Stabilization of LTI systems with planar anti-stable dynamics using saturated linear feedback

In this paper, we first, study the stabilization of an LTI anti-stable planar system with a saturated linear state feedback. We show that the domain of attraction of such a system under any saturated linear stabilizing feedback can be obtained easily by simulating the time-reversed closed-loop system. We then show that a saturated linear state feedback can be designed for such a system so that the equilibrium of the closed-loop system has a domain of attraction that is arbitrarily close to the null controllable region. Finally we present an extension of this result to general LTI systems with planar anti-stable dynamics

Compensated Single Input Multiple Output Flyback Converter

A new single-input multiple-output (SIMO) converter is proposed in this work by incorporating flyback and buck converters in a master–slave configuration. The objective of this work is to address the cross regulation problem, achieve tight voltage regulation, improve the circuit form factor and attain a fast transient response for a SIMO flyback converter. The flyback converter maintains the output channels within 10% of their rated voltages and the SIMO buck converter is placed in series with the flyback converter such that it compensates for the output voltage deviation. Moreover, a time multiplexing switching scheme decouples output channel to eliminate the cross-regulation problem and remove the need for an additional winding transformer per each output channel. A type II compensator with a peak current mode controller was designed to achieve faster transient response which is critical for the proposed configuration. A thorough steady-state analysis was carried out on a triple output channel topology to obtain the design criteria and component values. MATLAB/Simscape modelling and simulation was used to validate the effectiveness of the proposed converter with the result yielding satisfactory transience even with load disturbance. Additionally, the result of the proposed converter is compared with previously published works

Controllability and stabilization of unstable LTI systems with input saturation

In this paper, we study the controllable region of a general unstable continuous-time LTI system with input saturation and we also study the stabilization of such a system by a saturated linear state feedback. We give simple exact descriptions of the controllable regions for certain classes of unstable systems. The study on stabilization is quite preliminary. We only deal with anti-stable planar systems. We conjecture that for such a system its asymptotic stability region (domain of attraction) under a saturated linear state feedback can be easily obtained from a stable limit cycle of its time-reversed system. We conjecture with convincing arguments that for such a system a saturated linear state feedback can be designed so that the asymptotic stability region is arbitrarily close to its controllable region

Modeling and control design for power systems driven by battery/supercapacitor hybrid energy storage devices

This paper addresses several important problems in a typical power system driven by battery/supercapacitor hybrid energy storage devices. The currents in the battery and the supercapacitor are actively controlled by two bidirectional buck-boost converters. Detailed investigation is conducted on deriving two state-space averaged models for the whole interconnected system. The control objective is to track the references of two variables. The control design problem is converted into a numerically efficient optimization problem with linear matrix inequality (LMI) constraints. When the optimization algorithm is applied to an experimental system, the resulting optimal control law is very close to a simple integrator control (with two inputs and two outputs). The simple integrator control is applied to the system in both simulation and experiment. The results confirm the effectiveness of the modeling and control design methods

Stability regions for saturated linear systems via conjugate lyapunov functions

Abstract — We use a recently developed duality theory for linear differential inclusions (LDIs) to enhance the stability analysis of systems with saturation. Based on the duality theory, the condition of stability for a LDI in terms of one Lyapunov function can be easily derived from that in terms of a Lyapunov function conjugate to the original one in the sense of convex analysis. This paper uses a particular conjugate pair, the convex hull of quadratics and the maximum of quadratics, along with their dual relationship, for the purpose of estimating the domain of attraction for systems with saturation nonlinearities. To this end, the nonlinear system is locally transformed into a LDI system with an effective approach which enables optimization on the local LDI description. The optimization problems are derived for both the convex hull and the max functions, and the domain of attraction is estimated with both the convex hull of ellipsoids and the intersection of ellipsoids. A numerical example demonstrates that the estimation of the domain of attraction by this paper’s methods drastically improve those by the earlier methods