# An immersion and invariance based input voltage and resistive load observer for DC–DC boost converter

- 208 Downloads

**Part of the following topical collections:**

## Abstract

In this paper, a new nonlinear observer is presented for DC–DC boost converter using immersion and invariance (I&I) technique. The proposed nonlinear observer is easy to implement, simple to tune and realizes global exponential convergence of the estimation error to zero. It is assumed that the input voltage and output load of converter are unavailable and the I&I observer is designed to estimate unavailable parameters using output voltage and inductor current information. Considering optimal performance of observer, an improved particle swarm optimization algorithm is employed to determine observer gains. The search space of parameters in the proposed optimization algorithm is modified and according to this modification, the weak parameters is eliminated and the new parameters are defined for optimization process instead of them. In order to validate the effectiveness of the proposed observer, the practical test is implemented and the experimental results confirm the efficiency of the proposed I&I observer.

## Keywords

DC–DC boost converter Immersion and invariance Observer Exponential stability IPSO## 1 Introduction

Nowadays, DC–DC power converters are employed to increase or decrease output voltage in various applications of power electronic. Providing reliable voltage with acceptable regulation is one of the topics studied by researchers in recent years [1, 2]. One of the most widely used converters in this field is DC–DC boost converter that is used to regulate the output voltage of systems requiring higher voltage levels. Therefore, this converter is applied in renewable energy sources such as solar energy [3], fuel cell [4] and hybrid vehicles [5]. So, designing an appropriate control scheme that leads to enhance the voltage regulation quality is one of the most important problems in industry. Due to its switching action, the dynamic of this converter is nonlinear. Also, DC–DC boost converter inherits a right-half-plane zero which can give rise to transient response oddities [6, 7]. Moreover, there is a constraint on the control input bound of a DC–DC boost converter. These characteristics make this converter to challenging case for researchers.

Although, linear controllers such as PI and PID present desirable performance in selected operation point. However, when the operation point is changed, their voltage regulation quality will decrease [8, 9]. So, some papers have suggested linear controller with adaptive coefficients but the complicated structure of this controller made it unattractive [10]. Another group of controllers that do not need exact information of mathematical model of system are intelligent controllers such as neural network [11] or fuzzy controllers [12]. However, because the use of these types of controllers requires considerable memory and computational efforts, their application in power electronics industry has not been welcomed [1]. Therefore, different studies have tried to eliminate mentioned weakness applying nonlinear controllers. In this regard, various nonlinear controller such as sliding mode [13, 14, 15], passivity-based control [8, 16] and backstepping control [17] have been suggested. However, this kind of controller requires an exact information of system states to present control effort and this drawback is significant. Because, when the converter is applied in noisy circumstance, the sensor cannot transfer exact information [18, 19]. Also, if the parameters of the system change drastically, the sensor performance will drop [20]. In order to unravel this problem, researchers have suggested observer. Observers could estimate required state and parameters using minimum sensor and sensorless control scheme will realize. High reliability, low cost and high efficiency make sensorless control scheme an application of interest in academy and industry [21].

In this regard, different observers are presented for DC–DC boost converter. Estimation of inductor current has been considered in [22]. In this paper, an observer is designed to estimate inductor current using input voltage and output voltage. This purpose has been improved in [23]. In this article, inductor current and input voltage have been estimated using output voltage. In addition, Estimation of inductor current has been considered in [21]. In this study, a unified observer is designed for a class of DC–DC converters such as DC–DC boost converter.

In this paper, a new nonlinear observer based on Immersion and Invariance (I&I) manifold is designed for DC–DC boost converter [23, 24]. The implementation of I&I based observer is simple and does need high gain to suppress nonlinear terms [24]. In addition, the observer does not require output injection error term to estimate unavailable states and parameters. The proposed observer estimates input voltage and resistive load using output voltage and inductor current. The exponential stability of the proposed observer is provided by Lyapunov stability theorem. Also, the closed-loop control stability is realized considering control input constraint. In order to obtain the gains of the observer, an improved particle optimization algorithm is considered. Particle swarm optimization algorithm is well-known algorithm in optimization problems and many researchers employ this algorithm in controller design [25, 26, 27, 28, 29, 30]. However, by applying some modifications to the movement of particles towards the optimal solution, the accuracy and convergence rate of the algorithm is improved in proposed algorithm. In order to confirm the advantages of I&I based observer, its performance is compared with conventional observer [14]. Furthermore, to validate the effectiveness of the propped control scheme, the practical test is implemented in this article. Therefore, hardware-in-loop structure is designed using Advantech card to realize experimental test. The rest of paper is organized as follows:

Section 2 presents general definition of DC–DC boost converter. In Sect. 3, the proposed observer is designed according to immersion and invariance method and the comparison with conventional observer is presented in Sect. 4. The definition of the improved optimization algorithm is rendered in Sect. 5. Sections 6 and 7 demonstrate simulation and experimental results respectively and the paper ends with conclusion section.

## 2 Problem statement

According to presented dynamic, observer will be designed in next section.

