RBF neural network based backstepping terminal sliding mode MPPT control technique for PV system

The energy demand in the world has increased rapidly in the last few decades. This demand is arising the need for alternative energy resources. Solar energy is the most eminent energy resource which is completely free from pollution and fuel. However, the problem occurs when it comes to efficiency under different atmospheric conditions such as varying temperature and solar irradiance. To achieve its maximum efficiency, an algorithm of maximum power point tracking (MPPT) is needed to fetch maximum power from the photovoltaic (PV) system. In this article, a nonlinear backstepping terminal sliding mode control (BTSMC) is proposed for maximum power extraction. The system is finite-time stable and its stability is validated through the Lyapunov function. A DC-DC buck-boost converter is used to deliver PV power to the load. For the proposed controller, reference voltages are generated by a radial basis function neural network (RBF NN). The proposed controller performance is tested using the MATLAB/Simulink tool. Furthermore, the controller performance is compared with the perturb and observe (P&O) MPPT algorithm, Proportional Integral Derivative (PID) controller and backstepping MPPT nonlinear controller. The results validate that the proposed controller offers better tracking and fast convergence in finite time under rapidly varying conditions of the environment.


Introduction
Energy plays a vital role in a modern-day economy. It is essential in running the machines of industrial units and factories, lightening the cities and empowering the vehicles. Due to the population growth and development of industries, the demand of energy has been immensely increased. In this regard, many types of energy resources are explored for power generation such as solar, wind, biomass, geothermal, etc. Solar energy is one of the most reliable, abundantly available, and prominent sources of energy. In 2015, Globally 55 Gigawatts (GWs) of  [18] and ANN [19] then it is highly appreciable. For designing the FLC rules, plenty of system knowledge and more training is required. That requires a huge amount of memory and processing time. Adaptive fuzzy logic controller (AFLC) is proposed to achieve MPPT which operates into two rules [20].
In the first one, the duty cycle of the electronic converter is adjusted while the controller gain is adjusted in the second rule. In [21], adaptive neuro-fuzzy inference system technique is applied to get MPPT for the PV system under different atmospheric conditions. Fuzzy based controllers are developed with expert system knowledge to produce MPPT rules. ANN method is gleaned from the behavior of the a human being. ANN has the thinking ability to decide and more knowledge is required for the training of neurons. It has three layers; input, hidden, and output. In [22], ANN based FLC for MPPT fetching is proposed. ANN and FLC based MPPT techniques results in better performance as compared to the optimization based algorithms. Demerits are implementation complexity and computational cost. These MPPT controllers need regular maintenance because the PV array electricity curve changes over time.
Many linear controllers have been proposed to attain MPP from a PV module. Among linear control techniques, the PID controller is normally used in literature and industrial plants due to its simplicity in implementation and low cost. These controllers have been utilized with numerous MPPT algorithms. In [23], the author optimized the PID controller parameters to fetch maximum power. Likewise, the PI controller gains for a standalone PV system were optimized using the ACO algorithm to get MPPT [24]. Gradient descent optimization (GDO) algorithm is used to optimize the PID controller gains for better performance [25]. Linear controllers show better performance but unable to effectively handle the system nonlinearities and operation over a wide range of operating conditions. These techniques are unreliable under varying conditions of the environment. It is essential to adapt the control strategy to handle nonlinearities and maintain performance under varying operating conditions.
In recent times, a lot of research work has been done in the nonlinear control area to achieve MPPT through different nonlinear control schemes. Several controllers are proposed to fetch maximum power like sliding mode control (SMC) [26] and backstepping [2]. The cell of a PV panel has a nonlinear nature. In [27], a nonlinear backstepping control technique is proposed to power up the towers of cellular networks. SMC method is widely used for nonlinear control systems. The control of an electronic converter is provided in this technique, which helps in tracking MPP under varying conditions of the environment. In the PV system, buck-boost converter transfers the power from panel to load. SMC mainly depends upon the switching frequency of the converter to obtain MPP. As the switching increases then speed of MPPT becomes faster. In [28], terminal sliding mode control (TSMC) is implemented to attain MPP for PV system with uncertainties. Similarly, backstepping based sliding mode (BSMC) controller is designed to obtain maximum power [29].
In the proposed work, RBF NN based BTSMC is proposed for MPPT of a PV system in varying environmental conditions. TSMC technique provides better results under varying atmospheric conditions. Backstepping technique [2] is highly efficient but not robust in varying conditions. For better robustness in varying conditions, Backstepping is synthesized with TSMC nonlinear control technique. When TSMC is compared with the other techniques, it offers fast convergence and better tracking precision in a finite time. BTSMC along RBF NN seems a better approach to extract maximum power due to less chattering effect, improve transient response, tracking with precision, and fast convergence.
The working principle of the proposed algorithm is completely different when it is compared with the conventional algorithms. The proposed technique senses irradiance and temperature on the PV panel. The set of data is provided to the RBF NN, as presented in Fig 1 The RBF NN utilizes the relation between varying conditions of the environment i.e., Temperature and Irradiance and V mpp to generate the reference voltage. The nonlinear controller can track the reference voltage V pvr . The controller is designed using a non-inverting converter mathematical model. The output signal of the controller controls the converter's duty ratio through the pulse width modulation.
The paper structure is organized as: following an introduction in section 1, radial basis function neural network is described in section 2. The modeling of the converter is presented in section 3. The proposed control scheme with system stability analysis is explained in section 4. The performance of the controller is analyzed in section 5. In the end, section 6 concludes the findings of the research article.

