Chung-Yao Kao

Comparison of Hybrid Control Techniques for Buck and Boost DC-DC Converters

Five recent techniques from hybrid and optimal control are evaluated on two power electronics benchmark problems. The benchmarks involve a number of practically interesting operating scenarios for fixed-frequency synchronous dc-dc converters. The specifications are defined such that good performance can only be obtained if the switched and nonlinear nature of the problem is accounted for during the design phase. A nonlinear action is featured in all methods either intrinsically or as external logic. The designs are evaluated and compared on the same experimental platform. Experiments show that the proposed methods display high performances, while respecting circuit constraints, thus protecting the semiconductor devices. Moreover, the complexity of the controllers is compatible with the high-frequency requirements of the considered application.

On Stability of Discrete-Time LTI Systems With Varying Time Delays

This technical note concerns robust stability analysis of discrete-time linear-time-invariant (LTI) systems with varying time delays. The stability problem is tackled under the integral quadratic constraint (IQC) framework. The time-delay system in question is viewed as feedback interconnection of an LTI stable operator and the so-called “delay-difference” operator, for which IQC characterizations are required in order to apply IQC analysis. One of the main contributions of the technical note is to derive novel IQC characterizations for the “delay-difference” operator, based on the assumption that the time-varying delay parameter and its variation are bounded. A set of new stability criteria emerges as the result. Numerical examples are given to illustrate the effectiveness of the new stability criteria. Another distinct contribution is the idea of introducing bounds on the so-called “m-step total variation” and “m-step average variation” of the time-varying delay parameter, which is proven to be useful in stability analysis.

Robust tracking with H∞ performance for PWM systems

Control synthesis for robust tracking is considered for a class of pulse-width modulated systems that appear, for example, in power electronics applications. The control objective is to regulate a high frequency ripple signal to robustly track a constant reference signal in an average sense. To achieve this goal, a new H~ control problem with integral action and average sampling is proposed. The solution of this problem involves a hybrid lifting framework which requires a careful elaboration in order to develop an algorithm that allows one to solve the design problem by the standard state space formulas for H~ control. The design procedure is verified on a synchronous buck converter.

Robustness Analysis for Feedback Interconnections of Distributed Systems via Integral Quadratic Constraints

A framework is established for directly accommodating feedback interconnections of unstable distributed-parameter transfer functions in robust stability analysis via integral quadratic constraints (IQCs). This involves transfer function homotopies that are continuous in a ν -gap metric sense. As such, the development includes the extension of ν-gap metric concepts to an irrational setting and the study of uncertainty-set connectedness in these terms. The main IQC based robust stability result is established for constantly-proper transfer functions in the Callier-Desoer algebra; i.e. finitely many unstable poles and a constant limit at infinity. Problems of structured robust stability analysis and robust performance analysis are considered to illustrate use of the main result. Several numerical examples are also presented. These include stability analysis of an autonomous system with uncertain time-delay and a closed-loop control system, accounting for both the gain and phase characteristics of the distributed-parameter uncertainty associated with the nominal rational plant model used for controller synthesis.

On Stability of Systems With Aperiodic Sampling Devices

This technical note is concerned with stability analysis of aperiodic sampled-data systems. The stability problem is tackled from a pure discrete-time point of view, where the at-sampling behavior of the system is modelled as the response of a nominal discrete-time LTI system in feedback interconnection with a structured uncertainty. Conditions under which the uncertainty is positive real (PR) are identified. Based on the PR property, a number of integral quadratic constraints (IQC) are derived and the IQC theory is applied to derive stability conditions. Numerical examples are given to illustrate the effectiveness of the proposed approach.

Consensus of Heterogeneous LTI Agents

A robust stability criterion is derived for a class of higher order consensus algorithms. In distinction to the standard consensus problem where the dynamics of all individual agents are the same and of low dimension, the criterion for reaching consensus now depends on the full spectrum of the communication graph and not only the largest nonzero eigenvalue. The new consensus criterion is posed as a Nyquist-like criterion that provides a clear separation between the individual dynamics and the spectrum of the graph. Our results are illustrated on a formation control problem for a target encircling task.

A scalable robust stability criterion for systems with heterogeneous LTI components

A scalable robust stability criterion for networked interconnected systems with heterogeneous linear time-invariant components is presented in this paper. The criterion involves only the properties of individual components and the spectrum of the interconnection matrix, which can be verified with relatively low computational effort, and more importantly maintains scalability of the analysis. Moreover, if the components are single-input-single-output (SISO), the criterion has an appealing graphical interpretation which resembles the classical Nyquist criterion.

IQC robustness analysis for feedback interconnections of unstable distributed parameter systems

In recent work the authors combined integral-quadratic-constraint (IQC) based analysis with ¿-gap metric based analysis to study the robustness of feedback interconnections of possibly unstable rational transfer functions. This is extended here to the case of irrational transfer functions without pure delays. Specifically, we restrict attention to the sub-algebra of Callier-Desoer class transfer functions that have a limit at infinity.

Sampled-Data H ∞ Control Design for a Class of PWM Systems

Robust control of a class of switched dynamical systems is considered. The switching is controlled by pulse-width modulation (PWM). This idea is used, for example, in power electronics for power conversion. The class of systems considered includes digitally controlled power converters of many different types. The traditional approach to control design for power converters rely on an averaged model that ignores the high frequency behavior and the inherent time delay due to sampling. In contrast, the method presented here is based on a sampled-data model which takes the switched nature of the system into account. The sampled-data model is approximated by a linear quadratic model to which sampled-data H∞theory can be extended. The approach is applied to a bidirectional boost converter which is subjected to a large load disturbance.

An IQC Approach to Robust Stability of Aperiodic Sampled-Data Systems

Conditions for robust stability of sampled-data systems with non-uniform sampling patterns and structural uncertainties are derived. The problem is tackled under the integral quadratic constraint (IQC) framework, where the “aperiodic sampling operation” is modelled by an “delay-integration” operator. Characterization based on integral quadratic constrains (IQC) is identified for this operator and the IQC theory is applied to derive convex stability criteria. Compared to the dominating Lyapunov approach where the candidate Lyapunov-Krasovskii functionals or looped functionals need to be tailored for the systems under consideration and therefore the stability conditions need to be re-derived whenever additional uncertainties are considered, the proposed approach has the advantage of avoiding such endeavor. Numerical examples are given to illustrate this main point and effectiveness of the proposed approach.