# Design and Development of Fixed-Frequency Double-Integral SM-Controlled Solar-Integrated Bidirectional QuasiZ-Source DC-DC Converter in Standalone Battery Connected System

Authors: Santhoshkumar Battula; Anup Kumar Panda; Man Mohan Garg
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

DC microgrids have been quite popular in recent times. The operational challenges like control and energy management of the renewable-driven standalone DC microgrids have been an interest of research. This paper presents a bidirectional quasiZ-source DC-DC converter (BQZSDC). This converter topology has been developed based on a conventional buck-boost type bidirectional converter, and it interfaces the storage system and the common DC bus. The challenge, however, lies in effectively managing the uncertain renewable energy sources and the storage system and catering for the loads simultaneously. An effective control strategy is needed for that energy management and to achieve various microgrid objectives. This paper deals with one such effective control strategy implemented for BQZSDC. That is, the fixed-frequency double-integral sliding mode control (FF-DISMC) controls the converter to regulate the DC bus voltage and battery current. A detailed analysis of the controller is conducted, and its performance is evaluated for both charging (buck) and discharging (boost) modes. Simulations have been performed in MATLAB, showing that the controller performs satisfactorily in achieving the objectives of voltage regulation and battery current regulation. Finally, the performance of the proposed controller is validated with the hardware setup.


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## Body

## 1. Introduction

Often, in applications requiring increased voltage, a conventional boost converter is a common choice. However, it is understood that voltage boosting is limited by duty cycle constraints because of the switching device performance and conduction loss [1–3]. Therefore, topologies with higher voltage gain have been of great research interest. In this line, the Z-source network’s novel and effective topology came into the limelight [4]. The initial implementation of this topology was limited to DC-AC application, where the topology was popularly known as Z-source inverter (ZSI). This converter also supports bidirectional operation with both buck and boost modes. A significant amount of literature has been devoted to the ZSI and its applications, such as interfacing renewable sources like PV wind [5–7]. An improved version of the inverter named quasi Z-Source inverter (QZSI), with added advantages of input current continuity and reduced voltage stresses of capacitors, was introduced [8].For DC-DC applications, the concepts ofZ-source converter and quasi Z-source converter (QZSC) are often used [9–11]. In [12], QZSC has been used in bidirectional power flow applications, where the buck and boost modes were individually controlled [13, 14]. However, in the case of the converter connected to a standalone microgrid, it is essential that the DC link voltage is regulated in both modes of operation based on the power demand [14–17].TheZ-source and quasi-Z-source converters have simple architectures, and they can provide a significant gain [12]. The switched-inductor DC-DC converter proposed in [18] has high gain and low voltage stress, but it has more inductors. Reference [19] proposes a switched-capacitor-based Z-source DC-DC converter. In this topology, despite increased voltage gain, there is no common ground between input and output and it has high voltage stress across the switches. The switched-capacitor quasi Z-source DC-DC converter proposed in [20] has high efficiency, but more switches are required. The bidirectional quasi Z-source converter proposed in [21] can provide high gain but does not have common ground. This produces a du/dt issue between input and output.The proposed BQZSDC can provide high voltage gain. Its design is based on the bidirectional quasiZ-source DC-DC two-level converter. The main difference is changing the primary power switch to a different position. This BQZSDC has minimal voltage stress on power switches. Consequently, the BQZSDC can choose power switches with low rated voltage and low on-state resistance, which causes improvement in efficiency. At the same time, when compared with basic quasi Z-source, its gain has been decreased slightly, but it still meets the requirements of connection with different sources. The presence of common ground also avoids the du/dt issue.The conventional proportional-integral (PI) and dual-loop PI-control techniques are commonly designed by linearizing the model at a particular operating point [22, 23]. For higher-order systems, deriving a linearized model is complex. A reduced-order small-signal closed-loop transfer function model was presented in [24]. In this paper, traditional model order reduction procedures are utilized, and the inaccuracy of input-output mappings between the original and reduced-order systems is considerable. Wang et al. [25] propose to give a preprocessing strategy for real-time modeling of large-scale converters with inhomogeneous initial conditions to address input-output mapping problems. However, the transient behavior of these systems with linear controllers is poor under large-signal perturbations. This is because of the variaiton in small-signal models at different dc operting points. Several nonlinear controllers are utilized for power electronic converters to solve the above problems.Sliding mode control (SMC) is a robust control approach that effectively handles parameter changes, external disturbances, and input disturbances. The hysteresis modulating sliding mode control (HM-SMC) technique used in [26–28] suffers from chattering and switching frequency variation under load fluctuations. In variable frequency operation, stabilizing the feedback control circuit could be difficult. Later, fixed-frequency SMC was developed using pulse width modulation [29], maintaining the constant frequency despite input voltage and load variations. This fixed-frequency SMC was based on an equivalent control switching function to harvest a trajectory near equivalent to an ideal sliding mode trajectory. SMC in conjunction with PWM reduces steady-state error (SSE) significantly. Integral SMC, which incorporates an integral term of the state variables into the SM controller, can further minimize SSE. A second integral component of the tracking error has been considered to improve the system’s steady-state accuracy even more. Double-integral sliding mode controller (DISMC) responds quickly for a broader range of operating circumstances while significantly reducing SSE [30].The model predictive control (MPC) computes the switch input from the converter’s active model and provides a resolution for trajectory optimization [31]. The optimization techniques in MPC necessitate many computations, and MPC is not appropriately aimed at converters with large values of switching frequencies. References [32, 33] proposed voltage source inverters based on adaptive error correction, with the error approach included in both the outer and inner prediction loops and a nonlinear state-space function to describe the AC microgrid along with an event-triggered consensus control technique. However, MPC requires a powerful processor to perform real-time calculations, but DISMC has very simple calculations. The advantage of the proposed FF-DISMC is its ability to reject disturbances and deal with system uncertainties better than MPC.The advantages of the proposed fixed-frequency double-integral SMC are as follows:(1)
Fast dynamic responses compared with conventional voltage and current mode controllers(2)
Characteristic robust features of SMC, but working at a fixed frequency(3)
Stability over a wider range of operating conditions(4)
The slight variation of the settling time over an extensive range of operating conditions(5)
Stabilizing the feedback control circuit can be more difficult in variable frequency operation than fixed-frequency controlThe key contribution of this paper is the design and implementation of an FF-DISMC for the BQZSDC. The controller scheme was designed to regulate the DC grid voltage against variations in reference voltage and load power with bidirectional power flow.Figure1 depicts the proposed system’s architecture. The suggested converter simultaneously manages the PV system’s power, battery, and load. When solar radiation is available, a maximum power point tracking (MPPT) algorithm ensures that the PV panel generates the most power possible. The suggested controller directs the battery to absorb excess energy from the PV panel or supply the load with the power it requires.Figure 1
The architecture of the proposed standalone system.Section2 presents the system design and steady-state mathematical model of BQZSDC. The control strategy of FF-DISMC is analyzed in Section 3. The simulation and hardware results are shown in Section 4, comparison analysis in Section 5, and conclusions in Section 6.


## 2. System Design and Modeling

The following assumptions are made in the proposed BQZSDC to simplify the analysis:(1)
The power switches’ on-state resistance and the equivalent series resistance of the inductorsL1, L2 and capacitors C1, C0 are Ignored. The ESR, r of capacitor C2, is considered to avoid complications in obtaining the state equations of the converter.(2)
The currents and voltages of the inductors and capacitors increase and decrease linearly.(3)
The voltage across the battery was constant.The topology of the BQZSDC is displayed in Figure2, interfacing the battery storage to the load and DC bus. The topology primarily consists of three active switches, S1, S2, and S3. The converter has the bidirectional capability to charge/discharge the battery by adequately choosing the switching signals. In this paper, the operation of the converter in boost mode (discharging mode) is only analyzed; however, buck mode can also be operated similarly. In the boost mode of the converter, the switch S1 acts as the main switch, whereas S2 and S3 are complementary switches to S1. The battery voltage Vb is assumed to be constant.Figure 2
Circuit diagram of BQZSDC.It is considered that BQZSDC is being operated in CCM, with switching inputu and a constant switching frequency f. The converter operation can best be analyzed by observing the following two modes individually.


### 2.1. Mode 1:S1 Is Turned On; S2 and S3 Are Turned Off (0 < t ≤ DT)

In mode 1,S1 is made on and switches S2 and S3 are made off. Once the switching status of the switches S1, S2, and S3 is declared, the topology can be seen in Figure 3. On analyzing the circuit, it can be understood that the energy from the battery is stored in the inductor L1 with S1 being turned on. The capacitor C2 gets energized through L2 and C1 (already charged). The load power in this mode is supplied by the output capacitor C0 because the load is straight away not attached to the battery.Figure 3
BQZSDC in mode 1 (0 <t ≤ DT).The switching states in this mode are as follows:(1)vL1=L1diL1dt=vb,(2)vL2=L2diL2dt=vC1−vC2−iL2r,(3)iC1=C1dvC1dt=−iL2,(4)iC2=C2dvC2dt=iL2,(5)iC0=C0dv0dt=−v0R0=−iLoad.