Radial basis function neural network
In this work, RBF NN generates reference voltage for the BTSMC. Recently, RBF NN has gained attention as compared to other feed-forward neural networks (FF NN) due to its simple structure and better generalization ability. The source nodes are present in the input layer which establishes a connection between the network and environment. In a hidden layer, a set of the activation functions is provided through hidden units. These units are hidden nodes. The activation function which produces the hidden layer output, is: where b j denotes positive scalar known as width and m denotes no. of hidden nodes. In proposed work, three hidden nodes are used in the hidden layer. The output layer which is the combination of linear weights, as follows: where n denotes no. of output, w denotes the weight of output layer and y denotes the output of the network. The result of the system is produced in an output layer which is the last layer of RBF NN. In this work, output of neural network is reference voltage V pvr . The data of reference voltage is obtained from characteristic curve of the PV module under various levels of irradiance (600 W/m 2 − 1100 W/m 2 ) and temperature (20˚C-85˚C). The data set having 29767 training points is used to train the neural network. The training data set has three entities: temperature, irradiance and voltage. Each entity has same number of training points. The 3-D plane of RBF NN obtained from this data is shown in Fig 2 while the inner view of the neural network is presented in Fig 3.

Non-inverting buck-boost DC-DC converter
The non-inverting topology of buck-boost converter is utilized which has ability to step down or step up the voltage according to the requirement. This converter is used to follow the output voltage of PV array, V pv to desired voltage, V mpp through adjustment of duty cycle. The converter's circuit diagram is presented in Fig 4. The assumption has been made that converter is operated in continuous conduction mode. There are two modes of operation i.e. mode 1 and mode 2. In mode 1, both switches S x and S y are turned on and the diodes D x and D y are in reverse biased condition. In mode 2, the switches S x and S y are turned off while the diodes are forward biased. According to Fig 4, state- Assuming x 1 , x 2 , x 3 and μ as the average values of v pv , i L , v c y and u, respectively. Under these assumptions, then desired state-space model is presented as:

Backstepping terminal sliding mode control design
A nonlinear BTSMC controller is designed to track x 1r = V pvr for maximum power extraction. The backstepping is a nonlinear control methodology that is generally used as a part of control design. The controller output μ t controls the duty ratio of the converter's switches. Firstly, define the tracking error: Taking derivative of Eq (7), Using dynamics of converter, we get Now introducing the stabilization function 'α 1 ', where O 1 , O 2 (1 < O 1 /O 2 < 2) and λ 1 , λ 2 are positive odd numbers. The tracking error has upgraded with the stabilization function.
Applying first Lyapunov stability function, Eq (12) can be re-written as; From Eq (11), then we get Applying second Lyapunov stability function; The sliding surface 's' is followed as: Taking the derivative of second lyapunov stability function; Total control law is characterized as: Substituting Eq (18) in Eq (17); _ s ¼ 0 gives the equivalent control law, _ m eq: . This control law is very essential for desired tracking without any consideration of uncertainties and disturbances i.e. _ m dis: .
Using Eqs (19) and (20), the expression for _ V is, To satisfy the condition of Lyapunov stability, the corrective control law ' _ m dis ' is described as: Subtitution of Eq (22) in Eq (21); where 'k' is sliding gain where |s| = s T sign(s), 'sign' function is replaced by tangent hyperbolic function, 'tanh'. Signum function causes chattering phenomenon, therefore term 'tanh' is introduced to diminish this impact.
_ V � l 1 je 2 1 j À ks T tanh ðsÞ ð25Þ The term 's T tanh(s)' in Eq (25) is constantly positive so that condition has to be negative (i.e. s T tanh(s)>0 if either s > 0 or s < 0). Therefore achieving control signal is characterized as: For total BTSMC control law, substituting Eqs (20) and (26) in Eq (18), The flow chart and closed-loop system for the proposed nonlinear control paradigm is presented in Figs 5 and 6, respectively.

Simulation results and discussion
The performance of the proposed BTSMC scheme is validated through the simulations performed in MATLAB/Simulink. The parameters of the PV system are presented in Table 1, and the BTSMC and PID control parameter are mentioned in Table 2. Firstly, the BTSMC performance is analyzed under varying temperature and irradiance with varying load. Secondly, the performance of the proposed controller is benchmarked against backstepping control, conventional PID control and P&O algorithm. To further investigate the performance, BTSMC technique is compared with above mentioned techniques with fault and uncertainty in the system.

Performance comparison of proposed controller with backstepping, P&O and PID under varying load and environmental conditions
The BTSMC performance is verified in the case of varying levels of irradiance and temperature, as shown in Fig 7 with varying residential load. Initially, level of irradiance and

Comparison of proposed controller with P&O, PID and backstepping under varying climatic and faulty conditions
In this case, multiple faults are injected in the plant under varying conditions of temperature, irradiance, and load. In this work, two uncertain conditions are introduced in the system. In the time interval 0.06 to 0.08 seconds, a fault, x 2f = 0.5μ sin(t)/C x , is inoculated in inductor current x 2 , Δx 2 = x 2 +x 2f . In the time interval of 0.16 to 0.18 seconds, a uncertainty of ΔC = 0.48nF is introduced in output capacitor 'x 3 ', as Δx 3 = C y + ΔC. The output voltage of PV deviates from the reference, as depicted in Fig 16. The proposed controller shows robustness as compared to other existing techniques in faulty conditions. It can be observed that the BTSMC controller attains steady-state earliest than the other MPPT techniques. The PV output power is shown in Fig 17. It clearly shows that the proposed control technique outperforms its contenders in this scenario.  Table 3.

Conclusion and future work
The article presented the BTSMC control scheme for the MPPT application of PV systems. The buck-boost converter is used as an interface between load and PV array. The non-inverting topology of the buck-boost converter has been utilized in this work. To attain maximum power, the duty cycle of the converter is controlled through BTSMC. The reference of voltage has been generated by the RBF NN. The finite-time stability of the system has been verified using the Lyapunov stability function. The proposed controller performance is validated by comparison with P&O, PID, and backstepping controller under varying conditions of temperature, irradiance, and load. Furthermore, the developed control technique is again compared with its existing contenders under varying conditions of load and environment with fault and uncertainty. The proposed controller has been outperformed its existing competitors in all scenarios. The performance indices show the best performance of the proposed control technique in all conditions as compared to other existing techniques. Although, the proposed controller performs exceptionally well but it depends upon the reference values of the RBF NN plane. It is needed to update the RBF NN plane due to any type of failure in the PV system for optimal performance of the controller. In this manner, the generation of reference may demand the amalgamation of other algorithms like ACO and PSO to generate maximum power successfully. The possible directions for future research work include; • Comparison of proposed control schemes with other different MPPT techniques under partial shading conditions (PSC).
• Integration of the PV system with grid and parallel operation with other renewable energy systems.
• Application of the different inverter topologies to transfer the PV array output power into AC electric appliances.
• Development of the hybrid energy storage system to store energy for peak hours.
• Hardware-level implementation of proposed nonlinear control algorithms under varying environmental conditions.