## 3 Observer design

*off*-

*the*-

*manifold*coordinate is defined as follows [22, 23]

## 4 Comparison and discussion

## 5 Improved particle swarm optimization algorithm (IPSO)

*Pbest*. The other best value is the best position ever reached by the particle population. This position is represented as

*gbest*. After finding the best values, the velocity and position of each particle are updated using Eqs. (1) and (2) [26].

- 1.
Select an initial search space suitable for the parameters of each particle, the initial population, the maximum number of iterations, c

_{1}, c_{2}, w, ep (Elimination period. This parameter has been added to the classical algorithm and is determined based on the number of iterations) and et (Elimination percentage. This parameter has been added to the classical algorithm and is determined based on the percentage of the initial population). - 2.
Create the initial population in the search space.

- 3.
Calculate the fitness function for each particle.

- 4.
Determine

*pbest*of each particle and*gbest*. - 5.
If the number of iterations is a multiple of ep, then make the following changes (elimination step):

- 5.1
If the value of the parameters of each particle is greater than a threshold, add a unit to the search space of that particle member. (The threshold is a percentage of the maximum or minimum of the search space, and the value is arbitrary).

- 5.2
Determine et percent of the initial population that has the worst fitness function.

- 5.3
Eliminate the selected et percent and create a new population in the new search space. The velocity (v) of the new particles is selected to be zero.

- 5.4
Calculate the fitness function for the new particles.

- 5.5
Determine

*pbest*for each particle and*gbest.*

- 5.1
- 6.
- 7.
Go to step 3 and repeat steps (3, 4, 5, 6, and 7) until satisfying the termination conditions.

## 6 Simulation results

Similar to previous condition, the response of the proposed control scheme is better than observer in [14].

## 7 Experimental test

As can be seen, the practical results confirm the capability of the proposed method in real time application.

## 8 Conclusion

In this study, a new nonlinear observer is presented for DC–DC boost converter. This observer is designed based on Immersion and Invariance technique with exponential stability. The proposed observer can estimate the input voltage and resistive load using output voltage and inductor current. In order to tune the observer gains, an improved particle optimization algorithm is employed. The effectiveness of this method is compared with conventional observer and the simulation results endorse the advantages of the proposed nonlinear observer. Also, the experimental test is implemented to confirm the capability of the proposed method in real time application.

## Notes

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no competing interests.

