Efficient Hardware-in-the-Loop and Digital Control Techniques for Power Electronics Teaching

Abstract

Power electronics is a core subject in electrical and electronics engineering at the undergraduate level. The rapid growth in the field of power electronics requires necessary changes in the curricula and practica for power electronics. The proposed next-generation power electronics teaching laboratory changes the learning paradigm for this subject and is for the first time used for teaching purposes in Pakistan. The proposed controller hardware-in-the-loop (CHIL) laboratory enabled students to design, control, and test power converters without the fear of component failure. CHIL setup allowed students to directly validate the physical controller without the need for any real power converter. This allowed students to obtain more repeatable results and perform extreme digital controller testing of power converters that are otherwise not possible on real hardware. Furthermore, students could start learning power electronics concepts with hardware from the beginning on a safe, versatile, fully interactive, and reconfigurable platform. The proposed laboratory meets the accreditation board for engineering and technology (ABET) student outcome criterion K such that students can continue with the same hardware and software toolset for graduate and research purposes. The knowledge and skills acquired during undergraduate years can help students create new solutions for power electronics systems and develop their expertise in the field of power electronics. The results obtained from the survey indicated that the majority of the students were satisfied with the laboratory setup. They also expressed appreciation over the provision of a high-level graphical language “LabVIEW” for the digital controllers compared to conventional low-level text-based languages such as VHDL, Verilog, C, or C++.

1. Introduction

Owing to an increasing interest in micro-grids, smart grids, integration of renewable energy resources into power systems, electrical vehicle technologies, motor controls, and driver applications, electrical and electronic engineers need to be proficient in the domain of power electronics. Consequently, power electronics is a vital subject in the electrical engineering domain at the undergraduate level. The relevance of the power electronics field can be observed in the fact that some universities offer dedicated undergraduate and postgraduate degrees in the domain of power electronics [1,2,3]. Although this study was more focused on universities with one or two power electronics courses, the proposed versatile platform is sufficient enough to expand degrees entirely focused on power electronics.

The teaching of power electronics is plagued by some key issues and challenges. The first and foremost problem commonly encountered is that power electronics courses often start with equation derivations, mathematical analysis, memorization, and highly theoretical lectures that fail to engage students [4]. This traditional approach discourages students from power electronics and is not beneficial. A literature review suggested that the practical knowledge conveyed during classes should not only increase motivation but also enhance the theoretical knowledge of engineering subjects. It is essential to encourage students to have practical and hands-on experience with laboratory equipment to prepare them for real-life applications.

The second most commonly encountered problem is that the laboratory experience for undergraduate students is limited in most electrical engineering universities, as it requires a high-cost and physically large hardware setup. Only 46.15% of universities in the United States offer lab-oriented courses in power electronics [5]. When compared to the United States, Pakistan and other developing countries are expected to have a much higher percentage. Although most of the universities have established power electronics laboratories, these traditional laboratories are not sufficiently equipped to prepare students for careers in power electronics and cope with 21st century teaching requirements. Moreover, owing to financial restrictions, a large number of universities rely entirely on simulation-based laboratories for teaching power electronics. The findings revealed that simulation-based laboratories alone are not effective in promoting learning in power electronics courses. Digital control circuits implemented in computer-based simulations for application of power converters are far from being considered ready for practical implementation in hardware. Hands-on laboratory practice can prepare students for industry applications and future research. Therefore, the second crucial challenge is to provide state-of-the-art power electronics laboratories to undergraduate students where they can design, control, and test power converters.

The third most commonly faced problem in the field of power electronics is the preservation of continuity between hardware and software among the undergraduate, graduate, and research levels. Unfortunately, most of the time, the hardware and software toolset crafted during undergraduate studies in power electronics are not versatile and flexible enough to be continued for graduate and research purposes [6]. An engineer needs to meet ABET student outcome K: an ability to use techniques, skills, and modern engineering tools necessary for engineering practice. Therefore, the third key challenge is to equip students with the latest hardware and software toolsets that ensure continuity for graduate and research purposes.

