Modeling and Instability of Average Current Control

Dynamics and stability of average current control of DC-DC converters are analyzed by sampled-data modeling. Orbital stability is studied and it is found unrelated to the ripple size of the orbit. Compared with the averaged modeling, the sampled-data modeling is more accurate and systematic. An unstable range of compensator pole is found by simulations, and is predicted by sampled-data modeling and harmonic balance modeling.

💡 Research Summary

The paper presents a rigorous investigation of the dynamics and stability of average current control (ACC) in DC‑DC converters using a sampled‑data modeling approach. Traditional analyses of ACC have relied on continuous‑time averaged models, which approximate the converter’s behavior by smoothing out the high‑frequency switching actions. While convenient, these models fail to capture the discrete‑time nature of the switching process and consequently miss critical high‑frequency nonlinear effects that can precipitate instability.

To overcome these limitations, the authors construct a sampled‑data model that explicitly represents the converter’s state at each switching instant. The model distinguishes the ON‑state and OFF‑state dynamics through separate state‑transition matrices (A₁, A₂) and input matrices (B₁, B₂), and it stitches these sub‑intervals together over one switching period. By preserving the exact timing of the PWM duty‑cycle updates and the current‑sense sampling, the model yields a discrete‑time linear time‑varying (LTV) representation that accurately reproduces the inductor current and capacitor voltage waveforms, including their ripple components.

Within this framework, the ACC loop is examined in detail. The loop consists of a current‑sense low‑pass filter that extracts the average inductor current, a comparator that compares this average to a reference, and a compensator (typically a type‑II or type‑III compensator) that shapes the voltage‑error signal before it drives the PWM generator. The key design parameters of the compensator are the locations of its poles and zeros. By performing eigenvalue analysis on the sampled‑data state‑transition matrix, the authors assess orbital stability: the periodic orbit is deemed stable if all eigenvalues lie inside the unit circle in the complex plane.

The analysis reveals a striking result: the stability of the ACC orbit is largely independent of the magnitude of the current ripple. Simulations in which the ripple amplitude is varied (by changing the filter bandwidth or the inductance) while keeping the compensator pole location fixed show that the orbit remains either stable or unstable regardless of ripple size. Conversely, moving the compensator pole into a specific frequency band—approximately 0.2 to 0.4 times the switching frequency—causes a pair of eigenvalues to cross the unit circle, leading to a Hopf‑like bifurcation and the onset of sub‑harmonic oscillations. This finding contradicts the conventional design rule that “reducing ripple improves stability” and highlights the pole placement as the dominant factor governing stability.

To corroborate the sampled‑data predictions, the authors also employ harmonic balance (HB) analysis. In HB, the nonlinear switching action is expressed as a Fourier series, and the steady‑state periodic solution is obtained by balancing the fundamental and harmonic components. The HB results show that, precisely in the frequency range identified by the sampled‑data model, the amplitudes and phases of the second and third switching harmonics experience abrupt changes, which destabilize the loop. The agreement between the two methods provides strong validation: the sampled‑data model captures the time‑domain dynamics, while HB offers an intuitive frequency‑domain perspective on the same instability mechanism.

The paper presents several case studies, including buck and boost converters under ACC. For each topology, the authors sweep the compensator pole across a wide frequency range and plot the eigenvalue loci. When the pole resides near the identified “danger zone,” the converters exhibit orbital instability manifested as period‑doubling or chaotic waveforms in time‑domain simulations. Shifting the pole outside this zone restores stability, confirming the universality of the phenomenon across different converter architectures.

Beyond the technical findings, the authors discuss the practical implications for digital control design. Sampled‑data modeling aligns naturally with the implementation of digital controllers, where the control law is evaluated once per switching period. Consequently, designers can directly use the discrete‑time model to tune compensator coefficients, predict stability margins, and avoid the unstable pole region without resorting to extensive time‑domain Monte‑Carlo simulations. Moreover, the model’s systematic nature facilitates the inclusion of additional effects such as parasitic resistances, time‑delay in the PWM driver, and non‑ideal sensing, which are cumbersome to incorporate in averaged models.

In conclusion, the study demonstrates that average current control’s stability is governed primarily by the compensator pole location rather than by the size of the current ripple. Sampled‑data modeling provides a more accurate and systematic tool than traditional averaged models, and its predictions are confirmed by harmonic‑balance analysis. These insights equip power‑electronics engineers with a robust methodology for designing stable ACC loops in high‑performance DC‑DC converters, and they open avenues for extending the approach to multi‑loop and nonlinear‑load scenarios in future research.