### 2.2. Mode 2:S1 Is Turned Off; S2 and S3 Are Turned On (DT < t ≤ T)

In mode 2,S1 is turned off and switches S2 and S3 are turned on. The topology can be seen as the equivalent circuit in Figure 4. As a consequence of the previous mode, the energy kept in the inductor L1 charges the capacitor C1 through S2. The energy kept in the inductor L2 is used to feed the load R0, and the capacitor C2 is discharged simultaneously.Figure 4
BQZSDC in mode 2 (DT <t ≤ T).The switching states in this mode are as follows:(6)vL1=L1diL1dt=vb−vC1,(7)vL2=L2diL2dt=vC1−v0,(8)iC1=C1dvC1dt=iL1−iL2+v0−vC1−vC2r,(9)iC2=C2dvC2dt=v0−vC1−vC2r,(10)iC0=C0dv0dt=iL2−v0−vC1−vC2r−v0R0.


#### 2.2.1. State-Model Representation

With (1) to (10), we derive the system modeled as follows:(11)X•=A+Bu,where u indicates the switching state of S1 and matrices A and B are as follows:(12)A=1L1vb−vC11L2vC1−v01C1iL1−iL2+1C1rv0−vC1−vC21C2rv0−vC1−vC21C0−v0R0+iL2C0−1C0rvC0−vC1−vC2,B=vC1L11L2v0−vC2−iL2r−iL1C1−1C1rv0−vC1−vC2iL2C2−1C2rv0−vC1−vC2−iL2C0+1C0rv0−vC1−vC2.The state vector includes five parameters: inductor currentsiL1 and iL2 and capacitor voltages vC1, vC2, and v0.The state vector is presented as follows:(13)X=iL1iL2vC1vC2v0T.


## 2.1. Mode 1:S1 Is Turned On; S2 and S3 Are Turned Off (0 < t ≤ DT)

In mode 1,S1 is made on and switches S2 and S3 are made off. Once the switching status of the switches S1, S2, and S3 is declared, the topology can be seen in Figure 3. On analyzing the circuit, it can be understood that the energy from the battery is stored in the inductor L1 with S1 being turned on. The capacitor C2 gets energized through L2 and C1 (already charged). The load power in this mode is supplied by the output capacitor C0 because the load is straight away not attached to the battery.Figure 3
BQZSDC in mode 1 (0 <t ≤ DT).The switching states in this mode are as follows:(1)vL1=L1diL1dt=vb,(2)vL2=L2diL2dt=vC1−vC2−iL2r,(3)iC1=C1dvC1dt=−iL2,(4)iC2=C2dvC2dt=iL2,(5)iC0=C0dv0dt=−v0R0=−iLoad.


## 2.2. Mode 2:S1 Is Turned Off; S2 and S3 Are Turned On (DT < t ≤ T)

In mode 2,S1 is turned off and switches S2 and S3 are turned on. The topology can be seen as the equivalent circuit in Figure 4. As a consequence of the previous mode, the energy kept in the inductor L1 charges the capacitor C1 through S2. The energy kept in the inductor L2 is used to feed the load R0, and the capacitor C2 is discharged simultaneously.Figure 4
BQZSDC in mode 2 (DT <t ≤ T).The switching states in this mode are as follows:(6)vL1=L1diL1dt=vb−vC1,(7)vL2=L2diL2dt=vC1−v0,(8)iC1=C1dvC1dt=iL1−iL2+v0−vC1−vC2r,(9)iC2=C2dvC2dt=v0−vC1−vC2r,(10)iC0=C0dv0dt=iL2−v0−vC1−vC2r−v0R0.


### 2.2.1. State-Model Representation

With (1) to (10), we derive the system modeled as follows:(11)X•=A+Bu,where u indicates the switching state of S1 and matrices A and B are as follows:(12)A=1L1vb−vC11L2vC1−v01C1iL1−iL2+1C1rv0−vC1−vC21C2rv0−vC1−vC21C0−v0R0+iL2C0−1C0rvC0−vC1−vC2,B=vC1L11L2v0−vC2−iL2r−iL1C1−1C1rv0−vC1−vC2iL2C2−1C2rv0−vC1−vC2−iL2C0+1C0rv0−vC1−vC2.The state vector includes five parameters: inductor currentsiL1 and iL2 and capacitor voltages vC1, vC2, and v0.The state vector is presented as follows:(13)X=iL1iL2vC1vC2v0T.


## 2.2.1. State-Model Representation

With (1) to (10), we derive the system modeled as follows:(11)X•=A+Bu,where u indicates the switching state of S1 and matrices A and B are as follows:(12)A=1L1vb−vC11L2vC1−v01C1iL1−iL2+1C1rv0−vC1−vC21C2rv0−vC1−vC21C0−v0R0+iL2C0−1C0rvC0−vC1−vC2,B=vC1L11L2v0−vC2−iL2r−iL1C1−1C1rv0−vC1−vC2iL2C2−1C2rv0−vC1−vC2−iL2C0+1C0rv0−vC1−vC2.The state vector includes five parameters: inductor currentsiL1 and iL2 and capacitor voltages vC1, vC2, and v0.The state vector is presented as follows:(13)X=iL1iL2vC1vC2v0T.


## 3. Fixed-Frequency Double-Integral Sliding Mode Control

The proposed FF-DISMC has two significant features. This controller is based on reduced state measures operating at a fixed frequency [29]. The advantage of fixed frequency operation is explained in Section 1. The output voltage measured and the remaining state variables are estimated to sense the minimum number of state variables. Here, the controller variables are errors in output voltage (v0) and input current (iL1). The reference current (iref) for inductor L1 is generated using voltage error:(14)iref=Kvref−v0.


### 3.1. Sliding Surface

The proposed FF-DISM control employs the output voltage (v0) and battery side inductor current (iL1) errors as control state variables. Correspondingly, two more control state variables are added to the sum of the first two state variables as integrals and double integrals.The control variables are further shown as follows:(15)x1=iL1ref−iL1,(16)x2=vref−v0,(17)x3=∫x1+x2dt,(18)x4=∫∫x1+x2dt.For the control of BQZSDC, the switch inputu should limit values between 0 and 1.(19)u=1,s>0,0,s<0.This control logic is developed by expressing the logic state ofS1. The switching function is as follows:(20)u=121+signs˙.The FF-DISM controller’s sliding surfaces are most likely to be interpreted as a linear combination of four state variables, which can be expressed as follows:(21)s=α1x1+α2x2+α3x3+α4x4,where α1, α2, α3, and α4 are the sliding coefficients.


### 3.2. Equivalent Control

The dynamic model of the BQZSDC can be obtained by substituting a set of equations in (11) into the time derivative converter variables given in (15)–(18). The derived equations are shown as follows:(22)x˙1=−KiC0C0−1L1Vb−vC11−u,x˙2=−iC0C0,x˙3=iC0C0K+1−1L1vb−vC11−u,x˙4=∫x1+x2dt.The equivalent control equation was derived by implementing equations˙=0.This gives the following:(23)ueq=1vC1−L1iC0C0K+α2α1−vb+vC1+α3L1α1x1+x2+1vC1α4L1α1∫x1+x2dt.


### 3.3. The Architecture of the Proposed Controller

A PWM block and a group of control rules, which were based on indirect SM control, are used to implement the proposed FF-DISM controller [34,35]. The equivalent controller consists of a control signal vCand a ramp signal vramp as follows:(24)vC=−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dt,vramp=vC1,where(25)k1=L1α3α1,k2=L1α4α1,k3=L1C0K+α2α1.The BQZSDC and the FF-DISM controller are shown in Figure5. The control law includes the comparison of the two signals vC and vramp. The ramp signal maintains the constant frequency.Figure 5
BQZSDC with the FF-DISM controller.For successful sliding mode operation, it is essential to satisfy three conditions. These conditions are hitting conditions, existing conditions, and stability conditions. The hitting condition confirms that the state trajectory hits the sliding surface, which was guaranteed by the switching function used in (20).


### 3.4. Existence Conditions

To examine the existence condition, it must satisfy the local reachability conditions given as follows:(26)lims⟶0ss˙>0.Replacing the derivative of (21) in (26), we can state the equation as follows:(27)s˙s⟶0+>0,(28)s˙s⟶0−>0.For BQZSDC, the existence conditions for the sliding mode operation are as follows:In the case-1,s⟶0+,s˙<0.Substitutingus⟶0+=1 into (27), we have the following:(29)k1x1+x2−vb−iC0k3+k2x3<0.In the case-2,s⟶0−,s˙>0.Substitutingus⟶0−=1 into (28), we have the following:(30)k1x1+x2−vb+vC1−iC0k3+k2x3>0.The values of battery voltageVb and output voltage V0 are assumed within a limit, which typically depict an operating range of the converter. The existing condition at maximum and minimum values is sufficient to ensure the broad range of abidance. While designing a sliding mode controller, the existing conditions should be met for steady-state operation. At steady-state condition, the state variables vC1, vC2 in (29), (30) are replaced by steady-state values VC1 (SS), VC2 (SS).Equations (31) and (32) can show the resulting existing condition considering all presumptions:(31)k1x1+k1vref−vomin−vbmin−iC0k3+k2∫x1dt+k2∫voref−vomin<0,(32)k1x1+k1voref−vomax−vbmax+vC1−iC0k3+k2∫x1dt+k2∫voref−vomax>0.


