Proceedings of the American Control Conference

We develop a new stability tests for systems with one uncertain parameter and with polynomial uncertainty structure. The test is derived using the resultant determinant for the real and imaginary parts of the polynomial evaluated on the imaginary axis. The resultant determinant is a function of the uncertain parameter as well as frequency. We evaluate the determinant using a known algorithm then test it for roots in a given interval using Sturm's theorem. We apply Sturm's test twice: over the allowable range of the uncertain parameter, and for positive angular frequencies. The procedure yields a necessary and sufficient stability condition with polynomial uncertainty structure and one uncertain parameter. We demonstrate the new test using two numerical examples.

This paper presents a delay-based output feedback control method, which, through placement of the zeros of the overall loop transfer function, is capable of realizing any full state feedback control algorithm with arbitrarily small errors. A systematic way for designing the delayed feedback controller is provided. Compared to full state feedback controls, LTR output feedback controls, the delayed output feedback is less sensitive to high frequency noises as it has much lower high-frequency gain. Also, the closed-loop bandwidth with the delayed output feedback can be much wider than that with full state feedback. A case study shows the effectiveness of the proposed control method.

We consider the problem of designing controllers for discrete-time LTI plants that render the closed loop impulse response non-negative. Such systems have a non-undershooting and non-overshooting step response. We first show that the impulse response of any discrete-time LTI system changes sign at least "r" times if it has "r" real, positive zeros outside a circular disk centered at the origin and containing all its poles. We then show that a necessary and sufficient condition on the plant for the existence of a compensator that makes the closed loop impulse response sign invariant is that there be no real, positive, nonminimum phase plant zeros. Finally, we show, by construction, how such a compensator may be synthesized when the plant does satisfy the existence condition.

In current industrial PLC programming there are a wide variety of logic control design methodologies in use. These languages include: ladder diagrams, function block diagrams, sequential function charts, and flow charts. At the same time, driven by a desire for verifiability, academics are developing additional methodologies, such as modular finite state machines and Petri nets. Using these languages important properties of programs can be verified and some code can be generated automatically. However, in the development of recent programming languages almost no mention has been made of the human factor, which becomes important when an existing program is modified, debugged, or incorporated into a new program. To begin addressing this issue, we present three ways to measure the complexity of a logic program (time to develop, direct measurements, and accessibility measures) and measure similar programs written in three logic control design methodologies (ladder diagrams, Petri nets and modular finite state machines). The goal of this paper is not to provide definitive answers regarding the suitability of a language for a particular purpose, but rather to explore the factors that may affect such decisions in the future.

We consider in this paper a class of dual control problems where there exists a parameter uncertainty in the observation equation of the linear-quadratic Gaussian problem. An analytical active dual control law is derived by a variance minimization approach. The issue of how to determine an optimal degree of active learning is then addressed, thus achieving an optimality for this class of dual control problems.

The paper addresses the aspects of control of real time systems with varying sampling rate. An example is given in which a stable continuous system is sampled at two different sampling rates. Two controllers are designed to minimize the same continuous quadratic loss function with the same weights. It is shown that although the design leads to stable controlled closed loop systems, for both discretizations, the resulting system can be unstable due to variations in sampling rate. To avoid that problem, we suggest an optimal controller design in which a bound on the cost, for all possible sampling rate variations, is computed. This results in a piecewise constant state feedback control law and guarantees stability regardless of the variations in sampling rate. The controller synthesis is cast into an LMI, which conveniently solves the synthesis problem. To illustrate the procedure, the introduction example is revised using the proposed LMI synthesis method and the stable control law is given, which is robustly stable against variations in sampling rate.

An algorithm for decomposing positive linear systems into monomial components is developed for the case when the system matrix contains zero columns. Criteria in digraph form for identifying the reachability and controllability properties of such systems are provided. The decomposition algorithm can be, used to generate a variety of reachable and controllable canonical form of positive linear systems. The graph-theoretic nature of the algorithm substantially simplifies the solution of large-scale problems arising in many application areas of positive systems.

Nuclear Magnetic Resonance (NMR) Spectroscopy in solution is an important modality for extracting structural information of macromolecules. In NMR spectroscopy, radio frequency electromagnetic pulses axe used to manipulate spin states of atomic nuclei. Pulse sequences that accomplish a desired spin control should be as short as possible in order to minimize the effects of thermal relaxation, and to optimize the sensitivity of the experiments. In this paper, we cast the problem of design of pulse sequences in NMR spectroscopy as a problem of time optimal control. It is shown that finding time optimal pulse sequences can be reduced to problems of computing subriemannian geodesics in certain homogeneous spaces. The use of geometric control techniques provides a systematic way of finding time optimal pulse sequences for transferring coherence and synthesizing unitary transformations in spin networks arising in coherent spectroscopy.

Control schemes and sensor types for the nonaxisymmetric resistive wall mode (RWM) stabilization in the DIII-D tokamak are compared. The analysis is based on a system response model for the RWMs in DIII-D and the modelling uses a toroidal current sheet to represent the plasma surface and a combination of helical and circulating "picture frame" currents to represent the conducting structure. The instability driving term and corresponding growth rate are derived from specification of the critical wall distance beyond which the mode will be magneto hydro dynamic unstable. Based on this model, control analysis is applied to investigate achievable closed loop behavior in terms of damping, robustness and control activity. The results show that with reasonable control signals, the RWMs can be stabilized. In addition, with sensors inside the wall, rather than outside, twice as good robustness towards variation in the RWM growth rate is achieved.

A next-generation air traffic decision support tool, known as the active final approach spacing tool (aFAST), will generate heading, speed and altitude commands to achieve more precise separation of aircraft in the terminal area. The techniques used to analyze the performance of earlier generation decision support tools are not adequate to analyze the performance of aFAST. The paper summarizes the development of a new and innovative fully closed-loop testing method for aFAST. This method, called trajectory feedback testing, closes each aircraft control loop inside of the aFAST scheduling algorithm. Validation of trajectory feedback testing by examination of the variation of aircraft time-of-arrival predictions between schedule updates and the variation of aircraft excess separation distances between simulation runs is presented.