Source-linked AI summary
Learning Higher Order DC-DC Converter Control from Inversion
Kamakshi Tatkare, Ufuk Topcu, Brian Johnson
TL;DR
High-order converter control is difficult because nonlinear methods can require complex models while linear controls may provide limited disturbance rejection. This paper trains a neural network on trajectories generated by numerically inverting converter dynamics. The learned controllers approximate the inversion-based control action and regulate three fourth-order converters under load and input-voltage disturbances.
Problem
Fourth-order converter regulation is challenging, and existing approaches involve tradeoffs in disturbance scope, operating conditions, transient shaping, and synthesis or implementation complexity.
Source: §I · p. 1Method
The method numerically inverts converter dynamics to generate desired state-input trajectories and trains an MLP to approximate the resulting state-to-duty mapping.
Source: §I · pp. 1–2Results
Across Cuk, zeta, and SEPIC converters, learned policies closely match inversion-based duty trajectories and maintain voltage regulation with small disturbance deviations and quick recovery.
Source: B. Inference · p. 7, §VI · p. 7Takeaways & Limitations
Simulations establish the viability of inversion-supervised neural-network regulation on higher-order averaged converter models over the tested operating envelope.
Source: §VI · p. 7The reported viability is limited to higher-order averaged converter models over the tested operating envelope.
Source: §VI · p. 7
Abstract
from arXiv · showhide
Control design for high-order converters with nonlinear dynamics is generally difficult. Nonlinear controls introduce formidable model complexity whereas linear controls suffer from poor disturbance rejection. Our objective in this paper is to develop a simple neural-network-based controller that learns the control law from supervised trajectories generated by a model-based bounded inversion framework. First, we establish strong invertibility for the converter models. Next, we prescribe the desired closed-loop behavior through a trajectory model that defines the target dynamics. We then invert the converter dynamics numerically to obtain the corresponding duty-cycle and state trajectories. We use these model-based trajectories as supervision and train a neural network to approximate the resulting state-to-duty control law. The results show that the learned controllers accurately recover the inversion-based control action and achieve effective regulation under load and input-voltage disturbances. We validate the method on fourth order Cuk, SEPIC, and zeta converters.
I. INTRODUCTION
Fourth-order converters pose control-design challenges because nonlinear methods can require complex synthesis, while existing approaches involve tradeoffs in disturbance scope, transient shaping, robustness, or implementation complexity. The paper generates desired state-to-duty behavior by numerically inverting converter dynamics, then trains a neural network to approximate that mapping; it also establishes strong invertibility for the converter models.
I. INTRODUCTION
- Prior fourth-order converter controllers face tradeoffs in disturbance scope, operating conditions, transient shaping, and synthesis or implementation complexity.Examples include methods limited to load disturbances or restricted conditions, and approaches relying on auxiliary loops, chattering, real-time optimization, or Hamilton-Jacobi-type conditions.Source: §I · p. 1
- The framework numerically inverts converter dynamics to generate labeled state-input trajectories, then trains an MLP to learn the structured state-to-duty mapping without topology-specific closed-form synthesis.The learned policy approximates the duty ratio induced by model-based trajectory generation rather than searching unrestricted control policies.Source: §I · pp. 1–2
II. INVERSION
- The paper establishes strong invertibility using Hirschorn’s framework when the regulated output has finite relative order and the input-output coefficient LBc(x) is nonzero.The proposed inversion regulates input inductor current because it is minimum-phase for the averaged linearized Cuk, zeta, and SEPIC converters, whereas output voltage is nonminimum-phase.Source: §II · p. 2
A. ´Cuk Converter
For the averaged Cuk converter, the paper establishes strong invertibility on a state domain excluding zero v1 and derives an inverse input that is well-defined there.
A. ´Cuk Converter
- The averaged Cuk converter is strongly invertible on M_C = {x ∈ R^4: v1 ≠ 0}.The stated state is x = [y, v1, i2, vo]ᵀ, with output c(x) = y = iL1.Source: A. ´Cuk Converter · p. 2
- On M_C, the output has relative order α = 1 because the decoupling term LBc(x) is nonzero.The proof applies Hirschorn’s Theorem 2.Source: A. ´Cuk Converter · p. 2
- The resulting inverse input is well-defined for every state in M_C.The domain excludes states with v1 = 0.Source: A. ´Cuk Converter · p. 2
B. Zeta Converter
For the averaged zeta converter, strong invertibility holds away from the state set where v1 equals Vin, where the decoupling term vanishes.
B. Zeta Converter
- The averaged zeta converter is strongly invertible on M_Z, excluding states where v1 = Vin.The proof states this is the only loss-of-invertibility condition.Source: B. Zeta Converter · pp. 2–3
- On M_Z, the decoupling term remains nonzero and the output has relative order α = 1.Hirschorn’s Theorem 2 then guarantees strong invertibility on that domain.Source: B. Zeta Converter · p. 3
- The inverse duty ratio is obtained by solving the output-derivative relation on the domain where its denominator is nonzero.That denominator is nonzero precisely on M_Z.Source: B. Zeta Converter · p. 3
C. SEPIC Converter
For the averaged SEPIC converter, the paper establishes strong invertibility on states where v1 + vo is nonzero and derives an inverse valid throughout that domain.