### 3.5. Stability Condition

The stability condition for the controller was proved by first determining the system’s ideal sliding dynamics and then analyzing its equilibrium point.


#### 3.5.1. Ideal Sliding Dynamics

By substitutingu by ueq in (11), the large-signal discontinuous system model of BQZSDC gets converted into an SM continuous system and is given as follows:(33)ddti∧L1i∧L2v∧C1v∧C2v∧0=vb−vC1L1vC1−v0L2iL1−iL2C1+v0−vC1−vC2C1rv0−vC1−vC2C2r−v0C0RL+iL2C0−v0−vC1−vC2C0r+vC1L1v0−vC2−iL2rL2−iL1C1−v0−vC1−vC2C1riL2C2−v0−vC1−vC2C2r−iL2C0+v0−vC1−vC2C0rueq.Then, substituting the equivalent control signal (23) in (33) gives the following:(34)di∧L1dtdi∧L2dtdv∧C1dtdv∧C2dtdv∧0dt=vb−vC1L1+1L1−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1−v0L2+v0−vC2−iL2rL2−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1iL1−iL2C1+v0−vC1−vC2C1r+−iL1C1−v0−vC1−vC2C1r−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1v0−vC1−vC2C2r+il2C2−v0−vC1−vC2C2r−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1−v0CoR0+iL2C0−v0−vC1−vC2C0r+−iL2Co+v0−vC1−vC2C0r−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1.


#### 3.5.2. Equilibrium-Point Analysis

Consider that the ideal sliding dynamics finally settle at a stable equilibrium point on the sliding surface. If there is no input or loading disturbance, the system’s dynamics will remain unchanged at this equilibrium point (steady state); i.e., the steady-state values at that operating point are given as follows:(35)IL1=V02VbRL,IL2=V0RL,VC1=V0+Vb2,VC2=V0−Vb2,V0=Vref.


#### 3.5.3. Linearization of Ideal Sliding Dynamic

The ideal SM continuous BQZSDC system’s small-signal state model was developed at stable equilibrium operating point (35).(36)dIL1+i¯L1dt=Vb−VC1−v¯C1L1+1L1−C0k3dV0+v¯0dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dt,dIL2+i¯L2dt=VC1+v¯C1L2−V0+v¯0L2+V0+v¯0−VC2−v¯C2−IL2r−i¯L2rL2×−C0k3dV0+v¯0/dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVc1,dVC1+v¯C1dt=IL1+i¯L1−IL2−i¯L2C1+V0+v¯0−VC1−v¯C1−VC2−v¯C2C1r+−IL1−i¯L1C1−V0−v¯0−VC1−v¯C1−VC2−v¯C2C1r×−C0k3dV0+v¯0/dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1,dVC2+v¯C2dt=V0−v¯0−VC1−v¯C1−VC2−v¯C2C2r+IL2+i¯l2C2−V0+v¯0−VC1−v¯C1−VC2−v¯C2C2r×−C0k3dV0+v¯0/dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1,dV0+v¯0dt=−V0−v¯0CoR0+IL2+i¯L2C0−V0+v¯0−VC1−v¯C1−VC2−v¯C2C0r+−IL2−iL2Co+V0+v¯0−VC1−v¯C1−VC2−v¯C2C0r×−C0k3dV0+v¯0/dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1.The above equations are derived by assuming the validity of the following conditions:vb=Vb,Vref−V0=0,Iref=IL1=Kvref−V0 and IL1≫i¯L1,IL2≫i¯L2,VC1≫v¯C1,VC2≫v¯C2,V0≫v¯0, by considering only AC terms. The linearized dynamic model at equilibrium point (35) is given by the following:(37)di¯L1dt=−v¯C1L1+1L1−k3−v¯0R0+i¯L2+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dt,di¯L2dt=v¯C1L2−v¯0L2+V0+v¯0−VC2−v¯C2−IL2r−i¯L2rL2×k3v¯0/R0−k3i¯L2−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVc1,dVC1+v¯C1dt=i¯L1−i¯L2C1+v¯0−v¯C1−v¯C2C1r+−IL1−i¯L1C1−V0−v¯0−VC1−v¯C1−VC2−v¯C2C1r×k3v¯0/R0−k3i¯L2−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1,dv¯C2dt=v¯0−v¯C1−v¯C2C2r+IL2+i¯l2C2−V0+v¯0−VC1−v¯C1−VC2−v¯C2C2r×k3v¯0/R0−k3i¯L2−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1,dv¯0dt=−v¯0CoR0+i¯L2C0−v¯0−v¯C1−v¯C2C0r+−IL2−iL2Co+V0+v¯0−VC1−v¯C1−VC2−v¯C2C0r×k3v¯0/R0−k3i¯L2−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1.By rearranging the above equations in standard form, we get the following:(38)di˜L1dt=α11i˜L1+α12i˜L2+α13v˜C1+α14v˜C2+α15v˜0+α16∫i˜L1dt+α17∫v˜0dt,di˜L2dt=α21i˜L1+α22i˜L2+α23v˜C1+α24v˜C2+α25v˜0+α26∫i˜L1dt+α27∫v˜0dt,dv˜C1dt=α31i˜L1+α32i˜L2+α33v˜C1+α34v˜C2+α35v˜0+α36∫i˜L1dt+α37∫v˜0dt,dv˜C2dt=α41i˜L1+α42i˜L2+α43v˜C1+α44v˜C2+α45v˜0+α46∫i˜L1dt+α47∫v˜0dt,dv˜0dt=α51i˜L1+α52i˜L2+α53v˜C1+α54v˜C2+α55v˜0+α56∫i˜L1dt+α57∫v˜0dt,d∫i˜L1dtdt=α61i˜L1+α62i˜L2+α63v˜C1+α64v˜C2+α65v˜0+α66∫i˜L1dt+α67∫v˜0dt,d∫v˜0dtdt=α71i˜L1+α72i˜L2+α73v˜C1+α74v˜C2+α75v˜0+α76∫i˜L1dt+α17∫v˜0dt.The characteristic equation of the linearized system is given by the following:(39)s−α11−α1200−α15−α16−α17−α21s−α22−α23−α24−α25−α26−α27−α31−α32s−α33−α34−α35−α36−α37−α41−α42−α43s−α44−α45−α46−α47−α51−α52−α53−α54s−α55−α56−α57−10000s00000−10s=s7+p1s6+p2s5+p3s4+p4s3+p5s2+p6s+p7=0,where(40)α11=−k1L1,α12=−k3L1,α13=0,α14=0,α15=−k3−k1KR0L1R0,α16=−k2L1,α17=−k2KL1,α21=−KV0−VC1−IL2rL2VC1,α22=−rVC1−Vb−k3V0−VC1−IL2rL2VC1,α23=V0−VC1−IL2rL2VC1,α24=V0−VC1−IL2rL2VC1+Vb−VC1L2VC1,α25=−1L2+k3−k1KR0V0−VC1−IL2rL2VC1+VC1−VbL2VC1,α26=−k2V0−VC1−IL2rL2VC1,α27=−k2KV0−VC1−IL2rL2VC1,α31=−k2IL1r−VbVC1rC1,α32=k3IL1r−VbC1VC1r,α33=−Vb−IL1rC1VC1r,α34=−VbC1VC1r,α35=k3−k1KR0R0V0−VC1−IL1r+VbL2VC1,α36=k2IL1C1VC1,α37=k2KIL1C1VC1,α41=−k2rIL2C2VC1,α42=−k3IL2r+VC1−VbC2VC1r,α43=IL2r−VbC2VC1r,α44=−VbC2VC1r,α45=−1C2+k3−k1KR0V0−VC1−IL2rC2VC1,α46=K2IL2C2VC1,α47=KK2IL2C2VC1,α51=k1IL2rC0VC1,α52=k3IL2r+VbC0VC1r,α53=IL2r+VbC0VC1r,α54=VbC0VC1r,α55=−1C0+k3−k1KR0V0−VC1−IL2rC2VC1,α56=K2IL2C0VC1,α57=K2KIL2C0VC1,α61=1,α62=0,α63=0,α64=0,α65=0,α66=0,α67=0,α71=0,α72=0,α73=0,α74=0,α75=1,α76=0,α77=0.The range of control gains obtained by applying the Routh–Hurwitz criterion to characteristic equation (39) is as follows:(41)p1>0,p2>p3p1,p3>p1p4−p5,p4>p1p2−p3p5−p1p2−p7+p5p1p1,p5>p1p2−p3p3−p12p6−p1p7p1p2−p3+p1,p6>p1p2−p3p3−p12p4−p1p7−p1p2−p3+p1p5p12,P7>0.The stability of the system is found by substituting (40) in (41). This, coupled with the existing condition (31) and (32), constitutes the foundation for selecting and designing the controller’s control gains in conjunction with the converter’s specified requirements.


