Theodore E. Djaferis

Robust control design: a polynomial approach

List of figures. List of tables. Preface. 1. Introduction. 2. System dynamics. 3. Stability tests. 4. Uncertainty and robust stability. 5. Some robust stability tests. 6. The finite inclusions theorem. 7. Fit based D-stabilization. 8. Fit synthesis for robust performance. 9. Fit synthesis for robust multiobjective performance. 10. Robust design via simultaneous polynomial stabilization. 11. Fit for robust multivariable design. References. Index.

To stabilize a k real parameter affine family of plants it suffices to simultaneously stabilize 4 4 polynomials

A controller stabilizes an entire family of plants with affine uncertainty, if it simultaneously stabilizes a finite number of polynomials. An upper bound for this number is 4k.

Representations of controllers that achieve robust performance for systems with real parameter uncertainty

Abstract Consider a family of single input single output plants described by transfer functions that involve real parameter uncertainty. Parameter values are known to lie in a hypercube. Assume that a class of available controllers has been prescribed, along with a bound for the sensitivity transfer function to ensure tracking. It is of interest to determine whether a controller from the given class exists that guarantees robust stability and robust asymptotic tracking. In this paper we present a problem formulation and then provide a solution based on it. Not only do we address the existence question but also give representation of controllers from the class that meet the robustness requirements.

A novel approach to the analysis and synthesis of controllers for parametrically uncertain systems

This paper presents a novel characterization of Hurwitz polynomials, and demonstrates its usefulness in analyzing parametrically uncertain systems and synthesizing robust controllers for such systems. The characterization is a variant of the Nyquist stability theorem, but unlike this theorem, it can prove a polynomial is Hurwitz from only approximate knowledge of the polynomials phase at finitely many points along the imaginary axis. >

The finite inclusions theorem

This paper presents a novel, necessary and sufficient condition for a polynomial to have all its roots in an arbitrary convex region of the complex plane. The condition may be described as a variant of Nyquists stability theorem; however, unlike this theorem it only requires knowledge of the polynomials value at finitely many points along the regions boundary. A useful corollary, the finite inclusions theorem (FIT), provides a simple sufficient condition for a family of polynomials to have all its roots in a given convex region. Since FIT only requires knowledge of the familys value set at finitely many points along the regions boundary, this corollary provides a new and convenient tool for the analysis and synthesis of robust controllers for parametrically uncertain systems.<<ETX>>

Robust observers for systems with parameters

Abstract In many cases linear multivariable models which describe physical systems contain structured parametric type uncertainties. Specifically it may be that the state space model is expressed in a form which involves parameters. We first consider circumstances in which a parameter independent observer can be constructed for the system, and suggest conditions that guarantee its existence. We also give conditions under which such a robust observer can be subsequently used with additional dynamics in a parameter free configuration for regulation.

Stability preserving maps and robust stabilization

The notion of a stability preserving map can be defined in a number of ways. In this paper we introduce one such definition and then demonstrate its impact on the problem of robust controller synthesis. Specifically, we show that the concept of a stability preserving map can be used to provide a different characterization of the existence of a fixed order controller that simultaneously stabilizes a finite number of plants. We also demonstrate how it can be used to state conditions for the robust stabilization of families of plants with real parameter uncertainty. In addition, the characterization provides new insight into how to construct robustly stabilizing controllers.

Compliant Control Using Robust Multivariable Feedback Methods

In this paper we deal with the problem of dynamic control of robotic manipulators in the presence of uncertainty. Specifically we focus on compliant control in the context of surface tracing. We use the Combined Force-Position control architecture and develop control laws based on a system model obtained by operating point linearization techniques. Robust analysis and design methods are presented using frequency domain multivariable feedback methods. Compensator design is carried out for a two link planar manipulator, and experimental results are shown while a guarded move is being executed.

Robust pole assignment for systems with parameters

In this paper we investigate the problem of arbitrarily assigning the closed loop poles of a linear time invariant multivariable system with a proper output feed-back compensator in a manner which is insensitive with respect to parameters. We consider a certain parameter structure, define the notion of robust pole assignment and give necessary and/or sufficient conditions for accomplishing it.

Stability preserving maps and robust design

In this paper we present the concept of a matrix stability preserving map and show its impact on the problem of robust controller design. We develop a number of tests for checking whether a given matrix is a stability preserving map. We show that the concept of a stability preserving map can be used to provide a different characterization of the existence of a fixed order controller that simultaneously stabilizes a finite number of plants. We also demonstrate how it can be used to state conditions for the robust stabilization of families of plants with real parameter uncertainty. In addition, we show how stability preserving map tests lead to robust stabilization techniques and apply the methodology to a number of examples.