A robust hybrid control algorithm for a single-phase DC/AC inverter with variable input voltage

Abstract

In this paper, we analyze the properties of the vector fields associated with all possible configurations of a single-phase DC/AC inverter with the objective of designing a hybrid controller for the generation of an approximation of a sinusoidal reference signal. Using forward invariance tools for general hybrid systems, a hybrid controller is designed for the switched differential equations capturing the dynamics of the DC/AC inverter. Then, global asymptotic stability of a set of points nearby the reference trajectory, called the tracking band, is established. This property is found to be robust to small perturbations, and variation of the input voltage. Simulations illustrating the major results are included.

A hybrid predictive control algorithm for tracking in a single-phase DC/AC inverter

“…Then, we may model the system as in [4]: where V DC is the input DC voltage and R, L, C are parameters of the circuit. As mentioned in Section I, a PWM-based controller switches among some of these configurations depending on the difference between a reference carrier and a modulating signal.…”

“…This approach is inspired by the work in [4] and provides an alternative to traditional PWM-based controls. The general idea behind the proposed approach is to generate an AC voltage at the output of the inverter circuit by tracking a sinusoidal reference signal.…”

On robust forward invariance of sets for hybrid dynamical systems

“…We devote this section to present an application for the proposed forward invariance analysis tools in this work. The system of interest is a controlled single-phase DC/AC inverter; see [35] for complete design details. As shown in Fig.…”

“…Then, for every x ∈ ∂T \ L, by applying Lemma .5 and the inner product properties listed in [35,Lemma 2], we have the value of q chosen by the designed controller always results in one of the two cases below:…”

Results on invariance-based feedback control for hybrid dynamical systems

“…Relying on forward invariance results, invariance-based control design techniques are widely used tools for controller design for systems with inputs. For example, invariancebased control designs are provided in [5] for power inversion, in [6] for a genetic network, and in [7] for collision avoidance in automotive systems. While tools for the study of forward invariance and viability in hybrid systems can be found in [8], [9], [10], to the best of our knowledge, results enabling the systematic design of feedback controllers inducing forward invariance for hybrid systems are not available.…”