Two-quadrant switched-inductor DC/DC converter controlled by neural network

Abstract: Classic DC/DC converters, such as Buck converter, Boost converter, Buck-Boost converter, Roche converter and Cuk converter [1-5], are usually composed of inductors and capacitors, so they are large in size and low in power density. Switching inductors have been successfully applied to DC/DC converters, creating a method for designing high power density converters. For example, Professor John G. Kassakian of the Massachusetts Institute of Technology (MIT) designed a new power supply system for future cars in the next century [6]. The core of this system is a two-quadrant DC/DC converter that converts between DC +42V and -14V.

Keywords: switched inductor, neural network, DC converter

Switched Inductor Two－ quadrant DC/DC Converter with Neural Network Control

Abstract:Classical DC/DC converters usually consist of inductors and capactors such as buck converter, boost converter, buck- boost converter, Luo- Converters and Cuk- Converter [1- 5]. Because all classical converters consist of capactors and inductors, they have big size and low power density. Switched- inductor has been successfully employed in DC/DC converters and opened the way to build the converters with high power density. For example, Professor John G.Kassakian of MIT designed a new power supply system for the future car in next century[6].The heart of this system is a Two－ Quadrant DC/DC Converter operating the conversion between＋ 42V and － 14VDC.

Keywords:Switched Inductor Neural Network DC/DC Converter

1 Introduction

The two-quadrant converter operating in the QⅢ and QⅣ quadrants is shown in Figure 1. It consists of two switches, two diodes and only one inductor L. It is usually considered that the source voltage V1 and the load voltage V2 are both constant voltages. The load voltage V2 can be the back electromotive force (EMF) of a battery or a motor. Because the circuit is completely symmetrical, either end of the circuit can be the power supply end or the load end. The source voltage does not have to be higher than the load voltage. R is the equivalent resistance of the circuit. There are two operating modes:

(1) Mode C (Quadrant III): Electric energy is transferred from terminal V1 to terminal V2;

(2) Mode D (Quadrant IV): Electric energy is transferred from V2 to V1.

Each mode has two states: "on" and "off". Usually each state can be operated at a different duty cycle k. The switching period is T, where T = 1/f. The switching states are shown in Table 1.

Table 1 Switching status (blank columns in the table indicate off status)

The mode C on-state is shown in Figure 2 (a): switch S1 is turned on, and the other switch S2 and all diodes are turned off. In this case, the inductor current flowing through the V1-S1-R-L loop increases, and the voltage on the inductor L approaches the constant voltage V1 value.

The off state of mode C is shown in Figure 2 (b): diode D2 is turned on, and the two switches and diode D1 are turned off. In this case, the inductor current iL flowing through the L-V2-D2-R loop decreases, and the voltage on the inductor L approaches the constant voltage V2 value. The inductor L transfers the power supply energy to the load. The inductor voltage and current waveforms are shown in Figure 2 (c).

The mode D on state is shown in Figure 3 (a). Switch S2 is turned on, and the other switches and diodes are turned off. In this case, the inductor current iL flowing through the V2-L-R-S2 loop increases. The voltage on the inductor L approaches the constant voltage V2 value.

Figure 1 Two-quadrant switched inductor DC/DC converter

The off state diagram of mode D is shown in Figure 3 (b), where diode D1 is turned on and the two switches and diode D2 are turned off. In this case, the inductor current iL flowing through the L-R-D1-V1 loop decreases, and the voltage on the inductor L approaches the constant voltage V1 value. The waveforms of the inductor current and voltage are shown in Figure 3 (C).

(a) Mode C on state diagram (b) Mode C off state diagram

(c) Inductor voltage and current waveforms

Figure 2 Mode C

(a) Mode D on state diagram (b) Mode D off state diagram

(c) Inductor voltage and current waveforms

Figure 3 Mode D

2 Mode C (Quadrant III operation)

2.1 Continuous Mode

If the equivalent resistance is very small, the voltage drop across the resistor can be considered as RIL.

It can be seen that the transmission efficiency depends only on the on-duty cycle k, source voltage and load voltage values, and has nothing to do with R, L and f.

2.2 Discontinuous Mode

From equation (9), we can see that when ζ ≥ 1, the current iL is discontinuous, so the boundary between the continuous region and the discontinuous region is defined as:

The boundaries of the continuous and discontinuous regions are shown in Figure 4. From equation (19), it can be seen that the discontinuous conduction region is caused by the following factors:

(1) The switching frequency f is too low;

(2) The on-duty cycle k;

(3) The size of the inductor L;

(4) The load resistance R is too large.

Figure 4 Boundary diagram of continuous and discontinuous areas

The entire conduction period is much shorter than T.

iL(kT) is the peak value of the inductor current iL(t), and is also the peak-to-peak value of the change ΔiL.

When t=t3, equation (22) shows that iL(t3)=0.