C. SEPIC Converter
- The averaged SEPIC converter is strongly invertible on M_S = {x ∈ R^4: v1 + vo ≠ 0}.The stated state is x = [y, i2, v1, vo]ᵀ, with output c(x) = y = iL1.Source: C. SEPIC Converter · p. 3
- When v1 + vo ≠ 0, the decoupling term is nonzero and the output has relative order α = 1.Hirschorn’s Theorem 2 establishes strong invertibility throughout M_S.Source: C. SEPIC Converter · p. 3
- The inverse input obtained from the input-output relation is valid for every state in M_S.The stated domain excludes states where v1 + vo = 0.Source: C. SEPIC Converter · p. 3
III. CONTROL DESIGN
The control design prescribes desired transient behavior and uses inversion dynamics to generate trajectories for training a neural network to produce duty-cycle commands.
III. CONTROL DESIGN
- The section presents data generation and training for the inversion-based controller.Source: §III · p. 3
A. Response Shaping
- A fourth-order critically damped reference transfer function shapes the averaged converter output trajectory using a desired natural frequency and amplitude.It is selected to produce a smooth transient with little overshoot.Source: A. Response Shaping · p. 3
III. CONTROL DESIGN
- The inversion pipeline uses desired output and frequency settings with sampled operating conditions to generate trajectory data for training an MLP to output duty cycle.The sampled conditions include load resistance, input voltage, and initial state.Source: Figure 3 · p. 4
B. Disturbance Profiles
The design models smooth changes in operating conditions and trains a neural policy to approximate duty ratios generated by inversion from desired trajectories.
B. Disturbance Profiles
- The disturbance profile parameter κ controls transition abruptness: larger values approach a step, while smaller values yield more gradual changes over a wider interval.The varying operating-point quantities are input voltage and load resistance.Source: B. Disturbance Profiles · p. 4
C. Learning State-to-duty Policy
- For a desired output trajectory, inversion produces state and duty trajectories satisfying the converter dynamics and output relation, which supervise a neural state-parameter policy.The policy uses measured state and exogenous variables to predict duty ratio.Source: C. Learning State-to-duty Policy · p. 4
- The finite dataset contains sampled trajectories with states, exogenous inputs, and inversion-generated duty ratios, and gradient-based optimization trains the MLP on them.The trained network computes duty from measured state and exogenous variables.Source: C. Learning State-to-duty Policy · p. 4
IV. APPLICATION TO DC-DC CONVERTERS
The application covers Cuk, zeta, and SEPIC converters, with topology-specific relations used to set equilibrium and initial-condition bounds.
IV. APPLICATION TO DC-DC CONVERTERS
- Cuk, zeta, and SEPIC converters can step up or step down output voltage; Cuk inverts output polarity, while zeta and SEPIC do not.Source: §IV · p. 4
A. Bounds
- Topology-specific algebraic relations define equilibrium-point and initial-condition bounds using load resistance, input voltage, and the desired or initial output voltage.The relations also provide corresponding equilibrium and initial duty ratios.Source: A. Bounds · p. 4
B. Trajectory Planning
Trajectory planning shapes desired output and current behavior, while simulations assess duty prediction and closed-loop regulation across nominal and disturbed conditions.
B. Trajectory Planning
- The response-shaping passages specify a desired output, a common equilibrium relation, and a critically damped fourth-order step factor for constructing a smooth current reference.The current trajectory is also tied to time-varying load resistance and input voltage.Source: B. Trajectory Planning · p. 4
- The learned duty predictions closely agree with inversion-generated duties on validation trajectories for Cuk, zeta, and SEPIC converters.Figure 4 compares predicted and reference duty traces, with zoomed views below.Source: Figure 4 · p. 5
- Under constant load and input voltage, closed-loop control drives converter states to equilibrium with faster settling and reduced oscillation than open-loop operation.Source: Figure 5 · p. 5
- Table I summarizes converter-specific equilibrium and initial-condition relations.Source: Table I · p. 5
- Load steps with nominal input voltage are paired with output-voltage responses to assess regulation under load variation across the three converter topologies.The figure caption reports small deviations and rapid recovery despite abrupt load changes.Source: B. Trajectory Planning · p. 4, Figure 6 · p. 6
- Input-voltage steps with nominal load and simultaneous load and input-voltage changes are evaluated through their corresponding output-voltage responses.The captions report small deviations and rapid recovery across converter topologies under both disturbance settings.Source: B. Trajectory Planning · pp. 4, 7, Figure 7 · p. 6, Figure 8 · p. 6
A. Configuration
The section describes model-based trajectory data and MLP training, then reports close agreement with inversion-generated duty trajectories and disturbance-robust regulation across three converters.
A. Configuration
- Latin-hypercube scenarios across operating points and load and input disturbances produce (z, d) labels; a 70/30 train-validation split trains the MLP by MSE with Adam.The scenarios vary reference, initial conditions, and disturbance profiles.Source: A. Configuration · p. 7
B. Inference
- Across Cuk, zeta, and SEPIC, the MLP closely matches inversion-generated duty trajectories and maintains voltage regulation with small disturbance deviations and quick recovery.The conclusion also reports improved closed-loop regulation relative to open-loop operation.Source: B. Inference · p. 7, §VI · p. 7
VI. CONCLUSION
- Strong invertibility supports the inversion-based data-generation procedure; simulations establish viability on tested higher-order averaged models, while parasitics and formal uncertainty guarantees remain future work.The reported simulations cover Cuk, zeta, and SEPIC converters.Source: §VI · p. 7