Control of Power Converters With Hybrid Affine Models and Pulse-Width Modulated Inputs

In this paper, hybrid dynamical systems theory is applied to the analysis and control of switched converters with Pulse-Width Modulated (PWM) inputs. The system is described by a state-space model with continuous flows and discrete jumps, without averaged equations. The modulation effects are captured in full without using time-dependent signals, by enlarging the state vector to include the PWM waveform generation process. Furthermore, the sample-and-hold mechanism associated with the sampling frequency is also taken into account with this approach. A control law is proposed based on a Lyapunov function candidate. Furthermore, convergence sets and the steady state jitter, inherent to PWM-based controllers, are analyzed estimating limit sets for the augmented state. Consequently, output chattering can be bounded. By using hybrid dynamical system theory, the control designer gains a deeper understanding of the effect of modulation in the closed-loop dynamics, avoiding the problems associated with the use averaged models. Experimental results validate the proposed method.

Automated summary

This paper applies hybrid dynamical systems theory to the analysis and control of switched converters with PWM inputs, capturing modulation effects by enlarging the state vector. A control law based on Lyapunov function is proposed, and steady state jitter is analyzed to limit output chattering. The approach provides a deeper understanding of modulation effects in closed-loop dynamics, avoiding issues associated with averaged models, with experimental validation of the method.