[Paper Review] Synchronous Multistep Predictive Spectral Control of the Switching Distortion in DC--DC Converters

Christian Korte, Till Luetje+1 more|arXiv (Cornell University)|Apr 30, 2022

Advanced DC-DC Converters4 citations

TL;DR

This paper proposes a synchronous multistep model-predictive control scheme for DC-DC converters that shapes switching distortion in real time by optimizing the output spectrum, switching frequency, and voltage ripple simultaneously. The method achieves a 48 dB reduction in the largest spectral peak compared to conventional PWM and enables real-time spectral gap insertion to suppress EMI in sensitive frequency bands.

ABSTRACT

In automotive power electronics, distortion and electromagnetic interference (EMI) generated by the switching action of power semiconductors can be a significant challenge for the design of a compact, lightweight vehicle. As semiconductor switching frequencies increase, e.g., through the introduction of new materials, such as gallium nitride and silicon carbide, this problem becomes more severe. We present a control scheme for an automotive dc-to-dc converter that reduces the EMI generated by shaping switching distortion predictively at the run time. The multistep model-predictive control scheme chooses the subsequent switching state that optimizes the output spectrum according to predefined criteria. To achieve real-time operation, it evaluates the possible switching state candidates for the next modulation step without explicitly solving a single Fourier transform. In addition, the switching rate and voltage ripple are controlled in a single unified control law. We present and experimentally validate that the control scheme can indeed run at real time already with currently available mid-range hardware. The results demonstrate that the largest spectral peak of the switching distortion can be decreased by 48 dB compared to conventional pulse-width modulation. Furthermore, spectral gaps can be implemented in the output distortion and altered in real-time, allowing certain frequency bands -- e.g., bands used by other sensitive electronics such as sensors, communication busses, or tuners -- to be kept free of EMI from the converter's switching actions.

Motivation & Objective

• To address the growing challenge of electromagnetic interference (EMI) from high-frequency switching in wide-bandgap semiconductor-based automotive DC-DC converters.
• To reduce conducted and radiated EMI without relying on bulky passive filters or shielding by shaping the spectral content of switching distortion at the source.
• To enable real-time, predictive control of the output spectrum while simultaneously regulating switching frequency and voltage ripple using a unified control law.
• To demonstrate feasibility of the control scheme on mid-range FPGA hardware with real-time performance and dynamic spectral adaptability.

Proposed method

• The control scheme uses a multistep model-predictive approach to evaluate all possible switching state candidates for the next modulation step without explicitly computing a Fourier transform.
• It employs a cost function that combines spectral shaping via a user-defined spectral filter G(ω), switching frequency minimization, and voltage ripple control using weighting parameters λ₁, λ₂, and λ₃.
• The spectral control is implemented by evaluating the discrete Fourier transform (DFT) of predicted output waveforms for each candidate switching state over a prediction horizon M.
• A real-time implementation avoids full DFT computation by leveraging precomputed DFT basis vectors and recursive updates, enabling fast spectral evaluation.
• The controller integrates a voltage regulator and a spectral controller in a two-loop structure, with the spectral controller selecting the optimal switching state based on the cost function.
• The scheme supports dynamic spectral gap insertion by adjusting G(ω) in real time, allowing suppression of EMI in specific frequency bands such as those used by radios or sensors.

Experimental results

Research questions

• RQ1 Can a predictive spectral control scheme reduce the peak spectral density of switching distortion in DC-DC converters without increasing hardware complexity?
• RQ2 How can switching frequency and output voltage ripple be jointly controlled with spectral shaping in a single predictive framework?
• RQ3 Can the control scheme achieve real-time operation on mid-range digital hardware without explicit Fourier transform computation?
• RQ4 To what extent can dynamic spectral gaps be implemented and adjusted in real time to protect sensitive electronic systems?
• RQ5 What is the achievable EMI reduction and spectral shaping performance compared to conventional PWM and spread-spectrum techniques?

Key findings

• The proposed control scheme reduces the largest spectral peak of switching distortion by 48 dB compared to conventional pulse-width modulation.
• The method enables real-time spectral gap insertion with a suppression depth of approximately 100× (40 dB) relative to surrounding frequency bands.
• The average switching frequency can be reduced by adjusting the cost function weight λ₂, with a 1.8× increase in peak-to-peak voltage ripple and a 2.7× increase in variance when switching is minimized.
• By enforcing switching every K_max steps, the voltage ripple variance can be reduced by more than a factor of 2 while increasing the average switching frequency by less than 5%.
• The control scheme successfully adapts the output spectrum in real time, demonstrated by shifting a spectral gap from 10 kHz to 23 kHz at a rate of 1.2 kHz/s with consistent suppression depth.
• The method operates in real time on mid-range FPGA hardware without explicit DFT computation, using efficient spectral evaluation techniques.