## References

- 1.Yazici İ, Yaylaci EK (2016) Fast and robust voltage control of DC–DC boost converter by using fast terminal sliding mode controller. IET Power Electron 9(1):120–125CrossRefGoogle Scholar
- 2.Cheng L, Acuna P, Aguilera RP, Jiang J, Wei S, Fletcher J, Lu DDC (2017) Model predictive control for DC–DC boost converters with reduced-prediction horizon and constant switching frequency. IEEE Trans Power Electron 33:9064–9075CrossRefGoogle Scholar
- 3.Pourmousa N, Ebrahimi SM, Malekzadeh M, Alizadeh M (2019) Parameter estimation of photovoltaic cells using improved Lozi map based chaotic optimization algorithm. Sol Energy 180:180–191CrossRefGoogle Scholar
- 4.Rakhtala SM, Shafiee Roudbari E (2016) Fuzzy PID control of a stand-alone system based on PEM fuel cell. Int J Electr Power Energy Syst 78:576–590CrossRefGoogle Scholar
- 5.Camara MB, Gualous H, Gustin F, Berthon A (2008) Design and new control of DC/DC converters to share energy between supercapacitors and batteries in hybrid vehicles. IEEE Trans Veh Technol 57(5):2721–2735CrossRefGoogle Scholar
- 6.Wang YX, Yu DH, Kim YB (2014) Robust time-delay control for the DC–DC boost converter. IEEE Trans Industr Electron 61(9):4829–4837CrossRefGoogle Scholar
- 7.Yazici İ (2014) Robust voltage-mode controller for DC–DC boost converter. IET Power Electron 8(3):342–349CrossRefGoogle Scholar
- 8.Son YI, Kim IH (2012) Complementary PID controller to passivity-based nonlinear control of boost converters with inductor resistance. IEEE Trans Control Syst Technol 20(3):826–834MathSciNetCrossRefGoogle Scholar
- 9.Alvarez-Ramirez J, Cervantes I, Espinosa-Perez G, Maya P, Morales A (2001) A stable design of PI control for DC–DC converters with an RHS zero. IEEE Trans Circuits Syst I Fundam Theory Appl 48(1):103–106CrossRefGoogle Scholar
- 10.Shirazi M, Zane R, Maksimovic D (2009) An autotuning digital controller for DC–DC power converters based on online frequency-response measurement. IEEE Trans Power Electron 24(11):2578–2588CrossRefGoogle Scholar
- 11.Wai RJ, Shih LC (2012) Adaptive fuzzy-neural-network design for voltage tracking control of a DC–DC boost converter. IEEE Trans Power Electron 27(4):2104–2115CrossRefGoogle Scholar
- 12.El Beid S, Doubabi S (2014) DSP-based implementation of fuzzy output tracking control for a boost converter. IEEE Trans Ind Electron 61(1):196–209CrossRefGoogle Scholar
- 13.Vidal-Idiarte E, Carrejo CE, Calvente J, Martínez-Salamero L (2011) Two-loop digital sliding mode control of DC–DC power converters based on predictive interpolation. IEEE Trans Ind Electron 58(6):2491–2501CrossRefGoogle Scholar
- 14.Oucheriah S, Guo L (2013) PWM-based adaptive sliding-mode control for boost DC–DC converters. IEEE Trans Ind Electron 60(8):3291–3294CrossRefGoogle Scholar
- 15.Lopez-Santos O, Martinez-Salamero L, Garcia G, Valderrama-Blavi H, Sierra-Polanco T (2015) Robust sliding-mode control design for a voltage regulated quadratic boost converter. IEEE Trans Power Electron 30(4):2313–2327CrossRefGoogle Scholar
- 16.del Puerto-Flores D, Scherpen JM, Liserre M, de Vries MM, Kransse MJ, Monopoli VG (2014) Passivity-based control by series/parallel damping of single-phase PWM voltage source converter. IEEE Trans Control Syst Technol 22(4):1310–1322CrossRefGoogle Scholar
- 17.Alvarez-Ramirez J, Espinosa-Pérez G, Noriega-Pineda D (2003) Current-mode control of DC–DC power converters: a backstepping approach. Int J Robust Nonlinear Control 13(5):421–442MathSciNetCrossRefGoogle Scholar
- 18.Malekzadeh M, Khosravi A, Tavan M (2018) Observer based control scheme for DC–DC boost converter using sigma–delta modulator. COMPEL Int J Comput Math Electr Electron Eng 37(2):784–798CrossRefGoogle Scholar
- 19.Malekzadeh M, Khosravi A, Tavan M (2019) Immersion and invariance-based filtered transformation with application to estimator design for a class of DC–DC converters. Trans Inst Meas Control 41(5):1323–1330CrossRefGoogle Scholar
- 20.Malekzadeh M, Khosravi A, Tavan M (2019) A novel adaptive output feedback control for DC–DC boost converter using immersion and invariance observer. Evol Syst. https://doi.org/10.1007/s12530-019-09268-7 CrossRefGoogle Scholar
- 21.Malekzadeh M, Khosravi A, Tavan M (2019) A novel sensorless control scheme for DC–DC boost converter with global exponential stability. Eur Phys J Plus 134(7):338CrossRefGoogle Scholar
- 22.Cho H, Yoo SJ, Kwak S (2014) State observer based sensor less control using Lyapunov’s method for boost converters. IET Power Electron 8(1):11–19CrossRefGoogle Scholar
- 23.Karagiannis D, Astolfi A, Ortega R (2003) Two results for adaptive output feedback stabilization of nonlinear systems. Automatica 39(5):857–866MathSciNetCrossRefGoogle Scholar
- 24.Morbidi F, Mariottini GL, Prattichizzo D (2010) Observer design via immersion and invariance for vision-based leader–follower formation control. Automatica 46(1):148–154MathSciNetCrossRefGoogle Scholar
- 25.Salahshour E, Malekzadeh M, Gholipour R, Khorashadizadeh S (2019) Designing multi-layer quantum neural network controller for chaos control of rod-type plasma torch system using improved particle swarm optimization. Evol Syst 10(3):317–331CrossRefGoogle Scholar
- 26.Salahshour E, Malekzadeh M, Gordillo F, Ghasemi J (2018) Quantum neural network-based intelligent controller design for CSTR using modified particle swarm optimization algorithm. Transactions of the Institute of Measurement and Control, p 0142331218764566Google Scholar
- 27.Ebrahimi SM, Salahshour E, Malekzadeh M, Gordillo F (2019) Parameters identification of PV solar cells and modules using flexible particle swarm optimization algorithm. Energy 179:358–372CrossRefGoogle Scholar
- 28.Gholipour R, Khosravi A, Mojallali H (2015) Multi-objective optimal backstepping controller design for chaos control in a rod-type plasma torch system using Bees Algorithm. Appl Math Model 39(15):4432–4444MathSciNetCrossRefGoogle Scholar
- 29.Alfi A, Khosravi A, Lari A (2013) Swarm-based structure-specified controller design for bilateral transparent teleoperation systems via μ synthesis. IMA J Math Control Inf 31(1):111–136MathSciNetCrossRefGoogle Scholar
- 30.Gholipour R, Khosravi A, Mojallali H (2012) Intelligent backstepping control for Genesio–Tesi chaotic system using a chaotic particle swarm optimization algorithm. Int J Comput Electr Eng 4(5):618CrossRefGoogle Scholar
- 31.Salahshour E, Noei AR, Malekzadeh M (2014) A computerized and on-line super twisting speed control of alternating current asynchronous machine using Omron V1000
^{®}Drive. J Eng Technol 4(1):12–17CrossRefGoogle Scholar