# Theoretical Design and Experimental Validation of a Nonlinear Controller for Energy Storage System Used in HEV

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions and global warming effects, to present a mean of transportation capable to concur the classical vehicles in performances with zero emissions [6]. Owing to their economic and environmental benefits, the State invites and encourages by scholarships and by tax exonerators the researchers and industrialists to combine them and to dig in the field of the hybrid automobile in order to develop the infrastructure of the HEV [7].

_{sc}to the reference current I

_{scref}and also show significant ripple in the current i

_{sc}, which influences the DC–DC bus voltage. Indeed, the robustness of the control proposed by [20] is low. The authors of [21] have presented an interleaved two-phase bidirectional DC–DC converter topology to control the SC current; this topology includes a small number of components based on a classical Proportional-Integral-Derivative (PID) control through the linearization of the nonlinear system. But the results of [21] show a significant ripple in the SC current, which introduces measurement and control errors. This is due to the fact that the system parameters are incorrectly dimensioned. Indeed, the control law proposed by [21] is not robust.

## 2. Storage System Presentation and Modeling

#### 2.1. Storage System Presentation

_{1}and u

_{2}applied on the gates of the two Insulated Gate Bipolar Transistor (IGBTs) S

_{1}and S

_{2}, respectively. The resistance R

_{L}represents the equivalent series resistance (ESR) of the inductor. The SC is represented by its capacity C

_{sc}and by its series resistance R

_{sc.}

#### 2.2. Modeling of a Reversible Power Buck–Boost Converter

_{sc}< 0), the converter operated as a boost converter, and in the charging mode of SC (i

_{sc}> 0), it operated as a buck converter. As our goal was to enforce the SC current i

_{sc}to track its reference I

_{scref}provided by the energy management system, in order to control this converter, we have defined a binary variable k as follows:

- Boost mode operation (k = 1)

_{2}was fixed to zero (u

_{2}= 0), and u

_{1}was a PWM variable input. From inspection of the circuit, shown in Figure 2, and taking into account that u

_{1}could take the binary values 1 or 0, the following bilinear switching model could be obtained:

- Buck mode operation (k = 0)

_{1}was fixed to zero (u

_{1}= 0), and u

_{2}acted as the Pulse Width Modulation (PWM) variable input. From Figure 2, and taking in account that u

_{2}∈ [0,1], the Buck model could be obtained by:

_{12}is the control input of BBC defined as follows:

_{1}the average value of the SC current (${x}_{1}=<{i}_{sc}>$), and µ

_{12}is the duty cycle, i.e., average values of the binary control input u

_{12}(${\mu}_{12}=<{u}_{12}>$), which takes values in [0,1]. The generation of effective control input signals u

_{1}and u

_{2}from u

_{12}is represented in Figure 3.

## 3. Storage Sliding Mode Control and Stability Analysis

#### 3.1. Control Objective

- (i).
- Monitoring of the supercapacitor current up to its reference,
- (ii).
- Asymptotic stability of the system.

#### 3.2. Sliding Mode Control

_{1}and K

_{2}are sliding surface coefficients, and ${I}_{scref}$ is the current reference, and $e={x}_{1}-{I}_{scref}$ is the surface error.

#### 3.3. The Limitations of SMC Technique

## 4. Simulation and Experimental Results

#### 4.1. System Characteristics

_{D}(f

_{s}) graph allowed us to choose the suitable switching frequency for our system, which was 25 kHz. Likewise, for the experiment, the type of transistor used was an IGBT transistor under the reference IG15 and its control box under the reference IG10. According to the Datasheet for this transistor, its suitable switching frequency was 15 kHz.

#### 4.2. Simulation and Experimental Bench for SCSS Control

^{®}and Matlab

^{®}/Simulink

^{®}, to easily test the systems or measure its quantities (Voltage, Current). The key point of this technology is the real-time control (RTC) process of the system. dSPACE systems are the solution for the development of embedded software in the automotive, aerospace, and industrial control [29,30].

^{®}/software

^{®}. In this figure, ${\mu}_{12}$ is the control law (the duty ratio), ${u}_{1}$ and ${u}_{2}$ are the binary input signals, i

_{sc}, V

_{sc}, and V

_{dc}are the measured variables, and I

_{scref}is the SC current reference.

^{®}/software

^{®}. This validation was carried out in the LGS Laboratory, ENSA, Ibn Tofail University.