3 Mode D (Quadrant IV operation)

3.1 Continuous mode

Figure 4 Boundary diagram of continuous and discontinuous areas

Figure 5 Boundary diagram of continuous and discontinuous areas

If the equivalent resistance R is very small, the voltage drop across the resistor R can be considered as RIL.

It can be seen that the transmission efficiency depends only on the on-duty cycle k, source voltage and load voltage, and has nothing to do with R, L and f.

3.2 Discontinuous Mode

The boundaries of the continuous and discontinuous regions are shown in Figure 5. From equation (49), it can be seen that the discontinuous conduction region is caused by the following factors:

(1) The switching frequency f is too low;

(2) The on-duty cycle k is too small;

(3) The inductance L is too small;

(4) The load resistance R is too large.

The entire conduction period is much shorter than T. Assuming that the conduction period is between 0 and t4, the voltage and current on the inductor L are:

Figure 5 Boundary diagram of continuous and discontinuous areas

iL(kT) is the peak value of the inductor current iL(t), and is also the peak-to-peak value of the change ΔiL. When t=t4, equation (52) shows that iL(t4)=0.

4 Neural Network Control

This converter works in an open-loop control mode. As can be seen from equations (17) and (47), since the circuit resistance R is a random parameter, it has a great influence on the operating point of the system. In order to obtain a stable conversion operation, we use neural network control in the system [7,8]. Neural network control includes a closed-loop control consisting of proportional plus integral (PI) operation and neural network. The full diagram of this system is shown in Figure 6.

The proportional plus integral (PI) operation is described in 4.1. The neural network consists of three layers, namely the input layer, the hidden layer and the output layer. The structure of the neural network is shown in Figure 7. The functions of all nodes in the three layers are shown in Figure 8. They are described in 4.2 and 4.3 respectively.

4.1 Mathematical model

The proportional plus integral (PI) operation consists of a proportional plus integral controller and a load. In the formula: τ = L/R, Vi is Vl when the switch is on and V2 when the switch is off.

Figure 6 Two-quadrant switched inductor DC/DC converter controlled by neural network

Figure 7 Neural Network

Figure 8 Node Function

This is a nonlinear control system. From the equation we can see that the resistance R seriously affects the stability and response of the system.

4.2 Back Propagation Neural Network (BPNN) Scheme

A little math shows that for a constant inductor current, there is a corresponding applied voltage Vi.

A back propagation neural network (BPNN) with multiple inputs and multiple outputs can be placed between the input and output terminals. After analysis, the current-power control uses three neuron layers, namely the input layer (IL), hidden layer (HL) and output layer (OL). The structure of the back propagation neural network (BPNN) is shown in Figure 7. It consists of three layers, each containing a large number of neurons. The functions of all neurons in the same layer are the same, while the functions of neurons in different layers are different. The schematic diagram of the control system layout is shown in Figure 6.

4.3 Structural Description

w1ij, w2ij and w3ij are the weights of the neurons in the input layer, hidden layer and output layer; θij is the activation width of the i-th element in the n-dimension; Pij is the i-th element in the r-dimension; λij is the i-th element of the width vector; ρij is the i-th activation value in the m-dimension.

4.4 Self-learning function

From the system requirements, we know that the optimal training limit is:

Current response overshoot ≤5%;

Power response overshoot ≤ 10%;

Waveform swing ≤ 2 cycles.

The weight coefficients of all neurons will affect the response of the output parameters. The weight coefficients are determined by back-propagation learning techniques to meet the above limits. In the design of the system, all weights of each neuron in the neural network must be determined, which is usually called the training process. Here we introduce an automatic adjustment technique to train these weights.

Back propagation learning technology is based on the least mean square (LMS) operation, which is a search method related to the slope. The learning process can start with a preset initial value, that is, all weighted values ​​(rates) are set to one unit. The learning process is completed when the difference between the actual output obtained using these weights and the target is the smallest. Since the neural network is a small-scale network, the training process does not take a long time to complete. Usually it only takes 5 to 15 seconds.

5 Experimental results

The test equipment includes a 14V battery as load and a 42V DC source as power supply. The test conditions are: f=1∽5kHz, V1=42V and V2=-14V, L=0.3mH, R=3mΩ, volume=4000(in3), and the measured results are shown in Table 2. The total average power density (PD) is 27.8W/in3. The power density of this circuit is much higher than that of the classic converter. The power density of the classic converter is usually less than 5W/in3. Because the switching frequency is very low, the electromagnetic interference (EMI) is very weak.

6 Conclusion

Artificial neural network control technology has been successfully applied in two-quadrant switched inductor DC/DC converters, which overcomes the instability of the system operation caused by the critical value of the conduction duty k, thereby obtaining a smooth energy transmission process. The experimental results confirm the advantages of our design and back propagation neural network (BPNN) technology.

Table 2 Measured results at different frequencies