⚡ electrical engineering

Robust Fractional-Order PID Control of a High-Frequency Aerospace DC–DC Converter under Parametric and Bus Disturbances

This paper presents a robust fractional-order PID controller design for a high-frequency aerospace DC–DC converter that, while not universally minimizing all disturbance peaks, offers superior nominal performance with zero overshoot, faster settling, and reduced high-frequency gain compared to an equivalent integer-order PID under significant parametric and bus disturbances.

Original authors: Taylan Demi̇r, Atakan Koçyiğit

Published 2026-09-23

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CC BY 4.0

Original authors: Taylan Demi̇r, Atakan Koçyiğit

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Modern aircraft are undergoing a quiet revolution. The heavy, complex systems of hydraulics and pneumatics that once powered flight controls and landing gear are being replaced by sleek, efficient electrical networks. This shift, known as the "more-electric aircraft" concept, demands a power grid that is lighter, more reliable, and capable of handling massive amounts of energy. At the heart of this system is a critical challenge: taking a high-voltage electrical supply, typically around 270 volts, and stepping it down to a safe, steady 28 volts to run sensitive avionics and mission equipment. This task is performed by a device called a DC–DC converter. While the goal sounds simple, the reality is fraught with difficulty. The electrical environment inside an aircraft is chaotic; the main power source fluctuates, the demand from engines and sensors changes in the blink of an eye, and the physical components that make up the converter can vary slightly from their ideal specifications due to manufacturing tolerances or temperature changes. If the converter cannot react instantly and precisely to these shifts, the voltage can spike or dip, potentially damaging expensive equipment or causing a system failure.

To solve this, engineers use a control system that acts like a thermostat for electricity, constantly adjusting the flow to keep the output steady. For decades, the standard tool for this job has been a specific type of controller known as a PID. Think of this controller as a driver who uses three distinct actions to keep a car on a straight road: a proportional push to correct the current error, an integral memory to fix any long-term drift, and a derivative look-ahead to anticipate future turns. However, in the extreme environment of aerospace, where components are pushed to their limits and space is at a premium, the standard "integer" version of this controller sometimes struggles to balance speed with stability. A team of researchers from Ankara University and Atılım University recently explored whether a more flexible version of this controller, known as a fractional-order PID, could offer a better solution for these high-frequency aerospace converters.

The researchers focused on a specific type of converter used to bridge the gap between the aircraft's main 270-volt bus and the 28-volt systems that power the plane's computers. They built a detailed computer model of this converter, one that included the messy realities of the real world: the resistance in the wires, the fluctuations in the input power, and the sudden surges in electrical load. Instead of testing their controller on just one perfect, ideal machine, they tested it against a vast range of possibilities. They simulated 32 extreme combinations of component variations and 500 random scenarios in between, ensuring that their design would hold up whether the components were at the very edge of their manufacturing limits or somewhere in the middle. They then compared their new fractional-order controller against a traditional PID controller, giving both the same uncertain conditions to handle.

The results of this simulation revealed a nuanced trade-off rather than a simple victory. The new fractional-order controller, which allows for more subtle adjustments than its traditional counterpart, performed exceptionally well when the system was running under normal, steady conditions. It brought the voltage to its target with almost no overshoot, meaning it didn't swing past the desired level before settling, and it reached that stable state slightly faster than the traditional controller. Crucially, it also required less aggressive action at the very high speeds where the converter switches on and off—500,000 times per second. This is a significant advantage because high-frequency switching can generate electrical noise that interferes with sensitive instruments; a controller that acts more gently at these frequencies helps keep the system clean and quiet.

However, the story changes slightly when the system is hit with a sudden shock. When the researchers simulated a sudden jump in the input power or a sharp increase in the electrical load, the traditional controller actually held the line slightly better at the very first moment, producing a smaller initial spike in voltage error. The fractional-order controller, while recovering to a stable state more quickly, allowed for a slightly larger initial deviation. This finding is important because it challenges the idea that newer, more complex mathematical tools are always superior in every situation. The fractional controller did not minimize every single error metric; instead, it offered a different set of strengths. It excelled at smooth, precise tracking and reducing high-frequency noise, while the traditional controller was slightly better at dampening the immediate impact of a sudden disturbance.

The study concludes that the fractional-order approach is a powerful tool, but it is not a magic bullet that solves every problem automatically. The researchers found that the extra flexibility of the fractional controller was most useful when it was tuned to make only moderate adjustments to the standard design, rather than pushing for extreme mathematical complexity. The real value lies in the ability to shape the system's response more finely, trading a tiny bit of initial shock resistance for faster recovery and cleaner operation at high speeds. While these results are currently limited to computer simulations and have not yet been tested on physical hardware in an aircraft, they provide a clear roadmap for the next stage of development. The path forward involves building physical prototypes using advanced wide-bandgap semiconductor devices, which can handle these high frequencies more efficiently, and testing the controllers in real-world conditions to see if the theoretical benefits translate into tangible improvements in aircraft reliability and performance.

Technical Summary: Robust Fractional-Order PID Control of a High-Frequency Aerospace DC–DC Converter

Problem Statement
Modern aerospace electrical architectures are transitioning toward high-voltage DC distribution (e.g., 270 V) to reduce feeder current and wiring mass, while avionic loads typically require a stable 28 V bus. This transition places stringent demands on DC–DC converters, which must operate under large bus-voltage ratios, rapid load changes, and tight stability margins. The integration of wide-bandgap (WBG) devices enables higher switching frequencies (e.g., 500 kHz), but this introduces challenges regarding controller noise amplification, sensor bandwidth limitations, and electromagnetic compatibility (EMI). Furthermore, the aircraft power bus is subject to significant parametric variations (input voltage, inductance, capacitance, load, and parasitic resistance) and disturbances (line and load steps). A controller tuned only for a nominal operating point often lacks the robustness required when these parameters deviate, leading to potential instability or poor dynamic performance.