### 3.6. Selection of Control Gains

The sliding coefficients were chosen after analyzing the effect of changing the control gains on the output voltage.The subsequent conclusions were attained:(1)
The increase inK minimizes the steady-state error but increases the settling time by making the transient response more oscillatory(2)
The slope of voltage responses can be increased or decreased by changingk1(3)
The increment ink2 reduces the settling time but raises the steady-state error(4)
The increment ink3 reduces transient response overshoot while slightly increasing settling timeThe values ofk1, k2, and k3 are selected based on the above observations until the controller provides the required performance.


## 3.1. Sliding Surface

The proposed FF-DISM control employs the output voltage (v0) and battery side inductor current (iL1) errors as control state variables. Correspondingly, two more control state variables are added to the sum of the first two state variables as integrals and double integrals.The control variables are further shown as follows:(15)x1=iL1ref−iL1,(16)x2=vref−v0,(17)x3=∫x1+x2dt,(18)x4=∫∫x1+x2dt.For the control of BQZSDC, the switch inputu should limit values between 0 and 1.(19)u=1,s>0,0,s<0.This control logic is developed by expressing the logic state ofS1. The switching function is as follows:(20)u=121+signs˙.The FF-DISM controller’s sliding surfaces are most likely to be interpreted as a linear combination of four state variables, which can be expressed as follows:(21)s=α1x1+α2x2+α3x3+α4x4,where α1, α2, α3, and α4 are the sliding coefficients.


## 3.2. Equivalent Control

The dynamic model of the BQZSDC can be obtained by substituting a set of equations in (11) into the time derivative converter variables given in (15)–(18). The derived equations are shown as follows:(22)x˙1=−KiC0C0−1L1Vb−vC11−u,x˙2=−iC0C0,x˙3=iC0C0K+1−1L1vb−vC11−u,x˙4=∫x1+x2dt.The equivalent control equation was derived by implementing equations˙=0.This gives the following:(23)ueq=1vC1−L1iC0C0K+α2α1−vb+vC1+α3L1α1x1+x2+1vC1α4L1α1∫x1+x2dt.


## 3.3. The Architecture of the Proposed Controller

A PWM block and a group of control rules, which were based on indirect SM control, are used to implement the proposed FF-DISM controller [34,35]. The equivalent controller consists of a control signal vCand a ramp signal vramp as follows:(24)vC=−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dt,vramp=vC1,where(25)k1=L1α3α1,k2=L1α4α1,k3=L1C0K+α2α1.The BQZSDC and the FF-DISM controller are shown in Figure5. The control law includes the comparison of the two signals vC and vramp. The ramp signal maintains the constant frequency.Figure 5
BQZSDC with the FF-DISM controller.For successful sliding mode operation, it is essential to satisfy three conditions. These conditions are hitting conditions, existing conditions, and stability conditions. The hitting condition confirms that the state trajectory hits the sliding surface, which was guaranteed by the switching function used in (20).


## 3.4. Existence Conditions

To examine the existence condition, it must satisfy the local reachability conditions given as follows:(26)lims⟶0ss˙>0.Replacing the derivative of (21) in (26), we can state the equation as follows:(27)s˙s⟶0+>0,(28)s˙s⟶0−>0.For BQZSDC, the existence conditions for the sliding mode operation are as follows:In the case-1,s⟶0+,s˙<0.Substitutingus⟶0+=1 into (27), we have the following:(29)k1x1+x2−vb−iC0k3+k2x3<0.In the case-2,s⟶0−,s˙>0.Substitutingus⟶0−=1 into (28), we have the following:(30)k1x1+x2−vb+vC1−iC0k3+k2x3>0.The values of battery voltageVb and output voltage V0 are assumed within a limit, which typically depict an operating range of the converter. The existing condition at maximum and minimum values is sufficient to ensure the broad range of abidance. While designing a sliding mode controller, the existing conditions should be met for steady-state operation. At steady-state condition, the state variables vC1, vC2 in (29), (30) are replaced by steady-state values VC1 (SS), VC2 (SS).Equations (31) and (32) can show the resulting existing condition considering all presumptions:(31)k1x1+k1vref−vomin−vbmin−iC0k3+k2∫x1dt+k2∫voref−vomin<0,(32)k1x1+k1voref−vomax−vbmax+vC1−iC0k3+k2∫x1dt+k2∫voref−vomax>0.


## 3.5. Stability Condition

The stability condition for the controller was proved by first determining the system’s ideal sliding dynamics and then analyzing its equilibrium point.


### 3.5.1. Ideal Sliding Dynamics

By substitutingu by ueq in (11), the large-signal discontinuous system model of BQZSDC gets converted into an SM continuous system and is given as follows:(33)ddti∧L1i∧L2v∧C1v∧C2v∧0=vb−vC1L1vC1−v0L2iL1−iL2C1+v0−vC1−vC2C1rv0−vC1−vC2C2r−v0C0RL+iL2C0−v0−vC1−vC2C0r+vC1L1v0−vC2−iL2rL2−iL1C1−v0−vC1−vC2C1riL2C2−v0−vC1−vC2C2r−iL2C0+v0−vC1−vC2C0rueq.Then, substituting the equivalent control signal (23) in (33) gives the following:(34)di∧L1dtdi∧L2dtdv∧C1dtdv∧C2dtdv∧0dt=vb−vC1L1+1L1−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1−v0L2+v0−vC2−iL2rL2−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1iL1−iL2C1+v0−vC1−vC2C1r+−iL1C1−v0−vC1−vC2C1r−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1v0−vC1−vC2C2r+il2C2−v0−vC1−vC2C2r−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1−v0CoR0+iL2C0−v0−vC1−vC2C0r+−iL2Co+v0−vC1−vC2C0r−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1.


### 3.5.2. Equilibrium-Point Analysis

Consider that the ideal sliding dynamics finally settle at a stable equilibrium point on the sliding surface. If there is no input or loading disturbance, the system’s dynamics will remain unchanged at this equilibrium point (steady state); i.e., the steady-state values at that operating point are given as follows:(35)IL1=V02VbRL,IL2=V0RL,VC1=V0+Vb2,VC2=V0−Vb2,V0=Vref.