The fourth most commonly encountered difficulty in the domain of power electronics is the significant gap in the education of power electronics controllers in undergraduate courses. A consistently significant challenge exists for power electronics students to implement digital controllers in power converter applications [6]. Students practicing power electronics are required to have substantial knowledge of microprocessors, microcontrollers, and digital signal processors, and such knowledge is acquired with a steep learning curve. However, knowledge of such subjects may not be sufficient for implementing advanced digital controls in power converter applications owing to the low processing and computational speed of these devices. FPGAs are recommended as control applications in power electronics when low jitter and highly deterministic behaviors are required. However, students must be well versed in text-based languages such as Very High-Speed Integrated Circuit Hardware Description Language (VHDL) and Verilog to access FPGA boards for control system applications in power electronics. All these difficulties in the roadmap discourage students from exploring the world of power electronics and conducting quality research in this domain. Most of the undergraduate students with specializations in power systems do not study Verilog or VHDL to access FPGA boards for digital control applications. Therefore, the fourth crucial challenge is to facilitate students with advanced controllers like FPGA for control in power electronics applications without any prior knowledge of VHDL and Verilog.

The proposed platform met the demands of all four key challenges highlighted. Section 2 illustrates a comparison of existing research studies with previous studies. Then, Section 3 discusses the CHIL laboratory facility at our university. Thereafter, Section 4 demonstrates real-time simulation results of the case study example where a simulated load was replaced with an actual load to verify the validity of the proposed model. Section 5 then exemplifies the students’ evaluations and assessments. Finally, a conclusion is drawn in Section 6.

2. Comparison with Previous Research

Many researchers have contributed to the issue of teaching power electronics effectively in undergraduate programs. Few of them have proposed a remote laboratory for undergraduate teaching in power electronics to allow better utilization of hardware [7]. Remote laboratories can be accessed from any location at any time [8], and results can be delivered to students via the Internet [9]. Few other researchers have proposed a hands-on power electronics laboratory to enhance the students’ learning experiences. Authors from the University of Tasmania, Australia, have proposed how to design, control, and test digital signal processor-based DC-DC and DC-AC converters for photovoltaic applications. This activity improves hands-on learning related to power converters and improves project management skills [10]. Similarly, authors from Purdue University implemented DSP and microcontroller-based digital controllers to test and design power converters [11]. Other examples of similar didactic tools have been proposed such as a microcontroller-based motor drive application illustrated for power electronics and variable speed drive subjects [12,13,14]. Although these authors have contributed significantly to provide hands-on experience, they have not exposed students to the latest FPGA-based digital controllers for power converters. In [15,16], a similar FPGA-based CHIL platform for power electronics research and educational purposes has been proposed. With this platform, students could successfully control and design simple power converters in a significantly less amount of time. However, a drawback to this test bench was the repetitive failure of power semiconductor switches and passive components due to the lack of proper control by new students [15,16]. Moreover, the authors realized that unsoldering failed components and building connection wires were time-consuming and frustrating. Compared to [15,16], when physical power converters are not available, the proposed CHIL setup allowed the early verification of FPGA or real-time processor-based rapid control prototyping. Power converters are virtual and simulated; thus, students could validate digital controllers without the fear of damaging power semiconductor devices or passive components. The research in this field is still ongoing to ensure that power electronics students are prepared to face challenges of the next century. Few other researchers have also tried to tackle this issue by proposing power electronics test beds for educational and research purposes [17,18,19].

We propose next-generation power electronics teaching laboratories that address all four key challenges highlighted above. The proposed controller hardware-in-the-loop (CHIL) can change the learning paradigm of power electronics. Students could start obtaining practical knowledge of the power electronics subject from the first day with a completely safe, fully interactive, and reconfigurable platform. It was possible to flip the power electronics classroom with the support of the latest trends of the CHIL setup. Teachers could make the power converter and its digital controls ready to let students interact with them first and get them quickly involved. Teachers could also discuss theoretical and mathematical concepts about a topic after seeking the attention of students and raising their interest. Finally, students were encouraged to implement digital control algorithms in an FPGA or real-time processor hardware to validate their real controllers for the virtual power converter. With this CHIL platform, students could successfully control and design power converters in lesser amounts of time. Students could continue with the same CHIL hardware and software toolset for graduate and research purposes. This reconfigurable rapid prototyping platform meets the ABET student outcome K requirement. Knowledge and skills acquired during undergraduate studies can turn the students into future experts in the fields of electric vehicle technologies, smart grids, micro-grids, motor drives, and other power electronics-related applications. Moreover, students could directly access an FPGA and real-time processor using the high-level graphical language LabVIEW. New students can implement digital control for power converters even after limited training time with LabVIEW, without any prior knowledge of text-based languages such as VHDL, Verilog, C, or C++.