Methodology
The paper proposes a robust Fractional-Order Proportional–Integral–Derivative (FOPID) controller for a high-frequency synchronous buck converter (270 V to 28 V, 800 W). The study employs the following methodological framework:

System Modeling: An averaged continuous-time model of the synchronous buck converter is developed, incorporating inductor copper loss, line perturbations, and load-current disturbances. The model is linearized around a nominal equilibrium point.
Controller Structure: The FOPID controller is defined as $C_{FO}(s) = K_p + K_i s^{-\lambda} + K_d s^{\mu}$ , where the fractional orders $\lambda$ and $\mu$ serve as additional design parameters to shape the loop phase and gain. For time-domain simulation, these fractional operators are realized using a fourth-order Oustaloup recursive filter over a frequency range of $10^{-1}$ to $10^7$ rad/s.
Uncertainty Quantification: Robustness is evaluated against a bounded uncertainty set covering:
- Input voltage: 230–300 V
- Inductance and Capacitance: $\pm 20\%$
- Load resistance: $0.65R_0$ to $1.35R_0$
- Parasitic resistance: $0.5r_{L0}$ to $1.5r_{L0}$
  The analysis includes all 32 interval corners of this five-parameter hyperrectangle and 500 randomly sampled interior points (using a fixed random seed).
Synthesis and Validation: Both a conventional integer-order PID and the FOPID are synthesized directly in the frequency domain to satisfy robust stability criteria. The primary validation metric is a sampled multiplicative-uncertainty envelope test (small-gain condition), ensuring that the product of the uncertainty envelope and the complementary sensitivity function remains below unity across the test set.

Key Contributions

Explicit Uncertainty Design: Unlike studies focusing solely on nominal performance, this controller is designed against a physically explicit uncertainty set, ensuring stability across the entire defined parameter range.
Direct Comparison: The paper provides a rigorous, apples-to-apples comparison between an integer-order PID and an FOPID using the same plant model, disturbance channels, and uncertainty descriptions.
Comprehensive Robustness Analysis: The study moves beyond corner-case analysis by incorporating 500 interior samples and constructing a finite-frequency multiplicative-uncertainty envelope to verify the small-gain condition for 532 distinct plant instances.
High-Frequency Implementation Metrics: The analysis explicitly monitors controller gain at the switching frequency (500 kHz), recognizing that high gain in this region exacerbates sensor noise amplification and EMI issues.

Results
The comparative analysis yields a nuanced picture of performance trade-offs rather than a universal superiority of one controller over the other:

Robust Stability: Both the PID and FOPID controllers satisfy the sampled small-gain test for all 532 tested plants. The maximum values of the uncertainty product $W_m |T_0|$ were 0.8965 for the PID and 0.9541 for the FOPID, both remaining below the stability boundary of 1.
Nominal Tracking: The FOPID achieves essentially zero nominal overshoot (< 0.1%) compared to 2.08% for the PID. It also demonstrates a slightly faster rise time (0.370 ms vs. 0.408 ms) and settling time (0.915 ms vs. 0.934 ms).
Disturbance Rejection:
- Line Disturbance (+30 V step): The FOPID exhibits a slightly larger initial peak deviation (2.83 V vs. 2.80 V) but recovers to the $\pm 0.28$ V band faster (0.84 ms vs. 0.90 ms).
- Load Disturbance (+5 A step): Similarly, the FOPID shows a marginally higher initial peak (1.05 V vs. 0.99 V) but achieves faster recovery (0.63 ms vs. 0.68 ms).
High-Frequency Behavior: The FOPID provides a significant advantage in high-frequency attenuation, with a controller gain at the switching frequency that is approximately 4.0 dB lower than the PID (−9.28 dB vs. −5.26 dB). This suggests reduced amplification of switching ripple and sensor noise.
Optimal Parameters: The optimized fractional orders were found to be $\lambda \approx 0.95$ and $\mu \approx 0.90$ . The study notes that these values are close to, but meaningfully distinct from, unity, indicating that moderate fractional orders are sufficient to reshape phase and slope without requiring extreme non-integer values.

Significance and Claims
The paper concludes that the additional degrees of freedom provided by fractional-order control offer practical benefits in specific areas—namely, eliminating nominal overshoot, improving recovery times after disturbances, and reducing high-frequency controller gain—without claiming universal superiority. The FOPID does not minimize every error metric; specifically, it trades a slightly larger initial peak deviation for faster recovery.

The authors emphasize that the study is a conservative interpretation of numerical results based on averaged models and rational fractional realizations. They explicitly state that these results do not constitute aircraft qualification, hardware-in-the-loop validation, or electromagnetic compliance certification. The significance lies in identifying where fractional control provides value (robustness and high-frequency attenuation) and demonstrating that the design must balance transient speed against robustness constraints imposed by parametric uncertainty. Future work is identified as necessary to transition from averaged simulations to switching models with discrete-time implementation, sensor noise, and hardware validation on wide-bandgap prototypes.

Technical Summary: Robust Fractional-Order PID Control of a High-Frequency Aerospace DC–DC Converter

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