Triet Nguyen-Van

Discretization of Nonautonomous Nonlinear Systems Based on Continualization of an Exact Discrete-Time Model

An innovative approach is proposed for generating discrete-time models of a class of continuous-time, nonautonomous, and nonlinear systems. By continualizing a given discrete-time system, sufficient conditions are presented for it to be an exact model of a continuous-time system for any sampling periods. This condition can be solved exactly for linear and certain nonlinear systems, in which case exact discrete-time models can be found. A new model is proposed by approximately solving this condition, which can always be found as long as a Jacobian matrix of the nonlinear system exists. As an example of the proposed method, a van der Pol oscillator driven by a forcing sinusoidal function is discretized and simulated under various conditions, which show that the proposed model tends to retain such key features as limit cycles and space-filling oscillations even for large sampling periods, and out-performs the forward difference model, which is a well-known, widely-used, and on-line computable model. [DOI: 10.1115/1.4025711]

An indirect hysteresis voltage digital control for half bridge inverters

An indirect hysteresis voltage digital control is proposed for single-phase half-bridge inverters. Because of the slow response to the switching modulation, it is difficult to control the voltage by hysteresis method directly. In this study, the output voltage is controlled indirectly by using the adaptive band hysteresis current control, which is fast response, robustness, and independent on the system parameters. The reference current is computed based on the desired reference output voltage, and the hysteresis band is controlled to maintain the switching frequency at a constant value. Simulation results show good performances of the proposed control method in both cases: ac and dc reference output voltage.

Sampled-data nonlinear control of a Lotka-Volterra system with inputs

Sampled-data control is attempted to a Lotka-Volterra type system with inputs, using a recently proposed, accurate discretization method which yields the discrete-time model in an affine-in-input form. While known exact discrete-time models are non-affine in general even for affine continuous-time nonlinear systems, the proposed discrete-time model retains the affine nature and is accurate, making the subsequent controller design simple and effective. The resulting closed-loop system under proposed sample-data control law is shown to preserve the original equilibrium states and the dynamics of the desired system. Simulations demonstrate that the proposed method has better performances, especially for large sampling periods, than the best conventional method known to the authors.

New hysteresis current band digital control for half bridge inverters

A new digital hysteresis current band control algorithm for half bridge inverters is proposed. The hysteresis current band is computed for each On-Off switching period, based on not only the measured voltage values at computing instant but also the information of the previous period. The proposed algorithm is derived by solving the optimization problem, where the switching frequency is maintained at constant and is guaranteed to be smaller than the probable maximum frequency of switching devices. Simulation results show good performances of the proposed algorithm comparing with the conventional one.

A discrete-time model of nonlinear non-autonomous systems

A discretization method is proposed for continuous-time, non-autonomous, and nonlinear systems. The concept of continualization is used to derive a sufficient condition for a given discrete-time system to be an exact discretization of a continuous-time system. The proposed discretization method is based on an approximate solution to this condition, which is computed using Peano-Baker series. As an example, an inverted pendulum subjected to high-frequency excitation is considered. Simulation results show that the proposed method has good performances even with a relatively large sampling interval.

A Discrete-Time Model for Lotka-Volterra Equations With Preserved Stability of Equilibria

A Lotka-Volterra differential equation is discretized using a method proposed recently by the same authors for nonlinear autonomous systems and the stability of equilibrium points of the resulting discrete-time model is investigated. It is shown that when Jacobian matrix of the nonlinear equation is invertible, the equilibrium points of the model are identical to those of the original continuous-time system, and their asymptotic stability and instability are retained for any sampling period. While the method can be applied to any Lotka-Volterra types, simulation results are presented for a competitive-type example, where the continuous-time system and their discrete-time models obtained by the forward-difference, Mickens’, Kahan’s, and the proposed methods are compared. They illustrate that, in general, the proposed model performs better than other discrete-time models.Copyright

LINEAR-FORM DISCRETIZATION AND ITS APPLICATION TO LEWIS OSCILLATORS

A discretization method proposed for 2nd-order nonlinear system in our previous study is modified to accommodate two design parameters in the resulting model. The nonlinear system is expressed in a linear-like form with state-dependent system matrix and includes the two design parameters, which decide how nonlinear terms are distributed among the linear terms. The resulting linearform system is then discretized in a way that would be exact if the system were indeed linear. Lewis oscillator is used as an example and discretized to show by simulations that the two design parameters affect the shape of the limit cycles and have potential for improving the accuracy of the model with improved ease than the previous method. As in the previous method, the proposed model gives better results than the forward-difference model and the non-standard model, with which limit cycles and numerical stability were found to disappear for Lewis oscillators as the sampling period increases.