Relationship between the controllability grammian and closed-loop eigenvalues: the single input case

Quantitative Feedback Theory (QFT), a robust control design method introduced by Horowitz, has been shown to be useful in many cases of multi-input, multi-output (MIMO) parametrically uncertain systems. Prominent is the capability for direct design to closed-loop frequency response specifications. In this paper, the theory and development of optimization-based algorithms for design of minimum-gain controllers is presented, including an illustrative example. Since MIMO QFT design is reduced to a series of equivalent single-input, single-output (SISO) designs, the emphasis is on the SISO case.

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Formulas for Computing Closed-Loop Time Responses of Flexible Systems Using Truncated Models

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2897728 ◽

1992 ◽

Vol 114 (4) ◽

pp. 589-591

Author(s):

N. F. Lacey ◽

Y. Chait ◽

C. B. MacCluer

Keyword(s):

Mechanical System ◽

Closed Loop ◽

Damping Ratio ◽

Time Response ◽

Upper And Lower Bounds ◽

Vibration Modes ◽

Flexible Systems ◽

Control Solution ◽

Single Input ◽

Flexible Mechanical System

In this paper we derive formulas for computing the closed-loop time response of an uncertain flexible mechanical system with a truncated model. It is assumed that the dynamics of the flexible mechanical system is described by an infinite series of lightly damped vibration modes. The modal parameters, damping ratio, and natural frequency, are assumed to lie within known ranges. Given a truncated model and a robust control solution, our formulaes define upper and lower bounds for the time response of single-input/output systems about the closed-loop response of the truncated model.

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Single-Input Planar Navigation via Proportional Heading Control Exploiting Nonholonomic Mechanics or Vortex Shedding

ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Volume 1 ◽

10.1115/dscc2011-6191 ◽

2011 ◽

Cited By ~ 6

Author(s):

Michael J. Fairchild ◽

Peter M. Hassing ◽

Scott David Kelly ◽

Parthesh Pujari ◽

Phanindra Tallapragada

Keyword(s):

Vortex Shedding ◽

Closed Loop ◽

Nonholonomic Constraint ◽

Hydrodynamic Force ◽

Nonholonomic Mechanics ◽

Motion Generation ◽

Chaplygin Sleigh ◽

Loop Control ◽

Heading Control ◽

Single Input

We present a strategy for coupled steering and motion generation applicable to a class of single-input planar robotic vehicles. We demonstrate this strategy through simulations of two different vehicles under closed-loop control, the first a novel variation of the Chaplygin sleigh and the second a fishlike swimmer in an ideal fluid. The dynamics of the former are influenced by a nonholonomic constraint and the dynamics of the latter by a hydrodynamic force associated with vortex shedding. The juxta-position of these two systems highlights a link between nonholonomic mechanics and hydrodynamics explored in a prior paper.

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Synthesising closed-loop single-input systems by response fitting

International Journal of Electronics ◽

10.1080/00207217208938408 ◽

1972 ◽

Vol 33 (6) ◽

pp. 717-720

Author(s):

F. FALLSIDE ◽

R. V. PATEL ◽

H. SERAJI

Keyword(s):

Closed Loop ◽

Single Input

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Synchronization of the Extended Bonhoffer-Van der Pol Oscillators

Mathematical Problems in Engineering ◽

10.1155/2012/962680 ◽

2012 ◽

Vol 2012 ◽

pp. 1-14

Author(s):

Mohamed Zribi ◽

Saleh Alshamali

Keyword(s):

Closed Loop ◽

Sliding Mode ◽

Lyapunov Theory ◽

Closed Loop System ◽

Van Der Pol ◽

Parameter Perturbations ◽

Van Der Pol Oscillators ◽

Response Systems ◽

Single Input ◽

Stability Results

This paper deals with the synchronization of two extended Bonhoffer-Van der Pol (B-VDP) oscillators. A Lyapunov-based controller and a sliding mode controller are proposed for the synchronization of the oscillators. Both design schemes use a single input controller acting on one state only. Asymptotic stability results for the closed-loop system are derived using Lyapunov theory. It is shown that the proposed controllers effectively synchronize the driver and the response systems for the case when nominal values of the system parameters are used, and for the case when parameter perturbations are introduced. Simulation results are presented to show the effectiveness of the proposed controllers.

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