Yossi Chait

Single-Loop QFT Design for Robust Performance in the Presence of Non-Parametric Uncertainties

This note focuses on the robust performance control design problem in single-loop systems from the viewpoint of the Quantitative Feedback Theory (QFT) method. Unlike the more general setup for QFT which allows arbitrary plant uncertainty description (i.e., value sets or templates), we assume that the plant uncertainty is described by multiplicative perturbation. A set of quadratic inequalities is developed for the robust performance problem in general, and, in particular, for the robust complimentary sensitivity problem. The so-called QFT bounds can be computed in a closed-form from these quadratic inequalities.

Parametric robust control by quantitative feedback theory

The problem of performance robustness, especially in the face of significant parametric uncertainty, has been increasingly recognized as a predominant issue of engineering significance in many design applications. Quantitative feedback theory (QFT) is very effective for dealing with this class of problems even when there exist hard constraints on closed loop response. In this paper, SISO-QFT is viewed formally as a sensitivity constrained multi objective optimization problem which can be used to set up a constrained H¿ minimization problem whose solution provides an initial guess at the QFT solution. In contrast to the more recent robust control methods where phase uncertainty information is often neglected, the direct use of parametric uncertainty and phase information in QFT results in a significant reduction in the cost of feedback. An example involving a standard problem is included for completeness.

A simplified multi-input multi-output formulation for the quantitative feedback theory

A simplified multi input/output formulation is developed for the quantitative feedback theory (QFT) for the 2×2 (n=2) case. This formulation is consistent with traditional QFT philosophy where performance is specified for each individual closed-loop transfer function and control bandwidths are minimized. The simplified formulation turns the solution of a simultaneous robust stability and robust model matching problem into a two (n in general) step procedure of solving quadratic inequalities (whose coefficients are linear functions of the plants and the performance constraints); the traditional procedure requires six (n+n 2 in general) steps for a similar problem

On the zero-input stability of control systems with Clegg integrators

We consider control systems utilizing so-called Clegg integrators. A Clegg integrator is a linear integrator with reset mechanism whose describing function 1.62//spl omega/ /spl ang/-38.1/spl deg/ has magnitude slope equivalent to that of a linear integrator, but with 51 less degrees of phase lag. The potential advantages of using Clegg integrators to meet stringent design specifications has been demonstrated in the literature, however, stability analyses are missing. This paper addresses the zero-input stability of such control systems and provides a definitive stability condition for second-order plants as well as a providing preliminary results for higher-order plants.

A mathematical model of parathyroid hormone response to acute changes in plasma ionized calcium concentration in humans

A complex bio-mechanism, commonly referred to as calcium homeostasis, regulates plasma ionized calcium (Ca(2+)) concentration in the human body within a narrow range which is crucial for maintaining normal physiology and metabolism. Taking a step towards creating a complete mathematical model of calcium homeostasis, we focus on the short-term dynamics of calcium homeostasis and consider the response of the parathyroid glands to acute changes in plasma Ca(2+) concentration. We review available models, discuss their limitations, then present a two-pool, linear, time-varying model to describe the dynamics of this calcium homeostasis subsystem, the Ca-PTH axis. We propose that plasma PTH concentration and plasma Ca(2+) concentration bear an asymmetric reverse sigmoid relation. The parameters of our model are successfully estimated based on clinical data corresponding to three healthy subjects that have undergone induced hypocalcemic clamp tests. In the first validation of this kind, with parameters estimated separately for each subject we test the models ability to predict the same subjects induced hypercalcemic clamp test responses. Our results demonstrate that a two-pool, linear, time-varying model with an asymmetric reverse sigmoid relation characterizes the short-term dynamics of the Ca-PTH axis.

Synchronization of TCP Flows in Networks with Small DropTail Buffers

A recent fluid-model formulation of an Internet congestion-control problem considers routers with small Droptail buffers. This paper is interested in the oscillatory regime of such networks and considers a topology where two TCP-controlled flows (each regulated by separate (edge) routers) merge to compete for bandwidth at a common (core) router. We describe this dynamic using a weakly-coupled oscillator model and analyze the coherence of oscillation as a function of coupling strength. We show that increased coupling leads to increased coherence and to larger variations in the arrival flow at the core router. The coupling strength can be expressed in terms of network parameters.

A computational model of the human thyroid.

The thyroid, the largest gland in the endocrine system, secretes hormones that help promote bodily growth and development. This gland regulates hormonal secretion rate in spite of changes in dietary iodine which is a key ingredient in the hormones biosynthesis. The thyroid relies on several feedback mechanisms for this regulation, and in this paper we use recent molecular-level and clinical observations to engineer a computational thyroid model. We use simulation and analysis to show that this models captures known aspects of thyroid physiology. We identify features in the model that are responsible for hormonal regulation, and use the model to identify and evaluate competing hypotheses associated with Wolff-Chaikoff escape.

Direct control design in sampled-data uncertain systems

Abstract This paper introduces a new direction for design of single input/output, sampled-data uncertain systems within the setting of Quantitative Feedback Theory (QFT). The control system consists of a continuous-time uncertain plant, a discrete-time controller connected via a sample-and-hold device and a discrete-time prefilter for reference tracking. The class of problems considered here includes robust stability, robust gain and phase margins, robust discrete-time tracking and robust continuous-time tracking. The new direction involves a QFT technique where control design is performed directly in the Z -domain. It is shown that QFT bounds can be computed in the Z -domain from a set of quadratic inequalities. A numerical example illustrates the salient features of the developed technique.

Iron dosing in kidney disease: inconsistency of evidence and clinical practice

The management of anemia in patients with chronic kidney disease (CKD) is difficult. The availability of erythropoiesis-stimulating agents (ESAs) has increased treatment options for previously transfusion-requiring patients, but the recent evidence of ESA side effects has prompted the search for complementary or alternative approaches. Next to ESA, parenteral iron supplementation is the second main form of anemia treatment. However, as of now, no systematic approach has been proposed to balance the concurrent administration of both agents according to individual patients needs. Furthermore, the potential risks of excessive iron dosing remain a topic of controversy. How, when and whether to monitor CKD patients for potential iron overload remain to be elucidated. This review addresses the question of risk and benefit of iron administration in CKD, highlights the evidence supporting current practice, provides an overview of standard and potential new markers of iron status and outlines a new pharmacometric approach to physiologically compatible individualized dosing of ESA and iron in CKD patients.

Stability analysis for control systems with reset integrators

In feedback control systems, it may be beneficial to reset integrators. For example, the so-called Clegg integrator is a linear integrator whose output is reset to zero whenever its input crosses zero. Its sinusoidal describing function is 1.69//spl omega/ /spl ang/-38.1/spl deg/ indicating possible advantage over its linear counterpart. In this paper, we develop some stability criteria for such systems based upon integral quadratic constraint models of the reset action.