Stabilizing first-order controllers with desired stability region

In this paper, we determine the set of all stabilizing first-order controllers that place the poles of the closed-loop system in a desired stability region. The solution is based on a generalization of the Hermite-Biehler theorem applicable to polynomials with complex coefficients and the application of a modified stabilizing gain algorithm to three subsidiary plants. The method given is also applicable to PID controllers

Fixed order controller design via parametric methods

Cataloged from PDF version of article.In this thesis, the problem of parameterizing stabilizing fixed-order controllers for linear time-invariant single-input single-output systems is studied. Using a generalization of the Hermite-Biehler theorem, a new algorithm is given for the determination of stabilizing gains for linear time-invariant systems. This algorithm requires a test of the sign pattern of a rational function at the real roots of a polynomial. By applying this constant gain stabilization algorithm to three subsidiary plants, the set of all stabilizing first-order controllers can be determined. The method given is applicable to both continuous and discrete time systems. It is also applicable to plants with interval type uncertainty. Generalization of this method to high-order controller is outlined. The problem of determining all stabilizing first-order controllers that places the poles of the closed-loop system in a desired stability region is then solved. The algorithm given relies on a generalization of the Hermite-Biehler theorem to polynomials with complex coefficients. Finally, the concept of local convex directions is studied. A necessary and sufficient condition for a polynomial to be a local convex direction of another Hurwitz stable polynomial is derived. The condition given constitutes a generalization of Rantzer’s phase growth condition for global convex directions. It is used to determine convex directions for certain subsets of Hurwitz stable polynomials.Saadaoui, KarimPh.D

Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers

System Level Synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty -- such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies.Comment: To appear in Annual Reviews in Contro

A passivity approach to controller-observer design for robots

Passivity-based control methods for robots, which achieve the control objective by reshaping the robot system's natural energy via state feedback, have, from a practical point of view, some very attractive properties. However, the poor quality of velocity measurements may significantly deteriorate the control performance of these methods. In this paper the authors propose a design strategy that utilizes the passivity concept in order to develop combined controller-observer systems for robot motion control using position measurements only. To this end, first a desired energy function for the closed-loop system is introduced, and next the controller-observer combination is constructed such that the closed-loop system matches this energy function, whereas damping is included in the controller- observer system to assure asymptotic stability of the closed-loop system. A key point in this design strategy is a fine tuning of the controller and observer structure to each other, which provides solutions to the output-feedback robot control problem that are conceptually simple and easily implementable in industrial robot applications. Experimental tests on a two-DOF manipulator system illustrate that the proposed controller-observer systems enable the achievement of higher performance levels compared to the frequently used practice of numerical position differentiation for obtaining a velocity estimat

Controlling spatiotemporal dynamics with time-delay feedback

We suggest a spatially local feedback mechanism for stabilizing periodic orbits in spatially extended systems. Our method, which is based on a comparison between present and past states of the system, does not require the external generation of an ideal reference state and can suppress both absolute and convective instabilities. As an example, we analyze the complex Ginzburg-Landau equation in one dimension, showing how the time-delay feedback enlarges the stability domain for travelling waves.Comment: 4 pages REVTeX + postscript file with 3 figure