There are known analogues available such as RTDS^®, OPAL-RT^®, Typhoon^®, and dSPACE^®. However, the proposed educational laboratory merges the advantages of computer simulation and hardware testing, which not only provides hardware experience for the students but also exploits the merits of software simulation. At first, students perform a software simulation to develop a digital controller in LabVIEW and its converter circuit using Multisim. By utilizing a key benefit of LabVIEW Multisim co-simulation, students validate and test the behavior of the power converter and its controller using software simulation at computer facilities. Once the power converter and its controller provide satisfactory results using software simulation, the same LabVIEW code with some minor changes can be deployed in MyRIO or CRIO and Multisim circuit can be loaded into NI PXIe for experimental measurements. Other than Multisim software, the proposed laboratory also supports MATLAB, PLECS, and PSIM software for building power converter models to directly load the circuit model in NI PXIe. Therefore, the proposed educational laboratory as shown in Figure 1 saves time and provides flexibility for effectively designing control algorithms and implementing them in FPGA for real-time (RT) model implementation. Moreover, the same laboratory setup can be continued for research purposes such as that in [20,21,22,23], where reconfigurable power quality analyzers and enhanced Modular Multilevel Converters (MMC) with reduced number of cells and harmonic content have been proposed.

3. Real-Time CHIL Laboratory Facilities

Real-time CHIL laboratories enable global visionaries to convert innovate ideas to reality. Real-time simulation as opposed to offline simulation offers a more deterministic outcome that is closer to experimental results [24,25]. To engineer-designers, real-time simulation is indispensable. CHIL laboratories enable students and researchers to design, control, and test power converters in a secure environment [26,27,28]. The CHIL platform not only offers a similarity to industrial environments but also allows students to continue graduate research on the same setup. When compared to the analog power electronics lab, the CHIL setup requires lower maintenance, time, and cost [29,30].

The company National Instruments (NI) offers reconfigurable input output (RIO) controllers such as MyRIO and Compact-RIO. Compact-RIO combines the RT operating system with an embedded floating-point processor, a remarkable FPGA performance, and hot-swappable analogue and digital input and output modules that provide quality and hardware flexibility. Each module in Compact-RIO is directly connected with the FPGA, thus realizing minimum jitter and high-speed input and output signal processing. The FPGA is physically linked to the RT processor via the PCI bus. The FPGA and RT processors are programmed in LabVIEW, which is a graphical-based programming language platform. LabVIEW has an integrated data-fetching mechanism for circulating data from the FPGA to the input and output modules and from the FPGA to the RT processor for the RT analysis, data logging, post-processing, and communication with a host computer. LabVIEW is used to allow relatively easy and fast implementation of a digital controller. However, the use of VHDL is the best option when the objective is to minimize FPGA resources and maximize the performance of FPGA.

An open electrical hardware solver (EHS) real-time simulation software developed by OPAL RT Technologies is used in CHIL laboratories. EHS is a floating-point solver that simulates an electrical circuit automatically on the NI PXIe platform without writing codes in VHDL or calculating mathematical equations [31]. EHS allows students to build power converter models using MATLAB, NI Multisim, PLECS, or PSIM and to directly load the circuit model in NI PXIe with a time step in the order of nanoseconds, as shown in Figure 2.

In this proposed laboratory setup, a physical controller is connected to a virtual plant that can be operated on a real-time simulator instead of a physical plant. In such a setup, the controller of the power converter is implemented using rapid control prototyping, which is connected to the simulated power converter via CHIL. MyRIO or Compact-RIO hardware with NI LabVIEW software is used for rapid control prototyping, and the simulated converter is designed using MATLAB, PLECS, PSIM, or NI Multisim software. This setup allowed students to directly validate the physical controller of power converters without the need for any real power converter. The CHIL setup eliminated the fear of damage to power semiconductor switches and other passive components because the converter is simulated. Students could work in a safe and secure environment, allowing for more repeatable results and extreme controller testing that are otherwise not possible on real hardware.

