Nonsmooth Modeling and Simulation for Switched Circuits

Reseña bibliográfica de: Vincent Acary, Olivier Bonnefon, Bernard Brogliato. (2011). Nonsmooth Modeling and Simulation for Switched Circuits. Francia: Springer. 284 pp

Addendum-Erratum to Nonsmooth Modeling and Simulation for Switched Circuits

This second version of the Addendum/Erratum corrects some typos present in the monograph

Switched networks and complementarity

A modeling framework is proposed for circuits that are subject both to externally induced switches (time events) and to state events. The framework applies to switched networks with linear and piecewise-linear elements, including diodes. We show that the linear complementarity formulation, which already has proved effective for piecewise-linear networks, can be extended in a natural way to also cover switching circuits. To achieve this, we use a generalization of the linear complementarity problem known as the cone-complementarity problem. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only first-order impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we show that within our framework, energy cannot increase as a result of a jump, and we derive a stability result from this

Decentralized formation control with connectivity maintenance and collision avoidance under limited and intermittent sensing

A decentralized switched controller is developed for dynamic agents to perform global formation configuration convergence while maintaining network connectivity and avoiding collision within agents and between stationary obstacles, using only local feedback under limited and intermittent sensing. Due to the intermittent sensing, constant position feedback may not be available for agents all the time. Intermittent sensing can also lead to a disconnected network or collisions between agents. Using a navigation function framework, a decentralized switched controller is developed to navigate the agents to the desired positions while ensuring network maintenance and collision avoidance.Comment: 8 pages, 2 figures, submitted to ACC 201

Dynamical analysis of an interleaved single inductor TITO switching regulator

We study the dynamical behavior of a single inductor two inputs two outputs (SITITO) power electronics DC-DC converter under a current mode control in a PWM interleaved scheme. This system is able to regulate two, generally one positive and one negative, voltages (outputs). The regulation of the outputs is carried out by the modulation of two time intervals within a switching cycle. The value of the regulated voltages is related to both duty cycles (inputs). The stability of the whole nonlinear system is therefore studied without any decoupling. Under certain operating conditions, the dynamical behavior of the system can be modeled by a piecewise linear (PWL)map, which is used to investigate the stability in the parameter space and to detect possible subharmonic oscillations and chaotic behavior. These results are confirmed by numerical one dimensional and two-dimensional bifurcation diagrams and some experimental measurements from a laboratory prototype.Peer ReviewedPostprint (published version

Nonsmooth pitchfork bifurcation in a dc-dc converter: coexisting attractors and intermittency

In this paper we deal with the analysis of nonlinear dynamical behavior of a single inductor two inputs two outputs (SITITO) power electronics DC-DC converter. The system can be used to regulate generally two outputs (one positive and one negative). Under certain operating conditions, the switching model can be approximated by a one dimensional piecewise constant vector field and, as a consequence, the corresponding map is piecewise linear (PWL). This model is derived and then it is used to study a nonsmooth pitchfork bifurcation in the system. Coexistence of attractors are detected by using the same model. Intermittent chaotic behavior is also addressed. Analytical results are confirmed by one dimensional and twodimensional bifurcation diagrams.Peer ReviewedPostprint (published version

Dynamics and stability issues of a single-inductor dual-switching DC-DC converter

A single-inductor two-input two-output power electronic dc–dc converter can be used to regulate two generally nonsymmetric positive and negative outputs by means of a pulsewidth modulation with a double voltage feedback. This paper studies the dynamic behavior of this system. First, the operation modes and the steady-state properties of the converter are addressed, and, then, a stability analysis that includes both the power stage and control parameters is carried out. Different bifurcations are determined from the averaged model and from the discrete-time model. The Routh–Hurwitz criterion is used to obtain the stability regions of the averaged (slow-scale) dynamics in the design parameter space, and a discrete-time approach is used to obtain more accurate results and to detect possible (fast-scale) subharmonic oscillations. Experimental measurements were taken from a system prototype to confirm the analytical results and numerical simulations. Some possible nonsmooth bifurcations due to the change in the switching patterns are also illustrated.Postprint (published version

Power System Control with an Embedded Neural Network in Hybrid System Modeling

Output limits of the power system stabilizer (PSS) can improve the system damping performance immediately following a large disturbance. Due to nonsmooth nonlinearities arising from the saturation limits, these values cannot be determined by the conventional tuning methods based on linear analysis. Only ad hoc tuning procedures can been used. A feedforward neural network (with a structure of multilayer perceptron neural network) is applied to identify the dynamics of an objective function formed by the states and, thereafter, to compute the gradients required in the nonlinear parameter optimization. Moreover, its derivative information is used to replace that obtained from the trajectory sensitivities based on the hybrid system model with the differential-algebraic-impulsive-switched structure. The optimal output limits of the PSS tuned by the proposed method are evaluated by time-domain simulation in both a single-machine infinite bus system and a multimachine power system