Advances in undergraduate control education: the analytical design approach

Introductory undergraduate control courses in the USA are generally limited to trial-and-error design techniques, based largely on the Nyquist stability criterion and root-locus analysis. The corresponding theory is well over fifty years old. Very little is presented on analytic design, where one has an existence theorem, and a computable algorithm to find a solution when one exists. One reason for the lack of analytic design in introductory courses is the level of mathematics required to understand much of this theory. Here we summarize some of the existing analytic design techniques, and their mathematical pre-requisites, and then we propose the interpolation approach for analytic design, as one requiring the least amount of mathematics

Forward Stochastic Reachability Analysis for Uncontrolled Linear Systems using Fourier Transforms

We propose a scalable method for forward stochastic reachability analysis for uncontrolled linear systems with affine disturbance. Our method uses Fourier transforms to efficiently compute the forward stochastic reach probability measure (density) and the forward stochastic reach set. This method is applicable to systems with bounded or unbounded disturbance sets. We also examine the convexity properties of the forward stochastic reach set and its probability density. Motivated by the problem of a robot attempting to capture a stochastically moving, non-adversarial target, we demonstrate our method on two simple examples. Where traditional approaches provide approximations, our method provides exact analytical expressions for the densities and probability of capture.Comment: V3: HSCC 2017 (camera-ready copy), DOI updated, minor changes | V2: Review comments included | V1: 10 pages, 12 figure

On the Relative Degree of Simultaneously Stabilizing Controllers

In this brief paper 1 we present new necessary and sufficient conditions on the controller for the existence of a single controller to stabilize a set of n SISO plants: P1; P2; :::; Pn. As is well known this is equivalent to the existence of a single stable controller that stabilizes n - 1 plants (strong stabilization). It was shown in (Blondel, 1994) that the simultaneous stabilization problem is transcendental and cannot be solved using algebraic functions. Our only hope in approaching the general solution to the simultaneous stabilization problem using algebraic functions is either to enlarge the class of controllers for which sufficient conditions exist, or to restrict the class of controllers from which a controller must exist. This paper restricts the search for existence of simultaneously stabilizing controllers to the class of exactly proper controllers

Survey of the robust control of robots

Browse Conference Publications \u3e American Control Conference, ... Page Help Survey of the Robust Control of Robots This paper appears in: American Control Conference, 1990 Date of Conference: 23-25 May 1990 Author(s): Abdallah, C. CAD Laboratory for Systems and Robotics, Electrical and Computer Engineering Department, University of New Mexico, Albuquerque, NM 87131. Dorato, P. ; Jamshidi, M. On Page(s): 718 - 721 Product Type: Conference Publications 4790827 searchabstract .Abstract In this survey, we discuss current approaches to the robust control of the motion of robots and summarize the available literature on the subject. The three major designs discussed are the Linear-Multivariable Approach, the Passivity approach and the Variable-Structure approach. The survey is limited to rigid robots and nonadaptive controllers

Static output feedback: a survey

This paper reviews the static output feedback problem in the control of linear, time-invariant (LTI) systems. It includes analytical and computational methods and presents in a unified fashion, the knowledge gained in the decades of research into this most important problem

Robust multiobjective feedback design via combined quantifier elimination and discretization

This paper deals with the application of computerized quantifier elimination (QE) methods for robust multiobjective feedback design, when design objectives are specified in the frequency domain. The class of design problems considered here has no analytical solutions, so that computerized solutions are of interest, even for relatively simple problems. However, due to the computational complexity of pure QE algorithms, a combined QE discretization approach is proposed and illustrated with an example

Analytic Gain and Phase Margin Design

In 5, algorithms are presented for analytic gain and phase margin design. Without special care however, the compensator computed with this algorithm is not a real rational function. In 3, it is shown that with some care, a real rational compensator for phase margin design can be computed from the theory in 5. In this paper both gain and phase margin problems are reduced to interpolation problems with positive-real functions, which saves a step in the algorithm shown in 5, where interpolation is done with bounded-real functions, in the case of gain margin design

CONTINUOUS AND DISCRETE TIME SPR DESIGN USING FEEDBACK

This paper presents necessary and sufficient conditions for the existence of a feedback compensator that will render a given continuous-time or discrete-time linear system SPR. When these conditions hold, the controller is explicitly found

Polynomial solutions for simultaneous stabilization

In this paper, we present a new necessary and sufficient condition for simultaneous stabilization and new sufficient conditions for the existence of a simultaneously stabilizing controller, both derived from a polynomial approach. The additional requirements for the controller itself to be either stable or a Unit in H1 are also given. These new sufficient conditions are general in nature and are shown to reduce in special cases to several published papers. Examples illustrate the extensions

Robust finite-time stability design via linear matrix inequalities

For linear systems with polytopic uncertainties, the problem of robust finite-time stabilization is reduced to a system of Linear Matric Inequalities