In summary, as shown in Figure 3, students designed and developed the circuit model on a development PC and directly load it on the NI PXIe FPGA using EHS software. The controller of power converters was designed using MyRIO or Compact-RIO using LabVIEW software. Digital and analog input and output signals were exchanged between the CRIO, MyRIO, and PXIe via physical wires. NI hardware is limited in its ability to generate voltages up to ±10 V. Therefore, a 4-quadrant power amplifier was used in the CHIL setup to test the load and amplify voltages when the need arises. The phase measurement unit (PMU) is a piece of additional equipment used by graduate students in the CHIL laboratory.

4. Demonstrative Examples with Results and Discussion

In this paper, a demonstrative example is presented to explain how students can use the CHIL laboratory facility. The demonstrative example illustrates how to use the external controller in a closed-loop configuration. Using this example, students can learn to implement closed-loop boost converter under different parametric variations.

4.1. Closed-Loop Boost Converter under Different Parametric Variations

MATLAB and SIMULINK simulation models of the boost converter were exported to FPGA, NI PXIe, with a time step of 260 ns using EHS software, as shown in Figure 4.

The external controller in a closed-loop configuration was exported to MyRIO using the LabVIEW environment, as shown in Figure 5.

A proportional-integral (PI) controller was used by students, which is a broadly used and favorable approach due to its simple design and easy control. The error value in the PI controller was calculated by the difference between the desired set point and the measured process variable. By adjusting the process of using manipulated variables, this error could be reduced in the controller. Finally, the external controller in a closed-loop configuration using MyRIO was connected to the PXIe simulated boost converter, as shown in Figure 6.

The PI controller has two parameters, namely K_p and K_i. These two terms can assume any real value, and the process of finding these values by different methods is called PI tuning. In 1942, Ziegler and Nichols presented two popular methods of tuning the P, PI, and PID controllers. The first method is the ultimate gain or closed-loop method and the second method is the process reaction curve or open-loop method [32]. The students focus on the closed-loop tuning method for PI controllers. The parameters by which the dynamic characteristics of this process are represented by the ultimate gain of a proportional controller and the ultimate period of oscillation were estimated.

4.2. Results and Discussion

To analyze and design the electrical system, both analog and digital domain designs must be considered. However, traditional platforms do not provide such facility for both domains, thus creating problems for both students and researchers. Therefore, co-simulation has become the focus of students and researchers, which provides the platform for designing in both analog and digital domains. In this study, the design of a boost converter was made with the help of the co-simulation of MATLAB and Simulink and LabVIEW, which are two distinct simulation engines. The real controller was burnt on an external controller (MyRIO), the boost converter was burnt on a PXIe, and their co-simulation was done with the help of OPAL-RT EHS software. Figure 7 shows the implementation of real-time digital controllers using MyRIO.

To grasp the practical concepts of closed-loop boost converters, students analyzed the output voltage regulation of boost converter by varying the controller gains, input voltage, reference voltage, and switching frequency using a PI controller. The parameters used for analyzing the behavior of a DC-DC boost converter are shown in

Table 1. Boost converter model parameters.

Parameter	Value
Input Voltage	100 V
Reference Voltage	125 V
Inductance	100 mH
Capacitance	400 µF
Resistive Load	25 Ω
Switching Frequency	2000 Hz

Students evaluated the digital controller at different values of PI controller gains considering the parameters, as shown in Table 1. The efficiency and speed at which a converter can reach its steady-state condition for various gain values is illustrated. The converter entered into a steady-state condition in 2.5 s at proportional and integral gains of 0.008 and 0.005, respectively, as shown in Figure 8a.

The converter entered into a steady-state at 2.24 s with a slight modification of the proportional gain value of 0.01, as shown in Figure 8b. The performance of the converter further improved at a proportional gain of 0.03 as the converter only requires 0.88 s to enter the steady-state region, as shown in Figure 8c. The performance of the converter at a proportional gain of 0.05 was further improved as it then only required 0.5 s to achieve steady-state condition, as shown in Figure 8d. Moreover, the disturbance is shown in Figure 8e in the form of a slight overshoot as the proportional gain was increased to 0.2; similarly, Figure 8f depicts the entire perturbed behavior of the converter as it had a high proportional gain of 0.3. This increased proportional gain may damage the converter and must be avoided. By performing this hands-on activity, students could learn to practically tune PI controller gains and design closed-loop controllers for the DC-DC converter. Teachers may discuss its relevant mathematical derivations in class after seeking the interest and attention of students.