- -
- a power supply from BK Precision,
- -
- a dSPACE DS1202 with Control Desk
^{®}/software^{®}plugged in a Pentium 4 personal computer, - -
- a Semikron IGBT module (SEMITEACH),
- -
- a 16 V supercapacitor module of Maxwell,
- -
- one ferrite inductance,
- -
- one Hall effect current sensor,
- -
- one voltage sensor,
- -
- a load.

_{1}and K

_{2}and $\lambda $ were nonlinear control parameters of the reversible buck–boost current power converter. The values of its parameters were determined from the simulation.

#### 4.3. Figures and Simulation Results

^{®}/Simulink

^{®}over a reduced duration compared to the duration of the experiment because we were limited by the memory of the PC opposite to the number of points that were taken.

_{sc}and its reference signal I

_{scref}for two scenarios: charging mode and discharging mode, respectively. In these figures, one could see that the controller behavior was satisfactory. Indeed, the SC current i

_{sc}perfectly tracked its reference I

_{scref}. The overshoot was zero, the system response time was less than 0.7 s, and the signal ripple was tolerable, less than 0.08 A.

_{sc}, and this mode was based on the value of I

_{scref}. The value of the difference that existed in the V

_{sc}curve was a function of the deviation of I

_{scref}at the time of its change.

_{sc}and i

_{sc}because the sliding surface was almost zero. On the other hand, the enlarged parts in the figures show the effect of the change of the value of the current on the control law because control law in Equation (17) was in function of the current i

_{sc}and V

_{sc}.

- ▪
- Charging mode of SC (Buck operation, k = 0):
- ▪
- Discharging mode of SC (Boost operation, k = 1)

#### 4.4. Figures and Experimental Results

^{®}block diagram environment, and all input/output were configured graphically.

_{sc}perfectly tracked its reference I

_{scref}. The overshoot was almost zero, the system response time was around 0.7 s, and the signal ripple was tolerable, less than 0.08A due to measurement noise. Its results were better compared to the results of [21]. Indeed, the authors of [21] control the current indirectly by controlling the voltage, which generates significant undulations at the level of the current (i

_{L}= i

_{sc}) and, consequently, the aging of the SC. On the other hand, it was necessary to control the current of SC instead of the voltage to protect the SC.

_{sc}, the difference between the experimental and simulation signals due to the voltage drop in the connection cables, and also the difference in the type of MOSFET transistor compared to IGBT. On the other hand, the enlarged parts in the figures show the effect of the internal resistance of the SC, in both cases, on the charge and discharge of the latter.

_{sc}and i

_{sc}because the sliding surface was almost zero. On the other hand, the enlarged parts in the figures show the effect of the change of the value of the current on the control law because control law in Equation (17) was in function of the current i

_{sc}and V

_{sc}.

- -
- The simulation and experimental results responded perfectly to the theoretical approach (ISMC, integral sliding mode control) used in this paper.
- -
- The results of the simulation of the reversible buck–boost current converter on Matlab
^{®}/Simulink^{®}were identical to the experimental results that were taken by the dSPACE DS1202 card.

- ▪
- Charging mode of SC (Buck operation, k = 0)
- ▪
- Discharging mode of SC (Boost operation, k = 1)

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Parameter | Value |
---|---|

Inductance L | 4 mH |

Inductances ESR, R_{L} | 620 mΩ |

Supercapacitor, C_{sc} | 500 F |

Supercapacitor ESR, R_{sc} | 2.1 mΩ |

Switching frequency, f_{simulation}Switching frequency, f _{experimental} | 25 kHz 15 kHz |

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**MDPI and ACS Style**

El Idrissi, Z.; El Fadil, H.; Belhaj, F.Z.; Lassioui, A.; Oulcaid, M.; Gaouzi, K.
Theoretical Design and Experimental Validation of a Nonlinear Controller for Energy Storage System Used in HEV. *World Electr. Veh. J.* **2020**, *11*, 49.
https://doi.org/10.3390/wevj11030049

**AMA Style**

El Idrissi Z, El Fadil H, Belhaj FZ, Lassioui A, Oulcaid M, Gaouzi K.
Theoretical Design and Experimental Validation of a Nonlinear Controller for Energy Storage System Used in HEV. *World Electric Vehicle Journal*. 2020; 11(3):49.
https://doi.org/10.3390/wevj11030049

**Chicago/Turabian Style**

El Idrissi, Zakariae, Hassan El Fadil, Fatima Zahra Belhaj, Abdellah Lassioui, Mostapha Oulcaid, and Khawla Gaouzi.
2020. "Theoretical Design and Experimental Validation of a Nonlinear Controller for Energy Storage System Used in HEV" *World Electric Vehicle Journal* 11, no. 3: 49.
https://doi.org/10.3390/wevj11030049