Synthesis of PID controllers for a class of time delay systems

In this paper we use the Hermite-Biehler theorem to establish results on the design of proportional plus integral plus derivative (PID) controllers for a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers. As far as we know, previous results on the synthesis of PID controllers rely on the solution of transcendental equations. This paper also extends previous results on the synthesis of proportional controllers for a class of delay systems Of retarded type to a larger class of delay systems. (C) 2009 Elsevier Ltd. All rights reserved.

Synthesis of PID controllers for a class of time delay systems

In this paper we use the Hermite-Biehler theorem to establish results on the design of proportional plus integral plus derivative (PID) controllers for a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers. As far as we know, previous results on the synthesis of PID controllers rely on the solution of transcendental equations. This paper also extends previous results on the synthesis of proportional controllers for a class of delay systems of retarded type to a larger class of delay systems. (C) 2009 Elsevier Ltd. All rights reserved.

New class of spin projection operators for 3D models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Conditionally exactly soluble class of quantum potentials

We present a different class of quantum-mechanical potentials. These are midway between the exactly solvable potentials and the quasiexactly ones. Their fundamental feature is that one can find the entire s-wave spectrum of a given potential, provided that some of its parameters are conveniently fixed. © 1993 The American Physical Society.

1.6 Lloyd Gaines, Valedictorian, Vashon Class of 1931

Lloyd Gaines also helped to support his family by selling magazine subscriptions. He graduated in 1931 after only three years and served as the Valedictorian of his class. As a senior, Gaines finished first in a local essay contest, winning a prize of $250 (equivalent to $3000 in modern currency) that he used to enroll as a student at Stowe Teachers College in St. Louis for the 1931-32 school year

Harvard College quarter bills, 1812-1818

This folder contains sixteen printed Harvard College quarter bills filled out in manuscript primarily for William Croswell's use of wood.

Payment order to the Harvard College Treasurer, 1715 September

This slip of paper contains a request from Harvard College President John Leverett to the College Treasurer John White to pay John Rogers for his work as library keeper, pursuant to a Harvard Corporation vote on September 27, 1714.

Payment order to the Harvard College Treasurer, 1721 August 15

This slip of paper contains a request from President John Leverett to the College Treasurer John White to pay William Cook for his work as library keeper, pursuant to a Harvard Corporation vote on June 28, 1720.

Bill to Harvard College from Bartholomew Green, 1723 November 19

This bill was rendered to Harvard College by Bartholomew Green for costs related to the printing of the Library Catalogue. The verso contains a receipt for payment signed by Green on January 11, 1723/4.