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Linear matrix inequality based Type-III compensator synthesis for DC-DC converters

Rıdvan Keskin, Ibrahim Aliskan

TL;DR

The paper tackles disturbance rejection for non-minimum phase DC-DC converters with mismatched disturbances by jointly synthesizing a fixed-order Type-III compensator and a disturbance observer (DOB) within a robust $H_\infty$ framework. It reformulates the design as a sequence of LMIs via a convex-concave procedure, introducing parameter vectors for the compensator and the DOB filter and solving with frequency-domain weighting. The approach is validated through simulations and DSP-based experiments on a 200 W multi-phase interleaved boost converter, showing improved tracking, disturbance rejection, and robustness compared to a traditional K-factor design. The results demonstrate that the proposed convex optimization method yields practically implementable fixed-order controllers that maintain tight voltage regulation under input and load disturbances and parameter variations, with close alignment between simulation and real-time measurements.

Abstract

Boost, buck-boost, and fly-back DC-DC converters which are utilized in power lines of any electric vehicles, solar energy, and power factor correction applications require control systems to regulate the output voltage under mismatched disturbances i.e. load current and input voltage. In continuous current mode operation, the converters, however, are bandwidth-limited control systems due to their non-minimum phase nature. Disturbance rejection performance of such bandwidth-limited control system is an open problem especially where input voltage and load current disturbances cannot be measured. A third-order integral-lead (Type-III) compensator with a disturbance observer (DOB) can suppress the disturbances and unmodeled dynamics of the converters. However, synthesizing such a fixed-order control system under performance constraints is generally challenging. This paper proposes a simultaneous design of a Type-III compensator and a fixed order DOB based on Hinf control approach using convex optimization. The optimization problem is formulated in a convex-concave procedure by including the estimated disturbance and sensor noise functions. We proposed a two-stage iterative algorithm to solve the problem in a convex optimization framework. Convex programming can therefore be used to synthesize an optimal fixed-order control system by removing the non-convex constraints on the parameter space. The approach leads to an easily resolvable control algorithm with linear matrix inequality constraints over parameterized controller parameters due to the convexity of the problem. The proposed control system is implemented on a 200W DC-DC multi-phase interleaved boost converter prototype using a TMS320F28335 digital signal processor. The performance of the approach is compared with the well-known K-factor design approach for the Type-III compensators.

Linear matrix inequality based Type-III compensator synthesis for DC-DC converters

TL;DR

The paper tackles disturbance rejection for non-minimum phase DC-DC converters with mismatched disturbances by jointly synthesizing a fixed-order Type-III compensator and a disturbance observer (DOB) within a robust framework. It reformulates the design as a sequence of LMIs via a convex-concave procedure, introducing parameter vectors for the compensator and the DOB filter and solving with frequency-domain weighting. The approach is validated through simulations and DSP-based experiments on a 200 W multi-phase interleaved boost converter, showing improved tracking, disturbance rejection, and robustness compared to a traditional K-factor design. The results demonstrate that the proposed convex optimization method yields practically implementable fixed-order controllers that maintain tight voltage regulation under input and load disturbances and parameter variations, with close alignment between simulation and real-time measurements.

Abstract

Boost, buck-boost, and fly-back DC-DC converters which are utilized in power lines of any electric vehicles, solar energy, and power factor correction applications require control systems to regulate the output voltage under mismatched disturbances i.e. load current and input voltage. In continuous current mode operation, the converters, however, are bandwidth-limited control systems due to their non-minimum phase nature. Disturbance rejection performance of such bandwidth-limited control system is an open problem especially where input voltage and load current disturbances cannot be measured. A third-order integral-lead (Type-III) compensator with a disturbance observer (DOB) can suppress the disturbances and unmodeled dynamics of the converters. However, synthesizing such a fixed-order control system under performance constraints is generally challenging. This paper proposes a simultaneous design of a Type-III compensator and a fixed order DOB based on Hinf control approach using convex optimization. The optimization problem is formulated in a convex-concave procedure by including the estimated disturbance and sensor noise functions. We proposed a two-stage iterative algorithm to solve the problem in a convex optimization framework. Convex programming can therefore be used to synthesize an optimal fixed-order control system by removing the non-convex constraints on the parameter space. The approach leads to an easily resolvable control algorithm with linear matrix inequality constraints over parameterized controller parameters due to the convexity of the problem. The proposed control system is implemented on a 200W DC-DC multi-phase interleaved boost converter prototype using a TMS320F28335 digital signal processor. The performance of the approach is compared with the well-known K-factor design approach for the Type-III compensators.
Paper Structure (10 sections, 41 equations, 15 figures, 2 tables)

This paper contains 10 sections, 41 equations, 15 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Low-frequency multi-variable models of the converter
  3. The convex optimization problem structure
  4. The formulation of feedback loop constraints
  5. The derivation of DOB constraints
  6. The derivation of general loop constraints
  7. K-factor method
  8. Implementation stage
  9. Simulation results of the converter
  10. Experimental results

Figures (15)

  • Figure 1: The power network of the interleaved boost converter for the duty cycle greater than $0.5$
  • Figure 2: The time domain responses of the output voltage and PRBS signal
  • Figure 3: The frequency responses of the mathematical and estimated transfer functions
  • Figure 4: The conventional feedback and DOB control systems for the output disturbances
  • Figure 5: Re-structured control scheme for robust $H_\infty$ Type-III feedback compensator and DOB design problem
  • ...and 10 more figures