### 3.5.3. Linearization of Ideal Sliding Dynamic

The ideal SM continuous BQZSDC system’s small-signal state model was developed at stable equilibrium operating point (35).(36)dIL1+i¯L1dt=Vb−VC1−v¯C1L1+1L1−C0k3dV0+v¯0dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dt,dIL2+i¯L2dt=VC1+v¯C1L2−V0+v¯0L2+V0+v¯0−VC2−v¯C2−IL2r−i¯L2rL2×−C0k3dV0+v¯0/dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVc1,dVC1+v¯C1dt=IL1+i¯L1−IL2−i¯L2C1+V0+v¯0−VC1−v¯C1−VC2−v¯C2C1r+−IL1−i¯L1C1−V0−v¯0−VC1−v¯C1−VC2−v¯C2C1r×−C0k3dV0+v¯0/dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1,dVC2+v¯C2dt=V0−v¯0−VC1−v¯C1−VC2−v¯C2C2r+IL2+i¯l2C2−V0+v¯0−VC1−v¯C1−VC2−v¯C2C2r×−C0k3dV0+v¯0/dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1,dV0+v¯0dt=−V0−v¯0CoR0+IL2+i¯L2C0−V0+v¯0−VC1−v¯C1−VC2−v¯C2C0r+−IL2−iL2Co+V0+v¯0−VC1−v¯C1−VC2−v¯C2C0r×−C0k3dV0+v¯0/dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1.The above equations are derived by assuming the validity of the following conditions:vb=Vb,Vref−V0=0,Iref=IL1=Kvref−V0 and IL1≫i¯L1,IL2≫i¯L2,VC1≫v¯C1,VC2≫v¯C2,V0≫v¯0, by considering only AC terms. The linearized dynamic model at equilibrium point (35) is given by the following:(37)di¯L1dt=−v¯C1L1+1L1−k3−v¯0R0+i¯L2+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dt,di¯L2dt=v¯C1L2−v¯0L2+V0+v¯0−VC2−v¯C2−IL2r−i¯L2rL2×k3v¯0/R0−k3i¯L2−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVc1,dVC1+v¯C1dt=i¯L1−i¯L2C1+v¯0−v¯C1−v¯C2C1r+−IL1−i¯L1C1−V0−v¯0−VC1−v¯C1−VC2−v¯C2C1r×k3v¯0/R0−k3i¯L2−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1,dv¯C2dt=v¯0−v¯C1−v¯C2C2r+IL2+i¯l2C2−V0+v¯0−VC1−v¯C1−VC2−v¯C2C2r×k3v¯0/R0−k3i¯L2−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1,dv¯0dt=−v¯0CoR0+i¯L2C0−v¯0−v¯C1−v¯C2C0r+−IL2−iL2Co+V0+v¯0−VC1−v¯C1−VC2−v¯C2C0r×k3v¯0/R0−k3i¯L2−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1.By rearranging the above equations in standard form, we get the following:(38)di˜L1dt=α11i˜L1+α12i˜L2+α13v˜C1+α14v˜C2+α15v˜0+α16∫i˜L1dt+α17∫v˜0dt,di˜L2dt=α21i˜L1+α22i˜L2+α23v˜C1+α24v˜C2+α25v˜0+α26∫i˜L1dt+α27∫v˜0dt,dv˜C1dt=α31i˜L1+α32i˜L2+α33v˜C1+α34v˜C2+α35v˜0+α36∫i˜L1dt+α37∫v˜0dt,dv˜C2dt=α41i˜L1+α42i˜L2+α43v˜C1+α44v˜C2+α45v˜0+α46∫i˜L1dt+α47∫v˜0dt,dv˜0dt=α51i˜L1+α52i˜L2+α53v˜C1+α54v˜C2+α55v˜0+α56∫i˜L1dt+α57∫v˜0dt,d∫i˜L1dtdt=α61i˜L1+α62i˜L2+α63v˜C1+α64v˜C2+α65v˜0+α66∫i˜L1dt+α67∫v˜0dt,d∫v˜0dtdt=α71i˜L1+α72i˜L2+α73v˜C1+α74v˜C2+α75v˜0+α76∫i˜L1dt+α17∫v˜0dt.The characteristic equation of the linearized system is given by the following:(39)s−α11−α1200−α15−α16−α17−α21s−α22−α23−α24−α25−α26−α27−α31−α32s−α33−α34−α35−α36−α37−α41−α42−α43s−α44−α45−α46−α47−α51−α52−α53−α54s−α55−α56−α57−10000s00000−10s=s7+p1s6+p2s5+p3s4+p4s3+p5s2+p6s+p7=0,where(40)α11=−k1L1,α12=−k3L1,α13=0,α14=0,α15=−k3−k1KR0L1R0,α16=−k2L1,α17=−k2KL1,α21=−KV0−VC1−IL2rL2VC1,α22=−rVC1−Vb−k3V0−VC1−IL2rL2VC1,α23=V0−VC1−IL2rL2VC1,α24=V0−VC1−IL2rL2VC1+Vb−VC1L2VC1,α25=−1L2+k3−k1KR0V0−VC1−IL2rL2VC1+VC1−VbL2VC1,α26=−k2V0−VC1−IL2rL2VC1,α27=−k2KV0−VC1−IL2rL2VC1,α31=−k2IL1r−VbVC1rC1,α32=k3IL1r−VbC1VC1r,α33=−Vb−IL1rC1VC1r,α34=−VbC1VC1r,α35=k3−k1KR0R0V0−VC1−IL1r+VbL2VC1,α36=k2IL1C1VC1,α37=k2KIL1C1VC1,α41=−k2rIL2C2VC1,α42=−k3IL2r+VC1−VbC2VC1r,α43=IL2r−VbC2VC1r,α44=−VbC2VC1r,α45=−1C2+k3−k1KR0V0−VC1−IL2rC2VC1,α46=K2IL2C2VC1,α47=KK2IL2C2VC1,α51=k1IL2rC0VC1,α52=k3IL2r+VbC0VC1r,α53=IL2r+VbC0VC1r,α54=VbC0VC1r,α55=−1C0+k3−k1KR0V0−VC1−IL2rC2VC1,α56=K2IL2C0VC1,α57=K2KIL2C0VC1,α61=1,α62=0,α63=0,α64=0,α65=0,α66=0,α67=0,α71=0,α72=0,α73=0,α74=0,α75=1,α76=0,α77=0.The range of control gains obtained by applying the Routh–Hurwitz criterion to characteristic equation (39) is as follows:(41)p1>0,p2>p3p1,p3>p1p4−p5,p4>p1p2−p3p5−p1p2−p7+p5p1p1,p5>p1p2−p3p3−p12p6−p1p7p1p2−p3+p1,p6>p1p2−p3p3−p12p4−p1p7−p1p2−p3+p1p5p12,P7>0.The stability of the system is found by substituting (40) in (41). This, coupled with the existing condition (31) and (32), constitutes the foundation for selecting and designing the controller’s control gains in conjunction with the converter’s specified requirements.


## 3.5.1. Ideal Sliding Dynamics

By substitutingu by ueq in (11), the large-signal discontinuous system model of BQZSDC gets converted into an SM continuous system and is given as follows:(33)ddti∧L1i∧L2v∧C1v∧C2v∧0=vb−vC1L1vC1−v0L2iL1−iL2C1+v0−vC1−vC2C1rv0−vC1−vC2C2r−v0C0RL+iL2C0−v0−vC1−vC2C0r+vC1L1v0−vC2−iL2rL2−iL1C1−v0−vC1−vC2C1riL2C2−v0−vC1−vC2C2r−iL2C0+v0−vC1−vC2C0rueq.Then, substituting the equivalent control signal (23) in (33) gives the following:(34)di∧L1dtdi∧L2dtdv∧C1dtdv∧C2dtdv∧0dt=vb−vC1L1+1L1−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1−v0L2+v0−vC2−iL2rL2−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1iL1−iL2C1+v0−vC1−vC2C1r+−iL1C1−v0−vC1−vC2C1r−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1v0−vC1−vC2C2r+il2C2−v0−vC1−vC2C2r−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1−v0CoR0+iL2C0−v0−vC1−vC2C0r+−iL2Co+v0−vC1−vC2C0r−iC0k3−vb+vC1+k1x1+x2+k2∫x1+x2dtvC1.


## 3.5.2. Equilibrium-Point Analysis

Consider that the ideal sliding dynamics finally settle at a stable equilibrium point on the sliding surface. If there is no input or loading disturbance, the system’s dynamics will remain unchanged at this equilibrium point (steady state); i.e., the steady-state values at that operating point are given as follows:(35)IL1=V02VbRL,IL2=V0RL,VC1=V0+Vb2,VC2=V0−Vb2,V0=Vref.


