Using a hybrid systems approach, we address the practical stabilization of operating points for switched affine systems, ensuring a minimum dwell time and an admissible chattering around the operating point. Two different solutions are shown to induce uni-form dwell time, based on time- or space-regularization. The proposed solutions provide useful tuning knobs to separately adjust the switching frequency during transients and at the steady state. The strengths of the method are illustrated by simulating a boost converter.

The paper deals with the problem of control of switched systems described by a set of affine differential equations. Among the potential applications, the DC-DC converters constitute an important class of systems, which concentrates the interest of the control community. The paper proposes a new formulation of the problem in the context of hybrid dynamic systems, which represents an adequate way for handling the requirements of DC-DC converters, while guaranteeing theoretically and practically all specications in terms of stability and performance. In this sense, the proposed approach encompasses several methods considered in the literature. The method is illustrated for the cases of buck and boost converters. The developed results are preliminary but constitute an interesting direction for reducing the gap between theoretical results and their practical applications in power electronics.

This paper presents the analysis and design of a min-type strategy to control a synchronous boost converter in continuous conduction mode. The strategy uses a nonlinear switching surface to establish the change of topology in the converter and is analyzed by means of a sliding-mode control approach. Subsequently, the min-type strategy is modified by a hybrid control formulation, which introduces a hysteresis width and a dwell-time to obtain a finite switching frequency in the start-up and steady-state respectively. The hybrid control formulation is implemented digitally by means of a microprocessor which processes the samples of inductor current and capacitor voltage to provide the control signal that activates the power switch. Experimental results in a prototype validate the proposed control strategy and show its potential in transient time and steady-state.

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.

This paper focuses on designing a robust control law to manage the demand response of islanded microgrids composed of shifting and adjusting loads. On one side, Hybrid Dynamical System theory is suited here, because the microgrid model is composed of continuous-time dynamics (the energy stored in the battery and the adjustable loads), and discrete-time dynamics (the shifting loads). On the other side, Multi Agent System theory is used to control the adjusting loads in order to guarantee a consensus between them. Hence, non-uniform convergence of the State of Charge of the battery to a given reference is ensured. Robustness with respect to plug and play of any load and parameter variations is also ensured. Experimental results from a laboratory-scale microgrid validate the approach.