Choppers are static DC-DC converters that generate a variable DC voltage source from a fixed DC voltage source. The chopper consists of capacitors, inductors and switches, see Figure 1. All these devices in the ideal case do not consume power, this is the reason why choppers have good efficiencies. Generally, the switch is a MOSFET transistor which is a semiconductor device operating in either off or saturated mode [8] [9] [10] .

The goal of the analysis of the static converters by the mathematical model is to expose this model by a continuous canonical writing. The model obtained makes it possible to obtain the transfer function [11] .

When the switch is closed Figure 2 we have:

{ L d i L d t = V e − V s C d V C d t = i L − V s R (1)

When the switch is open Figure 3 we have:

{ L d i L d t = − V s C d V C d t = i L − V s R (2)

BOOST sizing is summarized in the following Table 1.

With ∆V_S = 5% (ripple of the voltage across the capacitor) and ∆I_L = 10% (ripple in the inductor).

In this study, we will synthesize a PI type controller in order to control the output voltage of the BOOST chopper. Figure 4 shows the model of the closed loop PID controller, from this model the Equation (3) below is given.

u = K P e ( t ) + K i ∫ e ( t ) d t + K d d e ( t ) d t (3)

The expression of the PI corrector is given in the Laplace domain by Equation (4):

C ( S ) = K P + K i S (4)

Depending on the needs imposed by the system to be regulated, the PI regulator is a combination of several components. A distinction is made between the proportional (P) components which improve speed and the integral (I) which eliminates the static error between the controlled quantity [12] [13] .

With the transfer function of the BOOST chopper obtained, a MATLAB script using the Ziegler Nichols method was developed to determine the parameters of the PI controller [14] .

This gives K_p = 0.0012, K_i = 12.1098.

After simulation, with the model given in Figure 5, and by varying the load, the following results are obtained, grouped together in Table 2.

The results obtained Figure 6 show that the PI control of the BOOST chopper offers a good efficiency of 96%. This remains stable near the nominal load and decreases when the load is doubled.

In 1948, two American researchers, Mac Culloch and Pitts, gave birth to the first mathematical model of a biological neuron, which they called: formal neuron. The formal neuron is a simplified mathematical model of the biological neuron, it has a certain number of inputs, the dendrites, a body processing the inputs according to the all or nothing method, and an axon conveying the response of the neuron. Figure 7 represents a basic model of a formal neuron [15] .

y = φ ( x ) (5)

x = ∑ i = 0 n W i x i (6)

The activation functions of neurons come in many forms. Most activation functions are continuous and offer an infinite number of possible values in the interval [0, +1] or [−1, +1]) (see Figure 8).

The neural network proceeds a high-speed computing time due to its high-speed response time. Therefore, the neural network is very useful for calculating the hash rate of power converters. Figure 9 shows a schematic diagram of a neural network that has two input layers, four hidden layers, one output layer [16] .

The main advantage of these networks lies in their learning capacity. Learning consists of modifying the weight of the connections between neurons. There are several modification rules: Hebb’s law, Widrow-Hoff’s rule, Grossberg’s rule… [17] .

In process control, the neural does not need an analytical model of the process to be controlled. This characteristic turns out to be interesting in the case of non-linear models that are difficult to model mathematically. Thus, thanks to its learning and approximation faculties, the neural command reproduce the behavior of the PI controller already developed using the matlab environment and proceeding as follows: [18]

➢ Step 1: Creating the database;

➢ Step 2: Choosing the neural network structure;

➢ Step 3: Training of the neural network (test and validation follow-up);

➢ Step 4: The development and implementation of the neural corrector.

At the end of learning, after five iterations, the results obtained are given by Figure 10 below. We notice that the error which represents the difference between the targets and the outputs obtained is very close to zero (8.55e−6).

Matlab allows us to develop a neural corrector Figure 11 and Figure 12 on Simulink that we will implement in the system to do the simulations.

Simulating the model in Figure 13 by varying the load gives the following results grouped together in Table 3.

The results obtained Figure 14 show that the neural control of the BOOST chopper offers a good efficiency of 97%. This remains stable near the nominal load and decreases when the load is doubled.

By plotting the data in Table 4, this comparison will be made by superimposing

the curves obtained and finally comparing their yield, performance and robustness.

The curves obtained in Figure 15, plotting the results grouped in the table,

show that both commands offer good performance, but the performance obtained with the neural command is better.

The curves in Figure 15 show that the neural control is much faster and more

stable than the PI control, and the efficiency in the neural control is higher in the vicinity of the nominal charge, Figure 16. It goes without saying that the neural controller is much more efficient.