## 3.5.3. Linearization of Ideal Sliding Dynamic

The ideal SM continuous BQZSDC system’s small-signal state model was developed at stable equilibrium operating point (35).(36)dIL1+i¯L1dt=Vb−VC1−v¯C1L1+1L1−C0k3dV0+v¯0dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dt,dIL2+i¯L2dt=VC1+v¯C1L2−V0+v¯0L2+V0+v¯0−VC2−v¯C2−IL2r−i¯L2rL2×−C0k3dV0+v¯0/dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVc1,dVC1+v¯C1dt=IL1+i¯L1−IL2−i¯L2C1+V0+v¯0−VC1−v¯C1−VC2−v¯C2C1r+−IL1−i¯L1C1−V0−v¯0−VC1−v¯C1−VC2−v¯C2C1r×−C0k3dV0+v¯0/dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1,dVC2+v¯C2dt=V0−v¯0−VC1−v¯C1−VC2−v¯C2C2r+IL2+i¯l2C2−V0+v¯0−VC1−v¯C1−VC2−v¯C2C2r×−C0k3dV0+v¯0/dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1,dV0+v¯0dt=−V0−v¯0CoR0+IL2+i¯L2C0−V0+v¯0−VC1−v¯C1−VC2−v¯C2C0r+−IL2−iL2Co+V0+v¯0−VC1−v¯C1−VC2−v¯C2C0r×−C0k3dV0+v¯0/dt−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1.The above equations are derived by assuming the validity of the following conditions:vb=Vb,Vref−V0=0,Iref=IL1=Kvref−V0 and IL1≫i¯L1,IL2≫i¯L2,VC1≫v¯C1,VC2≫v¯C2,V0≫v¯0, by considering only AC terms. The linearized dynamic model at equilibrium point (35) is given by the following:(37)di¯L1dt=−v¯C1L1+1L1−k3−v¯0R0+i¯L2+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dt,di¯L2dt=v¯C1L2−v¯0L2+V0+v¯0−VC2−v¯C2−IL2r−i¯L2rL2×k3v¯0/R0−k3i¯L2−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVc1,dVC1+v¯C1dt=i¯L1−i¯L2C1+v¯0−v¯C1−v¯C2C1r+−IL1−i¯L1C1−V0−v¯0−VC1−v¯C1−VC2−v¯C2C1r×k3v¯0/R0−k3i¯L2−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1,dv¯C2dt=v¯0−v¯C1−v¯C2C2r+IL2+i¯l2C2−V0+v¯0−VC1−v¯C1−VC2−v¯C2C2r×k3v¯0/R0−k3i¯L2−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1,dv¯0dt=−v¯0CoR0+i¯L2C0−v¯0−v¯C1−v¯C2C0r+−IL2−iL2Co+V0+v¯0−VC1−v¯C1−VC2−v¯C2C0r×k3v¯0/R0−k3i¯L2−Vb+VC1+v¯C1−k1Kv¯0−k1i¯L1−k2K∫v¯0dt−k2∫i¯L1dtVC1.By rearranging the above equations in standard form, we get the following:(38)di˜L1dt=α11i˜L1+α12i˜L2+α13v˜C1+α14v˜C2+α15v˜0+α16∫i˜L1dt+α17∫v˜0dt,di˜L2dt=α21i˜L1+α22i˜L2+α23v˜C1+α24v˜C2+α25v˜0+α26∫i˜L1dt+α27∫v˜0dt,dv˜C1dt=α31i˜L1+α32i˜L2+α33v˜C1+α34v˜C2+α35v˜0+α36∫i˜L1dt+α37∫v˜0dt,dv˜C2dt=α41i˜L1+α42i˜L2+α43v˜C1+α44v˜C2+α45v˜0+α46∫i˜L1dt+α47∫v˜0dt,dv˜0dt=α51i˜L1+α52i˜L2+α53v˜C1+α54v˜C2+α55v˜0+α56∫i˜L1dt+α57∫v˜0dt,d∫i˜L1dtdt=α61i˜L1+α62i˜L2+α63v˜C1+α64v˜C2+α65v˜0+α66∫i˜L1dt+α67∫v˜0dt,d∫v˜0dtdt=α71i˜L1+α72i˜L2+α73v˜C1+α74v˜C2+α75v˜0+α76∫i˜L1dt+α17∫v˜0dt.The characteristic equation of the linearized system is given by the following:(39)s−α11−α1200−α15−α16−α17−α21s−α22−α23−α24−α25−α26−α27−α31−α32s−α33−α34−α35−α36−α37−α41−α42−α43s−α44−α45−α46−α47−α51−α52−α53−α54s−α55−α56−α57−10000s00000−10s=s7+p1s6+p2s5+p3s4+p4s3+p5s2+p6s+p7=0,where(40)α11=−k1L1,α12=−k3L1,α13=0,α14=0,α15=−k3−k1KR0L1R0,α16=−k2L1,α17=−k2KL1,α21=−KV0−VC1−IL2rL2VC1,α22=−rVC1−Vb−k3V0−VC1−IL2rL2VC1,α23=V0−VC1−IL2rL2VC1,α24=V0−VC1−IL2rL2VC1+Vb−VC1L2VC1,α25=−1L2+k3−k1KR0V0−VC1−IL2rL2VC1+VC1−VbL2VC1,α26=−k2V0−VC1−IL2rL2VC1,α27=−k2KV0−VC1−IL2rL2VC1,α31=−k2IL1r−VbVC1rC1,α32=k3IL1r−VbC1VC1r,α33=−Vb−IL1rC1VC1r,α34=−VbC1VC1r,α35=k3−k1KR0R0V0−VC1−IL1r+VbL2VC1,α36=k2IL1C1VC1,α37=k2KIL1C1VC1,α41=−k2rIL2C2VC1,α42=−k3IL2r+VC1−VbC2VC1r,α43=IL2r−VbC2VC1r,α44=−VbC2VC1r,α45=−1C2+k3−k1KR0V0−VC1−IL2rC2VC1,α46=K2IL2C2VC1,α47=KK2IL2C2VC1,α51=k1IL2rC0VC1,α52=k3IL2r+VbC0VC1r,α53=IL2r+VbC0VC1r,α54=VbC0VC1r,α55=−1C0+k3−k1KR0V0−VC1−IL2rC2VC1,α56=K2IL2C0VC1,α57=K2KIL2C0VC1,α61=1,α62=0,α63=0,α64=0,α65=0,α66=0,α67=0,α71=0,α72=0,α73=0,α74=0,α75=1,α76=0,α77=0.The range of control gains obtained by applying the Routh–Hurwitz criterion to characteristic equation (39) is as follows:(41)p1>0,p2>p3p1,p3>p1p4−p5,p4>p1p2−p3p5−p1p2−p7+p5p1p1,p5>p1p2−p3p3−p12p6−p1p7p1p2−p3+p1,p6>p1p2−p3p3−p12p4−p1p7−p1p2−p3+p1p5p12,P7>0.The stability of the system is found by substituting (40) in (41). This, coupled with the existing condition (31) and (32), constitutes the foundation for selecting and designing the controller’s control gains in conjunction with the converter’s specified requirements.


## 3.6. Selection of Control Gains

The sliding coefficients were chosen after analyzing the effect of changing the control gains on the output voltage.The subsequent conclusions were attained:(1)
The increase inK minimizes the steady-state error but increases the settling time by making the transient response more oscillatory(2)
The slope of voltage responses can be increased or decreased by changingk1(3)
The increment ink2 reduces the settling time but raises the steady-state error(4)
The increment ink3 reduces transient response overshoot while slightly increasing settling timeThe values ofk1, k2, and k3 are selected based on the above observations until the controller provides the required performance.


## 4. Results and Discussion

The proposed control technique was developed in MATLAB/Simulink and tested on a prototype. These details are addressed in the subsections that follow.


### 4.1. Simulation Results

The efficiency and performance of the proposed controller for the converter are examined based on a set of simulations. Even though the controller was developed using the boost mode approach, it can also be used in buck mode. This section analyzes the converter’s responses for reference and load changes in both buck and boost modes.


#### 4.1.1. Reference Change

The effect of changing the reference voltage on the controller and its tracking ability is analyzed. The reference voltage was varied from 48 V to 36 V at 0.2 sec, and it is observed that thev0is tracking the new reference of 36 V, as shown in Figure 6. Furthermore, it can be seen that at 0.4 sec, the voltage is restored to 48 V, and the controller tracks the output voltage in line with the reference voltage of 48 V.Figure 6
Waveforms of BQZSD under reference output voltage variation with double-integral sliding mode controller.The parameters of the converter are mentioned in Table1.Table 1
Parameters of the converter.
ParameterValuePower100 WOutput voltageV048 VBattery voltageVb12 VInductorsL1 and L21 mH, 3.3 mHCapacitorsC1 and C2100μFResistorr0.216 ΩCapacitorC0470μFThe converter can operate in step-up and step-down modes, thereby enabling the battery to charge or discharge depending on the power flow. The system was connected to a PV source interface with a load attached to the common bus. The load is desired to be catered for at a constant voltage of 48 V. If the PV power is more than the load power, the BQZSDC is switched to buck mode, and the excess energy is used to charge the battery. If the PV power is less than the load power required, the BQZSDC goes into boost mode, and the battery is discharged to make up the difference.As a part of this work, a 12 V battery is considered, and the output reference voltage is taken as 48 V. The PV system acts as a constant source (operating at constant irradiation) current of 4.17 A supplying 200 W, connected at the load side of the BQZDC. The converter performance was observed under load variations.


#### 4.1.2. Boost Mode (Discharging Mode)

In this mode, the battery starts discharging through the converter supplying the deficit power to maintain the power balance and a stable output voltage. As shown in Figure7, the initial load demand is 5.2 A, out of which the PV source is supplying 4.17 A. The converter provides the remaining current of 1.03 A (stepping down the battery current from 4.16 A) and maintains the load voltage at 48 V. The load current was observed to be enhanced to 6.25 A at time t = 0.2 sec. The results show that the excess current of 2.08 A was supplied by the converter (stepping down the battery current from 8.33 A). Moreover, at t = 0.4 sec, the load current returns to 5.2 A, and the converter supplies excess current even under this condition. Figure 8 shows the variation of SOC of battery and load voltage.Figure 7
Different currents waveforms of BQZSDC when the load varied from 5.208 A to 6.25 A and vice versa in boost mode.Figure 8
Output voltage and SOC of the battery when the load varied from 5.208 A to 6.25 A and vice versa in boost mode.


#### 4.1.3. Buck Mode (Charging Mode)

In this mode, the battery starts charging through the converter absorbing the excess power to maintain the power balance and a stable output voltage. Initially, the load current was 4.17 A which was exactly catered for by the PV. Thus, the battery remains idle with no current being supplied or absorbed. The load demand decreased to 2.08 A att = 0.2 sec, and as shown in Figure 9, the surplus current absorbed by the battery to charge itself and the battery current is negative. Consequently, at t = 0.4 sec, the load current is increased again to 4.17 A, and at this point, the battery and the converter remain idle without any current. The load voltage is sustained at 48 V throughout, and Figure 10 shows the variation of SOC of battery and load voltage profile.Figure 9
Different current waveforms when the load varied from 4.17 A to 2.08 A and vice versa in buck mode.Figure 10
Output voltage and SOC of the battery when load varied from 4.17 A to 2.08 A and vice versa in buck mode.


