performance parameters. Genetic Algorithm is a probabilistic search algorithm which is substantially used as an optimization technique in power electronics. A bunch of modifications have already been introduced to enhance the performance depending upon the applications. However, in this paper, modified genetic algorithm has been used in order to tune the key parameters in the converter. Hence, an analysis is carried out where the performance of the converter is illustrated in terms of rise time, settling time and percentage of overshoot by deploying GA based PID controller and the overall comparative study is presented. Responses of the overall system are accumulated through rigorous simulation in MATLAB environment.

As human civilization is stepping into 22^{nd} century the researchers are more enthusiastic to build robust and electrically stable systems. In this regard, DC-DC converters [

Therefore, Buck converters significantly overcome the above problems and can be controlled by numerous controlling methods. Among various methods, PID (Proportional, Integral, and Differential) controller [

In Section 2, the circuit of conventional Buck converter is studied and State Space Modeling of the converter is illustrated. The elaborate discussion on implementation of Genetic Algorithm is depicted in Section 3 where overviews, objective function of the algorithm and design of the GA based PID Controller are stated. Finally, the results of the simulation and stability analysis of the system are shown and discussed in Section 4. Lastly, the overall comparative analysis is presented. All the simulations are carried out in MATLAB.

The conventional DC-DC Buck Converter comprises of inductor (L), capacitor (C), diode D, switch (S) and load resistance (R) which is shown in

When the switch S is ON, the diode becomes open and capacitor (C) discharges through load resistance (R). When the switch (S) is OFF, the diode is closed and current i_{L} passes through the capacitor (C) and load resistance (R). For mathematical modeling of DC-DC Buck Converter, State Space Modeling [

The system matrix is denoted as A, B, C and D; u and y are referred as input and output respectively. The state variable is indicated as x and xꞌ is the derivative of state variables. Here, current i_{L} and voltage v_{C} are system variables which are mapped as i_{L} = x_{1} and v_{C} = x_{2}._{ }

x ′ = A x + B u (1)

y = C x + D u (2)

The circuit diagrams for ON and OFF condition of the switch (S) are shown in

When S is ON:

v S = L d i L d t + v C (3)

i L = C d v C d t + v C R (4)

x ′ 1 = − 1 L x 2 + 1 L v S (5)

x ′ 2 = 1 C x 1 − 1 R C x 2 (6)

( x ′ 1 x ′ 2 ) = ( 0 − 1 L 1 C − 1 R C ) ( x 1 x 2 ) + ( 1 L 0 ) v S (7)

When S is OFF:

0 = v C + L d i L d t (8)

i L = C d v C d t + v C R (9)

x ′ 1 = − 1 L x 2 (10)

x ′ 2 = − 1 C x 1 − 1 R C x 2 (11)

( x ′ 1 x ′ 2 ) = ( 0 − 1 L 1 C − 1 R C ) ( x 1 x 2 ) + ( 0 0 ) v S (12)

The average of the state space model is illustrated below where switching duty cycle (d) is taken into consideration.

A ′ = A ON d + A OFF ( 1 − d ) (13)

A ′ = ( 0 − 1 L 1 C − 1 R C ) d + ( 0 − 1 L 1 C − 1 R C ) ( 1 − d ) = ( 0 − 1 L 1 C − 1 R C ) (14)

B ′ = B ON d + B OFF ( 1 − d ) (15)

B ′ = ( 1 L 0 ) d + ( 0 0 ) ( 1 − d ) = ( d L 0 ) (16)

Hence, the completed buck converter state space model is shown below:

( x ′ 1 x ′ 2 ) = ( 0 − 1 L 1 C − 1 R C ) ( x 1 x 2 ) + ( d L 0 ) v S (17)

Genetic algorithm (GA) is the method for solving both constrained and unconstrained optimization problems based on natural selection process that mimics biological evolution. The algorithm repeatedly modifies a population of individual solutions. At each step, the genetic algorithm randomly selects individuals from the current population and uses them as parents to produce the children for the next generation [

