[Paper Review] Model-free control of nonlinear power converters

Loïc Michel, Wim Michiels+1 more|arXiv (Cornell University)|Oct 9, 2013

Advanced DC-DC Converters9 references3 citations

TL;DR

This paper proposes a model-free control strategy for nonlinear power converters, specifically the boost converter, using intelligent PI (i-PI) controllers that do not require system model identification. The method leverages online estimation of an ultra-local model and adaptive feedback to ensure robustness and stability under large load variations and switching between continuous and discontinuous conduction modes, with simulations showing near-insensitivity to disturbances and mode transitions.

ABSTRACT

A new "model-free" control methodology is applied to a boost power converter. The properties of the boost converter allow to evaluate the performances of the model-free strategy in the case of switching nonlinear transfer functions, regarding load variations. Our approach, which utilizes "intelligent" PI controllers, does not require any converter model identification while ensuring the stability and the robustness of the controlled system. Simulation results show that, with a simple control structure, the proposed control method is almost insensitive to fluctuations and large load variations.

Motivation & Objective

• To develop a control methodology for nonlinear power converters that avoids complex system modeling and identification procedures.
• To ensure robust performance under large load variations that induce switching between continuous and discontinuous conduction modes (CCM/DCM).
• To demonstrate that a simple control structure can achieve stable voltage regulation without prior knowledge of the converter's mathematical model.
• To validate the effectiveness of the model-free approach in handling nonlinear, time-varying, and switching dynamics inherent in DC-DC power converters.

Proposed method

• The method employs an ultra-local model representation: $ y^{(n)} = F + \alpha u $, where $ F $ captures unknown system dynamics and $ \alpha $ is a tunable constant.
• An intelligent PI (i-PI) controller is implemented via the control law: $ u = -\frac{[F]}{\alpha} + \frac{y^{(n)*}}{\alpha} + \mathcal{C}(\varepsilon) $, with $ \mathcal{C}(\varepsilon) = K_p\varepsilon + K_i\int\varepsilon $.
• Online estimation of $ [F] = [y^{(n)}] - \alpha u $ is performed using finite-difference approximations of output derivatives at each sampling instant.
• The control input is updated in discrete time using the sampled-data formula: $ u_k = u_{k-1} - \frac{1}{\alpha T_c^2}\left\{ (y_{k-1} - 2y_{k-2} + y_{k-3}) - (y^{*}_{k-1} - 2y^{*}_{k-2} + y^{*}_{k-3}) \right\} + C(y^{*}_{k-1} - y_{k-1}) $, with $ T_c = 0.1 $ ms.
• The approach is applied to a state-space averaged model of the boost converter, with output voltage $ V $ as feedback and $ d_1 $ as the duty cycle input.
• Noise amplification from differentiation is mitigated using moving average filters, as suggested in prior work.

Experimental results

Research questions

• RQ1 Can a model-free control strategy achieve stable and robust voltage regulation in a boost converter without requiring an explicit mathematical model?
• RQ2 How does the model-free controller perform under large load variations that trigger transitions between continuous and discontinuous conduction modes?
• RQ3 To what extent is the control system insensitive to disturbances and nonlinear switching dynamics in the power converter?
• RQ4 What is the role of the single tunable parameter $ \alpha $ in ensuring performance across diverse operating conditions?
• RQ5 Can the i-PI controller maintain tracking accuracy and stability during transient events such as sudden load changes or mode switches?

Key findings

• The model-free control method successfully stabilizes the output voltage of the boost converter across both continuous and discontinuous conduction modes without requiring model identification.
• Simulations show that the controller maintains robust performance under large load variations—specifically, from $ R = 100\,\Omega $ to $ R = 50\,\Omega $ and vice versa—without re-tuning.
• The controller achieves near-insensitive response to load changes, with minimal overshoot and fast settling, even during mode transitions induced by the load change at $ t = 0.06 $ s.
• The system remains stable and tracks the reference voltage accurately during initial resonant transients, as demonstrated in Fig. 5 with a load change from $ 100\,\Omega $ to $ 200\,\Omega $ in DCM.
• The method achieves effective disturbance rejection and robustness despite the nonlinear, time-varying, and switching nature of the boost converter’s transfer function.
• With tuning parameters $ K_p = 2 $, $ K_i = 10 $, and $ \alpha = 30 $, the controller achieves stable regulation across all tested operating conditions without model-based adaptation.