Stability-Oriented Prediction Horizons Design of Generalized Predictive Control for DC/DC Boost Converter

TL;DR

This paper addresses the stability-sensitive problem of selecting a prediction horizon for generalized predictive control (GPC) in a DC-DC boost converter. It develops a closed-loop model of the GPC-controlled system and analyzes the discrete-time transfer function $\frac{V_o(k+1)}{\omega(k)}=\frac{N(z)}{D(z)}$ to establish a stability boundary for the prediction horizon $P$, showing how the minimum $P$ depends on operating conditions and the weight $\lambda$ in the cost $J(P,N_u)$. The method is validated experimentally on a 50–70 V boost converter, finding $P=13$ as the nominal minimum and $P=16$ under load and reference variations, with horizons above the boundary offering robustness at the cost of modest increases in computation (10–20%). The study provides a simple, first-principles design guideline for horizon selection in GPC and can be extended to tune other parameters such as the receding horizon $N_u$ and weights.

Abstract

This paper introduces a novel approach in designing prediction horizons on a generalized predictive control for a DC/DC boost converter. This method involves constructing a closed-loop system model and assessing the impact of different prediction horizons on system stability. In contrast to conventional design approaches that often rely on empirical prediction horizon selection or incorporate non-linear observers, the proposed method establishes a rigorous boundary for the prediction horizon to ensure system stability. This approach facilitates the selection of an appropriate prediction horizon while avoiding excessively short horizons that can lead to instability and preventing the adoption of unnecessarily long horizons that would burden the controller with high computational demands. Finally, the accuracy of the design method has been confirmed through experimental testing. Moreover, it has been demonstrated that the prediction horizon determined by this method reduces the computational burden by 10\%-20\% compared to the empirically selected prediction horizon.

Figures (12)

• Figure 1: Diagram of the DC/DC boost converter.
• Figure 2: Closed-loop diagram of the GPC-controlled boost converter.
• Figure 3: Poles of the GPC-controlled system with different control parameters. (a) Poles with different prediction horizons P and with a weighting factor $\lambda=10$. (b) Poles with different weighting factors $\lambda$ and with the prediction horizon $P=13$.
• Figure 4: Poles of the GPC-controlled system with different system parameters with the prediction horizons $P=13$ and the weighting factor $\lambda=10$. (a) Poles with different loads from 40-70 $\Omega$. (b) Poles with different output voltage references from 60-90 V.
• Figure 5: Poles of the GPC-controlled system with $R=70 \Omega$ and $V_{oref} = 90 V$ and P varies from 13 to 17.