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A New Partial State-Feedback IDA-PBC for Two-Dimensional Nonlinear Systems: Application to Power Converters with Experimental Results

Rafael Cisneros, Leyan Fang, Wei He, Romeo Ortega

TL;DR

This work introduces a PDE-free, Poincaré's Lemma-based variant of IDA-PBC for globally stabilizing two-dimensional nonlinear systems using output feedback, replacing the challenging matching PDE with an ordinary differential equation. It applies the method to Buck, Boost, and Buck–Boost DC–DC converters, deriving explicit voltage-feedback controllers and assignable equilibrium sets under general load models described by a static current–voltage relation. An adaptive extension handles a parallel resistor plus constant-power load by online identification of load parameters via a finite-convergence-time least-squares estimator, enabling robust regulation under varying loads. The approach is validated through extensive simulations and experimental tests, demonstrating stable regulation, reasonable domain of attraction estimates, and robustness to load variations, with potential impact on practical converter control where only output voltage is measured.

Abstract

In this paper we propose a variation of the widely popular Interconnection-and-Damping-Assigment Passivity-Based Control (IDA-PBC) based on Poincare's Lemma to design output feedback globally stabilizing controllers for two dimensional systems. The procedure is constructive and, in comparison with the classical IDA-PBC, whose application is often stymied by the need to solve the (infamous) matching partial differential equation (PDE), in this new method the PDE is replaced by an ordinary differential equation, whose solution is far simpler. The procedure is then applied for the design of voltage-feedback controllers for the three most typical DC-to-DC power converter topologies: the Buck, Boost and Buck-Boost. It is assumed that these converters feed an uncertain load, which is characterized by a static relation between its voltage and current. In the case when the load consists of the parallel connection of a resistive term and a constant power load we propose an adaptive version of the design, adding an identification scheme for the load parameters. This allows the controller to regulate the converter output when the load varies-that is a typical scenario in these applications. Extensive numerical simulations and experimental results validate the approach.

A New Partial State-Feedback IDA-PBC for Two-Dimensional Nonlinear Systems: Application to Power Converters with Experimental Results

TL;DR

This work introduces a PDE-free, Poincaré's Lemma-based variant of IDA-PBC for globally stabilizing two-dimensional nonlinear systems using output feedback, replacing the challenging matching PDE with an ordinary differential equation. It applies the method to Buck, Boost, and Buck–Boost DC–DC converters, deriving explicit voltage-feedback controllers and assignable equilibrium sets under general load models described by a static current–voltage relation. An adaptive extension handles a parallel resistor plus constant-power load by online identification of load parameters via a finite-convergence-time least-squares estimator, enabling robust regulation under varying loads. The approach is validated through extensive simulations and experimental tests, demonstrating stable regulation, reasonable domain of attraction estimates, and robustness to load variations, with potential impact on practical converter control where only output voltage is measured.

Abstract

In this paper we propose a variation of the widely popular Interconnection-and-Damping-Assigment Passivity-Based Control (IDA-PBC) based on Poincare's Lemma to design output feedback globally stabilizing controllers for two dimensional systems. The procedure is constructive and, in comparison with the classical IDA-PBC, whose application is often stymied by the need to solve the (infamous) matching partial differential equation (PDE), in this new method the PDE is replaced by an ordinary differential equation, whose solution is far simpler. The procedure is then applied for the design of voltage-feedback controllers for the three most typical DC-to-DC power converter topologies: the Buck, Boost and Buck-Boost. It is assumed that these converters feed an uncertain load, which is characterized by a static relation between its voltage and current. In the case when the load consists of the parallel connection of a resistive term and a constant power load we propose an adaptive version of the design, adding an identification scheme for the load parameters. This allows the controller to regulate the converter output when the load varies-that is a typical scenario in these applications. Extensive numerical simulations and experimental results validate the approach.

Paper Structure

This paper contains 26 sections, 5 theorems, 79 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction and Background on IDA-PBC
  2. Proposed Poincare's Lemma-Based IDA-PBC
  3. Three DC-to-DC Power Converters
  4. Dynamic models of the converters
  5. A particular representation of the load
  6. Normalized models of the converters
  7. Assignable equilibrium set
  8. Control Design of the Power Converters
  9. Buck Converter
  10. Proposed controller
  11. Numerical estimation of the region of attraction
  12. The Boost and Buck-Boost converters
  13. Proposed controller
  14. Numerical estimation of the region of attraction: Buck-Boost converter
  15. Indirect Adaptive Control for Load \ref{['ym']}
  16. ...and 11 more sections

Key Result

Proposition 1

Consider the two-dimensional nonlinear system with $x(t) \in \mathds{R}^2$, $u(t) \in \mathds{R}$, $y(t) \in \mathds{R}$ and a desired assignable equilibrium point $x^\star \in \mathds{R}^2$. Assume there exist mappings such that the following conditions hold true. $\hat{\alpha}_1(x) \hat{\alpha}_2(x) + \hat{\beta}^2(x) \neq 0$. $\hat{\alpha}_1(x) \leq 0,\;\hat{\alpha}_2(x) \leq 0$, The scalar

Figures (15)

  • Figure 1: The Buck, Boost and Buck-Boost converters---the signal $s\in\{0,1\}$ opens or closes the converter switch.
  • Figure 2: The converter load for the Lyapunov function derivation
  • Figure 3: Phase plot of the Buck converter with zoomed-in view
  • Figure 4: Phase plot of the Buck-Boost converter with zoomed-in view
  • Figure 5: The states and control input of the Buck converter.
  • ...and 10 more figures

Theorems & Definitions (16)

  • Proposition 1
  • proof
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Proposition 2
  • proof
  • Remark 6
  • ...and 6 more