Y. Chait

Fundamental properties of reset control systems

Reset controllers are linear controllers that reset some of their states to zero when their input is zero. We are interested in their feedback connection with linear plants, and in this paper we establish fundamental closed-loop properties including stability and asymptotic tracking. This paper considers more general reset structures than previously considered, allowing for higher-order controllers and partial-state resetting. It gives a testable necessary and sufficient condition for quadratic stability and links it to both uniform bounded-input bounded-state stability and steady-state performance. Unlike previous related research, which includes the study of impulsive differential equations, our stability results require no assumptions on the evolution of reset times.

Experimental demonstration of reset control design

Abstract Using the describing function method, engineers in the 1950s and 1960s conceived of novel nonlinear compensators in an attempt to overcome performance limitations inherent in linear time-invariant (LTI) control systems. This paper is concerned with a subset of such devices called “reset controllers”, which are LTI systems equipped with mechanisms and laws to reset their states to zero. This paper reports on a design procedure and a laboratory experiment, the first to be reported in the literature, in which the resulting reset controller provides better design tradeoffs than LTI compensation. Specifically, it is shown that reset control increases the level of sensor-noise suppression without sacrificing either disturbance-rejection performance or gain/phase margins.

Nonlinear stability analysis for a class of TCP/AQM networks

Recent work has shown the benefit of using proportional feedback in TCP/AQM (transmission control protocol/active queue management) networks. By proportional feedback we mean the marking probability is proportional to the instantaneous queue length. Our earlier work (2001) relied on linearization of nonlinear fluid-flow models of TCP. In this work we address these nonlinearities directly and establish some stability results when the marking is proportional. In the case of delay-free marking, we show the systems equilibrium point to be asymptotically stable for all proportional gains. In the more realistic case of delayed feedback, we establish local asymptotic stability and quantify a region of attraction.

A single-input two-output feedback formulation for ANC problems

This paper explores inherent feedback limitations of active noise control in ducts by using a single-input, two-output framework and observing properties of closed-loop transfer functions. Performance is assessed using the plant and disturbance alignment angle. We show that the sound levels at the measurement microphone axe amplified when attenuating acoustic energy at the error microphone. We also show that the stability margins can be improved over feedforward control using measurements from two sensors.

Providing throughput differentiation for TCP flows using adaptive two-color marking and two-level AQM

In this paper we propose a new paradigm for a Differentiated Service (DiffServ) network consisting of two-color marking at the edges of the network using token buckets coupled with differential treatment in the core. Using fluid-flow modelling, we present existence conditions for token-bucket rates and differential marking probabilities at the core that result in all edges receiving at least their minimum guaranteed rates. We then present an integrated DiffServ architecture comprising of an active rate management controller at the marking edge and a two-level active queue management controller at the core. The validity of the fluid flow model and performance of this new scheme are verified using ns simulations.

Automatic Loop-Shaping of QFT Controllers Via Linear Programming

In this paper we focus on the following loop-shaping problem: Given a nominal plant and QFT bounds, synthesize a controller that achieves closed-loop stability, satisfies the QFT bounds and has minimum high-frequency gain. The usual approach to this problem involves loop shaping in the frequency domain by manipulating the poles and zeroes of the nominal loop transfer function. This process now aided by recently-developed computer-aided design tools, proceeds by trial and error, and its success often depends heavily on the experience of the loop-shaper. Thus, for the novice and first-time QFT users, there is a genuine need for an automatic loop-shaping tool to generate a first-cut solution. Clearly, such an automatic process must involve some sort of optimization, and, while recent results on convex optimization have found fruitful applications in other areas of control design, their immediate usage here is precluded by the inherent nonconvexity of QFT bounds. Alternatively, these QFT bounds can be over-bounded by convex sets, as done in some recent approaches to automatic loop-shaping, but this conservatism ca have a strong and adverse effect on meeting the original design specifications. With this in mind, we approach the automatic loop-shaping problem by first stating conditions under which QFT bounds can be dealt with in a non-conservative fashion using linear inequalities. We will argue that for a first-cut design, these conditions are often satisfied in the most critical frequencies of loop-shaping and are violated in frequency bands where approximation leads to negligible conservatism in the control design, These results immediately lead to an automated loop-shaping algorithm involving only linear program-ming techniques, which we illustrate via an example.

Analysis of reset control systems consisting of a FORE and second-order loop

Reset controllers consist of two parts a linear compensator and a reset element. The linear compensator is designed, in the usual ways, to meet all closed-loop performance speci cations while relaxing the overshoot constraint. Then, the reset element is chosen to meet this remaining step-response speci cation. In this paper, we consider the case when such linear compensation results in a second-order (loop) transfer function and where a rst-order reset element (FORE) is employed. We analyze the closed-loop reset control system addressing performance issues such as stability, steadystate response and transient performance. This material is based upon work supported by the National Science Foundation under Grant No.CMS9800612. MIE Department, University of Massachusetts, Amherst, MA 01003; chen@ecs.umass.edu. Now with Motorola, Inc. MIE Department, University of Massachusetts, Amherst, MA 01003; chait@ecs.umass.edu. ECE Department, University of Massachusetts, Amherst, MA 01003; hollot@ecs.umass.edu.

Stability of a reset control system under constant inputs

Reset controllers are standard linear compensators equipped with mechanism to instantaneously reset their states. With respect to pure linear control, there is evidence that this reset action is capable of improving control system tradeoffs. This papers objective is to analyze the stability of a particular example of reset control system when excited by constant inputs. Our main result shows that the equilibrium point of the closed-loop dynamics is asymptotically stable.

Stability and asymptotic performance analysis of a class of reset control systems

Bodes gain-phase relationship places a hard limitation on performance tradeoffs in linear, time-invariant feedback control systems. It has long been suggested that reset control has the potential to improve this situation. Experimental studies support this claim. The paper focuses on the analysis of such reset control systems which has been missing in this past work. Specifically, we give results on bounded-input bounded-output stability, asymptotic stability and steady-state performance. These results are applied to an experimental demonstration of reset control of a flexible mechanism.

An Efficient Algorithm for Computing QFT Bounds

An important step in Quantitative Feedback Theory (QFT) design is the translation of closed-loop performance specifications into QFT bounds. These bounds, domains in a Nichols chart, serve as a guide for shaping the nominal loop response. Traditionally, QFT practitioners relied on manual manipulations of plant templates on Nichols charts to construct such bounds, a tedious process which has recently been replaced with numerical algorithms. However, since the plant template is approximated by a finite number of points, the QFT bound computation grows exponentially with the fineness of the plant template approximation. As a result, the designer is forced to choose between a coarse approximation to lessen the computational burden and a finer one to obtain more accurate QFT bounds. To help mitigate this tradeoff, this paper introduces a new algorithm to more efficiently compute QFT bounds. Examples are given to illustrate the numerical efficiency of this new algorithm.