### 4.2. Hardware Implementation and Results

The laboratory setup for the hardware implementation of the proposed work is shown in Figure11.Figure 11
Experimental setup for hardware implementation.A programmable DC power supply (Chroma-62020H-150S) from Chroma was employed as a PV source. Three LEM voltage sensors (LV25-P/SP213205) and two current sensors (LA55-P14316) were used to sense different voltages and currents. Outputs of sensors were given to dSPACE-1104 ADC channels with appropriate gain. This was used to implement the proposed control algorithm.To capture the experimental results, RIGOL-DS1054 was used. The presented control algorithm was implemented by generating three gate pulses with an adjustable duty cycle using dSPACE-1104. A distinct gate pulse was given to switch the parallel-connected load to change the load.The experimental tests were carried out in fewer than two conditions: (i) change in the reference voltage and (ii) change in the load (boost and buck mode).


#### 4.2.1. Reference Change

The reference voltage is varied from 48 V to 36 V at a particular time, and it is shown that the output voltagev0 is tracking the new reference of 36 V, as shown in Figure 12. Furthermore, it can be seen that the reference voltage has been restored to 48 V, and the controller tracks the output voltage in line with the reference voltage of 48 V.Figure 12
Hardware results when the reference voltage is varied from 48 V to 36 V and vice versa.The converter can work in both modes, making it easier to charge or discharge the battery depending on the power flow.


#### 4.2.2. Boost Mode (Discharging Mode)

The battery begins discharging through the converter in boost mode, which supplies the deficit power to keep the power balance and output voltage stable. The initial load requirement is 5.2 A, as illustrated in Figure13, with the PV source contributing 4.17 A. The converter supplies 1.03 A of the remaining current (stepping down the battery current from 4.16 A). As load demand increases, the battery supplies even more current while keeping the load voltage at 48 V.Figure 13
Hardware results when the load current was varied from 5.208 to 6.25 V and vice versa (boost mode).


#### 4.2.3. Buck Mode (Charging Mode)

The battery begins charging through the converter in buck mode, absorbing excess power to keep the power balance and output voltage stable. Initially, the load current is 4.17 A, which the PV can handle perfectly. As a result, the battery stays uncharged, and no current is delivered or absorbed. As the load demand decreases, the battery absorbs the excess current to charge itself, as seen in Figure14.Figure 14
Hardware results when the load current is varied from 4.17 A to 2.08 A and vice versa (buck mode).


## 4.1. Simulation Results

The efficiency and performance of the proposed controller for the converter are examined based on a set of simulations. Even though the controller was developed using the boost mode approach, it can also be used in buck mode. This section analyzes the converter’s responses for reference and load changes in both buck and boost modes.


### 4.1.1. Reference Change

The effect of changing the reference voltage on the controller and its tracking ability is analyzed. The reference voltage was varied from 48 V to 36 V at 0.2 sec, and it is observed that thev0is tracking the new reference of 36 V, as shown in Figure 6. Furthermore, it can be seen that at 0.4 sec, the voltage is restored to 48 V, and the controller tracks the output voltage in line with the reference voltage of 48 V.Figure 6
Waveforms of BQZSD under reference output voltage variation with double-integral sliding mode controller.The parameters of the converter are mentioned in Table1.Table 1
Parameters of the converter.
ParameterValuePower100 WOutput voltageV048 VBattery voltageVb12 VInductorsL1 and L21 mH, 3.3 mHCapacitorsC1 and C2100μFResistorr0.216 ΩCapacitorC0470μFThe converter can operate in step-up and step-down modes, thereby enabling the battery to charge or discharge depending on the power flow. The system was connected to a PV source interface with a load attached to the common bus. The load is desired to be catered for at a constant voltage of 48 V. If the PV power is more than the load power, the BQZSDC is switched to buck mode, and the excess energy is used to charge the battery. If the PV power is less than the load power required, the BQZSDC goes into boost mode, and the battery is discharged to make up the difference.As a part of this work, a 12 V battery is considered, and the output reference voltage is taken as 48 V. The PV system acts as a constant source (operating at constant irradiation) current of 4.17 A supplying 200 W, connected at the load side of the BQZDC. The converter performance was observed under load variations.


### 4.1.2. Boost Mode (Discharging Mode)

In this mode, the battery starts discharging through the converter supplying the deficit power to maintain the power balance and a stable output voltage. As shown in Figure7, the initial load demand is 5.2 A, out of which the PV source is supplying 4.17 A. The converter provides the remaining current of 1.03 A (stepping down the battery current from 4.16 A) and maintains the load voltage at 48 V. The load current was observed to be enhanced to 6.25 A at time t = 0.2 sec. The results show that the excess current of 2.08 A was supplied by the converter (stepping down the battery current from 8.33 A). Moreover, at t = 0.4 sec, the load current returns to 5.2 A, and the converter supplies excess current even under this condition. Figure 8 shows the variation of SOC of battery and load voltage.Figure 7
Different currents waveforms of BQZSDC when the load varied from 5.208 A to 6.25 A and vice versa in boost mode.Figure 8
Output voltage and SOC of the battery when the load varied from 5.208 A to 6.25 A and vice versa in boost mode.


### 4.1.3. Buck Mode (Charging Mode)

In this mode, the battery starts charging through the converter absorbing the excess power to maintain the power balance and a stable output voltage. Initially, the load current was 4.17 A which was exactly catered for by the PV. Thus, the battery remains idle with no current being supplied or absorbed. The load demand decreased to 2.08 A att = 0.2 sec, and as shown in Figure 9, the surplus current absorbed by the battery to charge itself and the battery current is negative. Consequently, at t = 0.4 sec, the load current is increased again to 4.17 A, and at this point, the battery and the converter remain idle without any current. The load voltage is sustained at 48 V throughout, and Figure 10 shows the variation of SOC of battery and load voltage profile.Figure 9
Different current waveforms when the load varied from 4.17 A to 2.08 A and vice versa in buck mode.Figure 10
Output voltage and SOC of the battery when load varied from 4.17 A to 2.08 A and vice versa in buck mode.


## 4.1.1. Reference Change

The effect of changing the reference voltage on the controller and its tracking ability is analyzed. The reference voltage was varied from 48 V to 36 V at 0.2 sec, and it is observed that thev0is tracking the new reference of 36 V, as shown in Figure 6. Furthermore, it can be seen that at 0.4 sec, the voltage is restored to 48 V, and the controller tracks the output voltage in line with the reference voltage of 48 V.Figure 6
Waveforms of BQZSD under reference output voltage variation with double-integral sliding mode controller.The parameters of the converter are mentioned in Table1.Table 1
Parameters of the converter.
ParameterValuePower100 WOutput voltageV048 VBattery voltageVb12 VInductorsL1 and L21 mH, 3.3 mHCapacitorsC1 and C2100μFResistorr0.216 ΩCapacitorC0470μFThe converter can operate in step-up and step-down modes, thereby enabling the battery to charge or discharge depending on the power flow. The system was connected to a PV source interface with a load attached to the common bus. The load is desired to be catered for at a constant voltage of 48 V. If the PV power is more than the load power, the BQZSDC is switched to buck mode, and the excess energy is used to charge the battery. If the PV power is less than the load power required, the BQZSDC goes into boost mode, and the battery is discharged to make up the difference.As a part of this work, a 12 V battery is considered, and the output reference voltage is taken as 48 V. The PV system acts as a constant source (operating at constant irradiation) current of 4.17 A supplying 200 W, connected at the load side of the BQZDC. The converter performance was observed under load variations.


## 4.1.2. Boost Mode (Discharging Mode)

In this mode, the battery starts discharging through the converter supplying the deficit power to maintain the power balance and a stable output voltage. As shown in Figure7, the initial load demand is 5.2 A, out of which the PV source is supplying 4.17 A. The converter provides the remaining current of 1.03 A (stepping down the battery current from 4.16 A) and maintains the load voltage at 48 V. The load current was observed to be enhanced to 6.25 A at time t = 0.2 sec. The results show that the excess current of 2.08 A was supplied by the converter (stepping down the battery current from 8.33 A). Moreover, at t = 0.4 sec, the load current returns to 5.2 A, and the converter supplies excess current even under this condition. Figure 8 shows the variation of SOC of battery and load voltage.Figure 7
Different currents waveforms of BQZSDC when the load varied from 5.208 A to 6.25 A and vice versa in boost mode.Figure 8
Output voltage and SOC of the battery when the load varied from 5.208 A to 6.25 A and vice versa in boost mode.