Students could further practically evaluate the performance of the system by introducing variations in reference voltage, input voltage, and output load resistance. Figure 9 shows the graph in which change was introduced to the reference voltage from 125 to 150 V that triggered the controller to change the duty cycle from 0.22 to 0.35 for achieving the desired reference voltage. The robustness of the controller is verified in the graph as the load voltage attained the reference voltage within 0.3 s. Students could also observe the effect of changing the input voltage. Figure 10 shows variations in input voltage from 100 to 80 V. This change in the input voltage triggered the duty cycle to change from 0.22 to 0.37 for the converter to achieve steady-state within 0.5 s. Students can also alter output load resistance. The converter entered the steady-state within 0.3 s as the load resistance was varied from 25 to 12.5 Ω, as shown in Figure 11.

Students could also observe the effects of switching frequency on output ripple voltage. The real-time output voltage of the DC-DC boost converter using a PI controller was measured at different switching frequencies, which are shown in Figure 12. As shown in the graphs, the output voltage had ripples owing to the switching action that are inversely proportional to switching frequencies. The above results show that the output voltage ripple decreased with an increase in switching frequencies. Therefore, using higher frequencies for the pulse width modulated signal, the ripples of the output voltage signal decreased, as shown and discussed above. The percentage ripples of the output load voltage of the boost converter at different switching frequencies are compared in

Table 2. Comparison of output voltage ripple at different switching frequencies.

Switching Frequency (Hz)	Reference Voltage (V)	Percentage Ripple
500	125	4.4%
1000	125	2.16%
1500	125	1.44%
2000	125	0.96%
3500	125	0.4%
4500	125	0.32%

.

The issue of ripples must be considered in the converter while designing because it can cause unsuitable deviations in the system, especially in DC-DC converters, which are used for regulating output voltage precisely. Therefore, voltage regulator modules must have their output voltage regulated within the requirements.

In summary, students could design, control, and test the closed-loop DC-DC boost converter by varying different parameters such as controller gain, input voltage, output load resistance, reference voltage, and switching frequencies for observing the voltage regulation of a boost converter under the closed-loop system using PI controllers. The behavior of the converter was analyzed at different switching frequencies, where a minimum percentage ripple of 0.32% was obtained at 4500 Hz. Additionally, the behavior of the converter was examined under different parametric variations where the system successfully entered the steady-state condition within 0.3–0.5 s. Finally, the simulated resistive load was replaced with actual DC loads, and the efficacy of the proposed model was verified through laboratory setup of power hardware-in-the-loop system, as shown in Figure 13. Undergraduate students can discover and master any power converter in open-loop or closed-loop such as the DC-DC converter, AC-DC rectifier, DC-AC inverter, AC-AC cycloconverter, or AC voltage regulator using the versatile and open-access CHIL platform.

Despite its several advantages, the major limitations of the proposed platform is the financial cost and need for well-trained supervisors. A significantly expensive budget is required to establish this state-of-the-art laboratory in universities. However, the benefit of this platform is in the fact that after the initial cost of setup, it requires less maintenance time and expenditure compared to its analog counterpart laboratories. This current platform is very beneficial to modern engineering curricula specifically for undergraduate and graduate students. Moreover, the same setup can be used for research and in final-year capstone projects.

5. Students Evaluation and Assessment

Power electronics is a compulsory subject in electrical and electronics engineering degree at the undergraduate level. This subject is offered to sixth semester students at Sukkur IBA University. During the fall of the 2020 academic year, 26 students were enrolled in the “power electronics” course in the Electrical Engineering program at Sukkur IBA University, Pakistan. The CHIL setup can be used for laboratory education of power electronics in a systematic way. Undergraduate students can practically implement and design power converters such as the DC-DC converter, AC-DC rectifier, DC-AC inverter, AC-AC cycloconverter, or AC voltage regulator using CHIL platform. The undergraduate students mainly cover four modules, summarized in

Table 3. Possible power electronics modules with teaching objectives.