However, crossover is a genetic operator used to vary the programming of a chromosome or chromosomes from one generation to the next. It is analogous to reproduction and biological crossover, upon which genetic algorithms are based on. Mutation is a used to maintain genetic diversity from one generation of a population to the next generations. It alters one or more gene values in a chromosome from its initial state. Moreover, Selection is the stage of a genetic algorithm in which individual genomes are chosen from a population for later breeding. The flow chart for the algorithm is shown in

In order to implement Genetic Algorithm, objective functions are chosen to evaluate the fitness of the chromosome [

IAE = ∫ 0 τ | e ( t ) | d t (18)

ITAE = ∫ 0 τ t | e ( t ) | d t (19)

ISE = ∫ 0 τ e ( t ) 2 d t (20)

ITSE = ∫ 0 τ t e ( t ) 2 d t (21)

The basic block diagram of the system is shown in _{P}, k_{I} and k_{D} are taken and the chromosome is formed. The main objective of the study is to minimize the error between the input and the plant’s output.

Model order reduction technique is carried out in MATLAB so that the higher order transfer function obtained from the state space modeling can be converted into a simpler form.

Firstly, Buck converter for the conventional PID controller is employed and the response is taken to observe the stability of the system which is shown in

So, from _{P}, k_{I} and k_{D} are accumulated, tabulated and shown in _{P}, k_{I} and k_{D}. The parameters are listed in

After rigorous simulation in MATLAB, the values of k_{P}, k_{I} and k_{D} are obtained for all of the four performance indices of GA based PID controller which is evident in

Step responses for IAE, ITAE, ISE and ITSE and performance parameters are illustrated in Figures 6-9 respectively.

Name of the Components | Values |
---|---|

Input Voltage, v_{S} | 12 V |

Output Voltage, v_{0} | 5.574 V |

Capacitor, C | 200 µF |

Inductor, L | 145 µH |

Output Resistor, R | 1 Ω |

Name of the Parameters | Values |
---|---|

Population | 50 |

Fitness Scaling | Rank |

Selection | Stochastic Uniform |

Mutation | 0.1 |

Crossover | 0.8 |

Gain | Conventional PID | GA-PID | |||
---|---|---|---|---|---|

IAE | ITAE | ISE | ITSE | ||

k_{P} | 19.1228 | 18.85 | 11.38 | 22.046 | 14.268 |

k_{I} | 60,517.0162 | 64,869.2 | 59,637 | 48,926.2 | 45,350.9 |

k_{D} | 0.00135 | 0.002 | 0.000943 | 0.001 | 0.001 |

The performance parameters like Percentage of Overshoot (%OS), Rise Time (Tr), Settling Time (Ts) and Peak Amplitude are tabulated for both conventional and GA based PID Controller which is presented in

It is evident from the results that IAE portrays better results than other controllers. The overall comparative analysis of the step responses is illustrated in

Performance Parameters | Conventional PID | GA-PID | |||
---|---|---|---|---|---|

IAE | ITAE | ISE | ITSE | ||

%OS | 10.8 | 4.17 | 13.2 | 18.1 | 11.4 |

TR | 0.0000573 | 0.0000504 | 0.0000784 | 0.0000575 | 0.0000712 |

TS | 0.000552 | 0.000538 | 0.000614 | 0.000634 | 0.000616 |

Peak Amplitude | 1.11 | 1.04 | 1.13 | 1.18 | 1.11 |

In this paper, an investigative study on stability analysis of closed loop Buck converter is brought into action by GA based PID controller. It is observed that IAE depicts more optimized results in terms of overshoot (4.17%), rise time (0.0000504 s), settling time (0.000538 s) than other performance indices. The overall comparative analysis of step response provides an idea of the stability of the converter. Hence, it can be concluded that GA based PID controller is more convenient than other tuning methods for Buck converter. Thus, more efficient and stable equipment can be designed by utilizing this modern algorithm based technique.

The authors declare no conflicts of interest regarding the publication of this paper.

Nishat, M.M., Faisal, F., Evan, A.J., Rahaman, Md.M., Sifat, Md.S. and Rabbi, H.M.F. (2020) Development of Genetic Algorithm (GA) Based Optimized PID Controller for Stability Ana- lysis of DC-DC Buck Converter. Journal of Power and Energy Engineering, 8, 8-19. https://doi.org/10.4236/jpee.2020.89002