## 4.1.3. Buck Mode (Charging Mode)

In this mode, the battery starts charging through the converter absorbing the excess power to maintain the power balance and a stable output voltage. Initially, the load current was 4.17 A which was exactly catered for by the PV. Thus, the battery remains idle with no current being supplied or absorbed. The load demand decreased to 2.08 A att = 0.2 sec, and as shown in Figure 9, the surplus current absorbed by the battery to charge itself and the battery current is negative. Consequently, at t = 0.4 sec, the load current is increased again to 4.17 A, and at this point, the battery and the converter remain idle without any current. The load voltage is sustained at 48 V throughout, and Figure 10 shows the variation of SOC of battery and load voltage profile.Figure 9
Different current waveforms when the load varied from 4.17 A to 2.08 A and vice versa in buck mode.Figure 10
Output voltage and SOC of the battery when load varied from 4.17 A to 2.08 A and vice versa in buck mode.


## 4.2. Hardware Implementation and Results

The laboratory setup for the hardware implementation of the proposed work is shown in Figure11.Figure 11
Experimental setup for hardware implementation.A programmable DC power supply (Chroma-62020H-150S) from Chroma was employed as a PV source. Three LEM voltage sensors (LV25-P/SP213205) and two current sensors (LA55-P14316) were used to sense different voltages and currents. Outputs of sensors were given to dSPACE-1104 ADC channels with appropriate gain. This was used to implement the proposed control algorithm.To capture the experimental results, RIGOL-DS1054 was used. The presented control algorithm was implemented by generating three gate pulses with an adjustable duty cycle using dSPACE-1104. A distinct gate pulse was given to switch the parallel-connected load to change the load.The experimental tests were carried out in fewer than two conditions: (i) change in the reference voltage and (ii) change in the load (boost and buck mode).


### 4.2.1. Reference Change

The reference voltage is varied from 48 V to 36 V at a particular time, and it is shown that the output voltagev0 is tracking the new reference of 36 V, as shown in Figure 12. Furthermore, it can be seen that the reference voltage has been restored to 48 V, and the controller tracks the output voltage in line with the reference voltage of 48 V.Figure 12
Hardware results when the reference voltage is varied from 48 V to 36 V and vice versa.The converter can work in both modes, making it easier to charge or discharge the battery depending on the power flow.


### 4.2.2. Boost Mode (Discharging Mode)

The battery begins discharging through the converter in boost mode, which supplies the deficit power to keep the power balance and output voltage stable. The initial load requirement is 5.2 A, as illustrated in Figure13, with the PV source contributing 4.17 A. The converter supplies 1.03 A of the remaining current (stepping down the battery current from 4.16 A). As load demand increases, the battery supplies even more current while keeping the load voltage at 48 V.Figure 13
Hardware results when the load current was varied from 5.208 to 6.25 V and vice versa (boost mode).


### 4.2.3. Buck Mode (Charging Mode)

The battery begins charging through the converter in buck mode, absorbing excess power to keep the power balance and output voltage stable. Initially, the load current is 4.17 A, which the PV can handle perfectly. As a result, the battery stays uncharged, and no current is delivered or absorbed. As the load demand decreases, the battery absorbs the excess current to charge itself, as seen in Figure14.Figure 14
Hardware results when the load current is varied from 4.17 A to 2.08 A and vice versa (buck mode).


## 4.2.1. Reference Change

The reference voltage is varied from 48 V to 36 V at a particular time, and it is shown that the output voltagev0 is tracking the new reference of 36 V, as shown in Figure 12. Furthermore, it can be seen that the reference voltage has been restored to 48 V, and the controller tracks the output voltage in line with the reference voltage of 48 V.Figure 12
Hardware results when the reference voltage is varied from 48 V to 36 V and vice versa.The converter can work in both modes, making it easier to charge or discharge the battery depending on the power flow.


## 4.2.2. Boost Mode (Discharging Mode)

The battery begins discharging through the converter in boost mode, which supplies the deficit power to keep the power balance and output voltage stable. The initial load requirement is 5.2 A, as illustrated in Figure13, with the PV source contributing 4.17 A. The converter supplies 1.03 A of the remaining current (stepping down the battery current from 4.16 A). As load demand increases, the battery supplies even more current while keeping the load voltage at 48 V.Figure 13
Hardware results when the load current was varied from 5.208 to 6.25 V and vice versa (boost mode).


## 4.2.3. Buck Mode (Charging Mode)

The battery begins charging through the converter in buck mode, absorbing excess power to keep the power balance and output voltage stable. Initially, the load current is 4.17 A, which the PV can handle perfectly. As a result, the battery stays uncharged, and no current is delivered or absorbed. As the load demand decreases, the battery absorbs the excess current to charge itself, as seen in Figure14.Figure 14
Hardware results when the load current is varied from 4.17 A to 2.08 A and vice versa (buck mode).


## 5. Comparison Analysis with Different Controllers

To analyze the performance quality of the proposed FF-DISMC controller, the transient and steady-state responses of system were observed with different controllers in terms of time-domain specifications (rise time, percentage undershoot, and settling time).To examine the converter with PI controller (voltage mode control), the duty cycle to output voltage transfer function is derived from small-signal analysis around the steady-state operating point. It is observed that the unity feedback closed-loop system with that transfer function is unstable. Hence, a PI controllerGvms is designed. To tune the parameters of the PI controller, the stability boundary locus method [36] is used with a specified phase margin of 60°.(42)Gvms=6.93795+300.33s.To analyze the BQZSDC with dual-loop PI controller (current mode controller), the two essential transfer functions, i.e., duty cycle to the inductor current (iL1) and duty cycle to the output voltage (v0), are required. The BQZSDC’s actual output voltage in the outer loop is compared to the reference DC link voltage, and the voltage error is sent to a voltage loop PI controller. The voltage loop PI generates a reference current signal for the inner loop. The current error is given to the current loop PI controller after comparing the reference current to the actual inductor current. This current PI controller regulates the duty cycle. The controllers are tuned in such a way that the bandwidth of the current control loop is greater than the outer voltage control loop bandwidth. As a result, the dynamics of the current loop are quicker than the outer voltage loop.Because of unity feedback, the inner loop transfer function was observed as unstable. A PI controller was developed. The PI controller’s parameter is tuned using the stability boundary locus approach. The PI controllerGcs is as follows:(43)Gcs=0.23795+850.33s.To design the outer loop voltage PI controller, the voltage to current transfer function was derived from the analysis. This transfer function’s frequency response exhibits a constant gain in the low-frequency range, resulting in a substantial steady-state inaccuracy. A PI controller is designed to eliminate the steady-state error. The PI controllerGvs is as follows:(44)Gvs=0.02371+36.79s.The DISMC results were also compared to the basic integral SMC (ISMC); the number of control variables used in the ISMC and DISMC equations is the main difference. Only three control variables,x1, x2, and x3, are used in ISMC. The sliding surface equation in ISMC is as follows:(45)S=α1x1+α2x2+α3x3,where the control variables are as follows:(46)x1=iL1,x2=v0,x3=∫v0∗−v0dt.The equivalent control signal of ISMC control input obtained after analysis is as follows:(47)ueq=−k1vb−vC1+k2−v0/RL+iL2−1/rv0−vC1−vC2−v0∗−v0k1vC1+k2−iL2+1/rv0−vC1−vC2.The equivalent controller comprises a control signalvCand a ramp signal vramp.(48)vC=−k1vb−vC1+k2−v0RL+iL2−1rv0−vC1−vC2−v0∗−v0,vramp=k1vC1+k2−iL2+1rv0−vC1−vC2.By considering all sliding mode conditions, the performances of the converter with all mentioned controllers with load change in both boost and buck mode are analyzed in Figures15 and 16.Figure 15
Waveforms of the load voltage of BQZSDC with different control techniques in boost mode for load change.Figure 16
Waveforms of the load voltage of BQZSDC with different control techniques in buck mode for load change.Tables2 and 3 examine the transient response of BQZSDC with different controllers in boost and buck modes in terms of time-domain specifications.Table 2
Time-domain specifications in boost mode.
ControllerRise time (ms)% peak undershoot (%)Settling time (ms)PI controller9.714.523Dual-loop PI controller86.120Integral SMC1.2625Double-integral SMC0.87.17Table 3
Time-domain specifications in buck mode.
ControllerRise time (ms)% peak overshoot (%)Settling time (ms)PI controller9.720.845Dual-loop PI controller86.135Integral SMC1.214.529Double-integral SMC0.88.315


## 6. Conclusion

In this work, an effective control (FF-DISMC) approach has been implemented for BQZSDC. In both buck and boost modes, energy management was achieved between PV, battery, and load. The controller was examined in depth, and its performance was analyzed in both charge (buck) and discharge (boost) modes. The controller met the voltage regulation and battery current regulatory requirements. The proposed controller’s performance was also compared to that of other controllers, such as voltage mode, current mode, and single integral SMC, in terms of time-domain specifications such as rise, settling, and percentage peak overshoot. Further, the experimental validation of the proposed control technique on BQZSDC was implemented in both boost and buck modes of operation.



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*Source: 4362886-2022-08-08.xml*