MODULE 1 DC-DC Choppers Objectives	MODULE 2 AC-DC Rectifiers Objectives	MODULE 3 DC-AC Inverters Objectives	MODULE 4 Three-Phase Multilevel Inverters
Learn different types of DC-DC converters (boost, buck, and buck-boost) and their characteristics in continuous conduction mode and discontinuous conduction mode. Understand the impact of duty cycle and switching frequency on the DC-DC Converter. Observe and understand the effect of the load type and value on the dc-dc converter. Introduce students with closed-loop control for DC-DC converters. Students design from scratch PI controllers adopted for DC-DC converters. Finally, find the suited controller parameters according to load characteristics.	Learn the principles of operation of the uncontrolled and controlled rectifier circuits. Design single-phase and three-phase uncontrolled and controlled rectifiers under different loading conditions. Observe and calculate the form factor and the ripple factor for different load scenarios. Speed control of DC shunt motor using controlled rectifiers.	Learn the principles of operation of single-phase and three-phase two-level inverter and PWM modulation technique. Observe the effect of various types of loads on the inverter output voltage and current. Observe the effect of filtering, varying PWM frequency, and dead time for the inverter output voltage and current. Implementation of gate signal generation (PWM Controller) for single- and three-phase inverter. Implementation of hysteresis closed-loop controller using MyRIO external controller.	Learn the principles of operation of three-phase multilevel inverter such as modular multilevel converter (MMC). Operate MMC in inverter and rectifier modes. Design of nearest level modulation (NLC) for MMC. Harmonic analysis of MMC.

. However, the proposed platform is editable and students can create new exercises. Students were invited to participate in a survey related to the pedagogical objectives of the CHIL laboratory. The core purpose behind this activity was to assess the students’ level of satisfaction. The instructional approach in the proposed laboratory was closely monitored. Learning statements used and students’ responses to them are given in

Table 4. Student feedback on the laboratory facility.

Statements	SD	D	N	A	SA	Mean Value
Practical knowledge delivered during class enhanced my motivation and also improved theoretical concepts of power electronics subject.	0	0	2	5	19	4.6
With this CHIL platform, we can successfully control and design power converters in significantly less amount of time.	0	0	3	7	16	4.5
Laboratory facility is versatile and flexible enough to be continued for graduate and research purposes.	0	0	2	2	22	4.7
CHIL laboratory facilitates students to implement digital controllers for power converter applications with great ease and excel in power electronics control education for undergraduate students.	0	0	0	4	22	4.8
Similar practical experiments must be created for other courses using this CHIL platform.	0	0	05	5	16	4.4
Compared to the analog power electronics laboratory, the CHIL setup not only offers a more accurate model of real industrial environments but also provides an entirely safe, fully interactive, versatile, and reconfigurable platform.	0	0	1	15	10	4.3

. Students were asked to submit a response to associated statements with one of five possible options: “strongly agree = 5,” “agree = 4,” “neutral = 3,” disagree = 2,” and “strongly disagree = 1.” Each response to a statement was converted to a numerical value and the mean (M) for all responses was calculated. The feedback from students was positive and statements were positively rated by the majority of the students. The written comments from students were encouraging. They appreciated the use of LabVIEW for rapid control prototyping as opposed to traditional languages such as VHDL, Verilog, C, or C++. Students emphasized the use of the same laboratory setup for other subjects such as specifically embedded systems, control engineering, smart grid, and other electrical engineering courses. After taking this laboratory course, a significant number of students joined the research groups working in the CHIL laboratory and decided to complete their final-year capstone project in this lab. Moreover, the CHIL laboratory also motivated students to pursue higher studies in the same university to continue their research.

6. Conclusions

Practical knowledge delivered during classes enhanced students’ motivation and improves the theoretical knowledge of power electronics. With the proposed platform, students could successfully control and design power converters in a significantly less amount of time. The laboratory facility was versatile and flexible enough to be sustained for graduate and research purposes. Undergraduate students implemented digital controllers with great ease and could excel in the education of power electronics control. The results from the survey indicate that the students may also encourage the same laboratory setup for other electrical engineering subjects. Compared to the counterpart analog power electronics laboratory, the CHIL setup required lower maintenance time, cost, and offers a more accurate model of real industrial environments. CHIL allowed elaborate experiments to be safely performed for any system without any risk involved, allowing for assessment of the system’s reaction in critical conditions and providing a versatile and fast solution. The major limitations of the proposed platform is the financial cost and need for well-trained supervisors. The demonstrative example highlighted output voltage regulations of the closed-loop DC-DC boost converter such that the performance of converter was analyzed by introducing variations in the gains of the PI controller, input voltage, reference voltage, output load resistance, and switching frequency.