Robust ℋ ₂ control applied to boost converters: design, experimental validation and performance analysis

Abstract

This study proposes a design procedure and experimental validation for a robust H 2 state feedback controller applied to a DC-DC boost converter modelled as a linear system affected by time-varying parameters lying in known intervals. The parameters considered as time-varying are the input voltage, the load resistance and the operating point duty cycle. A polytopic representation of the system is derived and the controller is designed by means of a convex optimisation problem based on linear matrix inequalities. The conventional H 2 controller is extended to cope with alpha-stability and robust linear quadratic regulator design, providing different strategies to trade-off the magnitude of the control gains and the response of the closed-loop system. Tight correspondences between numerical simulations and the experimental results prove the viability of the application of this technique for this kind of plant. Finally, a robust performance analysis illustrates the capacity of the closed-loop system to reject energy bounded disturbances, with interpretation for the cases of time-varying and time-invariant parameters.

Robust discrete linear quadratic control applied to grid-connected converters with LCL filters

“…which is equivalent to (13) with N = 0, as follows from [10]. An important remark concerning the synthesized robust gain given in (18) is that the closed-loop systems is robustly stable for grid inductance variations, as will be shown in the next section.…”

“…It is known that LQRs can ensure good stability margins and allow to tradeoff performance and energy of control signal by means of proper choice of matrices in the LQR cost function. The problem of synthesizing LQRs that have robustness against parametric uncertainties was addressed in the context of power electronics applications in [10], [11], [12]. The LQR optimizes a function that represents the energy of the state variables and of the control signal simultaneously, and the controller that ensures this optimization is a state feedback controller.…”

A LQR Design With Rejection of Disturbances and Robustness to Load Variations Applied to a Buck Converter

“…To ensure that the converter output voltage tracks a constant reference, with zero steady state error, it is necessary to include an integral action of the system error. The integral of the error can be included in the system model by means of an additional state variable x , as in [15], [30], leading to the representationq…”

“…For the implementation of the control circuit of Figure 6, the following values for resistors and capacitor can be used: R 1 = R 3 = R f 1 = R f 2 = 47 kW and C 1 = 47 µF. The values of the other resistors are obtained from (15).…”

“…The robust control of buck converters was addressed, for instance, in [11]- [13]. Linear matrix inequalities (LMIs) are interesting to deal with the design of controllers robust to parametric uncertainties and disturbances, as in [14], [15], where polytopic models of the plant were used to describe parametric uncertainties and LMIs were used to determine the gains of robust LQR controllers. LMIs were also used in [16]- [18] to provide robust controllers for boost converters.…”