Noncollocated passivity-based PD control of a single-link flexible manipulator

Robotica ◽  
2003 ◽  
Vol 21 (2) ◽  
pp. 117-135 ◽  
Author(s):  
Liang-Yih Liu ◽  
King Yuan
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Sufficient Conditions ◽  
Angular Acceleration ◽  
Flexible Manipulator ◽  
Infinite Dimensional ◽  
Single Link ◽  
Acceleration Feedback ◽  
Necessary And Sufficient ◽  
Irrational Transfer Function

The passivity property of a noncollocated single-link flexible manipulator with a parameterized output is studied. The system can be characterized by either the irrational transfer function of an infinite-dimensional model or its truncated rational transfer functions. Necessary and sufficient conditions for these transfer functions to be passive are found. It is also shown that a non-passive, marginal minimum-phase, truncated transfer function can be rendered passive by using either the root strain feedback or the joint angular acceleration feedback. For the noncollocated truncated passive transfer function, a PD controller suffices to stabilize the overall system. Numerical results are given to show the efficacy of the proposed approaches.

PASSIVITY-BASED INTEGRAL CONTROL AND STABILITY ANALYSIS OF A CONSTRAINED SINGLE-LINK FLEXIBLE ARM

2013 ◽  
Vol 37 (3) ◽  
pp. 673-683
Author(s):  
Liang Y. Liu ◽  
Hsiung C. Lin
Keyword(s):  
Contact Force ◽  
Angular Acceleration ◽  
Flexible Manipulator ◽  
Distributed Parameter ◽  
Integral Control ◽  
Flexible Arm ◽  
Single Link ◽  
Integral Controller ◽  
Poles And Zeros ◽  
Necessary And Sufficient

The design of flexible manipulator is complicated due to inherently infinite dimension in nature. The sequential challenge is the problem such a non-minimum phase that is the cause of system instability. In this paper, a constrained single-link flexible arm is fully investigated using a linear distributed parameter model. In order to overcome the inherent limitations, a new input induced by the joint angular acceleration and an output generated using the contact force and root shear force are defined. A necessary and sufficient condition is thus derived so that all poles and zeros of the new transfer function lie on the imaginary axis. Also, the passive integral control is designed to accomplish the regulation of the contact force. The excellent performance of the passive integral controller is verified through numerical simulations.

Transient Response of Linear Systems Under Integral Constraints

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Bilal Salih ◽  
Tuhin Das
Keyword(s):  
Transfer Function ◽  
Power Systems ◽  
Transfer Functions ◽  
Adaptive Estimation ◽  
Sufficient Conditions ◽  
Parametric Uncertainty ◽  
Step Response ◽  
Integral Constraints ◽  
Second Order Systems ◽  
Necessary And Sufficient

Abstract The requirement of satisfying an integral constraint imposed on a linear system's transient step-response is considered in this paper. The problem is first analyzed to determine the specific structure of a system's transfer function that helps satisfy such constraints. Analytical results are derived for a class of second-order systems with an additional zero. The results are extended to higher order transfer functions. Subsequently, a standard compensation consisting of a combination of feedforward and feedback actions is proposed to transform a given transfer function to the desired structure. Necessary and sufficient conditions to guarantee stability of the resulting closed-loop system are derived. Next, the problem of satisfying integral constraints in the presence of parametric uncertainty is addressed by augmenting adaptive estimation strategies to the feedforward and feedback compensation structure. Simulation results are provided for validation. The theory presented here is an abstraction from power management algorithms for hybrid power systems, such as a fuel cell hybridized with an ultracapacitor. Further work is ongoing to extend the theory to nonlinear systems.

Transfer functions and conditions for stationarity of bilinear models with gaussian residuals

1985 ◽  
Vol 400 (1819) ◽  
pp. 315-330 ◽  
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Function System ◽  
Bilinear Models ◽  
Special Cases ◽  
Necessary And Sufficient

The aim of this paper is to construct the transfer function system of bilinear models with gaussian residuals and to give necessary conditions and sufficient conditions for stationarity. In some special cases, the necessary and sufficient conditions are given.

Positive stable realizations of discrete-time linear systems

2012 ◽  
Vol 60 (3) ◽  
pp. 605-616
Author(s):  
T. Kaczorek
Keyword(s):  
Transfer Function ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Abstract The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.

scholarly journals On an infinite dimensional linear-quadratic problem with fixed endpoints: The continuity question

2014 ◽  
Vol 24 (4) ◽  
pp. 723-733
Author(s):  
K.Maciej Przyłuski
Keyword(s):  
Minimum Energy ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
Minimum Norm Solution ◽  
Quadratic Problem ◽  
Infinite Dimensional ◽  
Necessary And Sufficient ◽  
Quadratic Control Problems

Abstract In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.

A class of simple non-weight modules over the virasoro algebra

2020 ◽  
Vol 63 (4) ◽  
pp. 956-970 ◽  
Author(s):  
Haibo Chen ◽  
JianZhi Han
Keyword(s):  
Tensor Product ◽  
Sufficient Conditions ◽  
Virasoro Algebra ◽  
Vector Spaces ◽  
Complex Numbers ◽  
Infinite Dimensional ◽  
Highest Weight ◽  
Alpha Omega ◽  
Necessary And Sufficient ◽  
Infinite Dimensional Lie Algebra

AbstractThe Virasoro algebra $\mathcal {L}$ is an infinite-dimensional Lie algebra with basis {Lm, C| m ∈ ℤ} and relations [Lm, Ln] = (n − m)Lm+n + δm+n,0((m3 − m)/12)C, [Lm, C] = 0 for m, n ∈ ℤ. Let $\mathfrak a$ be the subalgebra of $\mathcal {L}$ spanned by Li for i ≥ −1. For any triple (μ, λ, α) of complex numbers with μ ≠ 0, λ ≠ 0 and any non-trivial $\mathfrak a$-module V satisfying the condition: for any v ∈ V there exists a non-negative integer m such that Liv = 0 for all i ≥ m, non-weight $\mathcal {L}$-modules on the linear tensor product of V and ℂ[∂], denoted by $\mathcal {M}(V,\mu ,\Omega (\lambda ,\alpha ))\ (\Omega (\lambda ,\alpha )=\mathbb {C}[\partial ]$ as vector spaces), are constructed in this paper. We prove that $\mathcal {M}(V,\mu ,\Omega (\lambda ,\alpha ))$ is simple if and only if μ ≠ 1, λ ≠ 0, α ≠ 0. We also give necessary and sufficient conditions for two such simple $\mathcal {L}$-modules being isomorphic. Finally, these simple $\mathcal {L}$-modules $\mathcal {M}(V,\mu ,\Omega (\lambda ,\alpha ))$ are proved to be new for V not being the highest weight $\mathfrak a$-module whose highest weight is non-zero.

APPROXIMATE CONTROLLABILITY OF SECOND-ORDER STOCHASTIC DIFFERENTIAL EQUATIONS WITH IMPULSIVE EFFECTS

2010 ◽  
Vol 24 (14) ◽  
pp. 1559-1572 ◽  
Author(s):  
RATHINASAMY SAKTHIVEL ◽  
YONG REN ◽  
N. I. MAHMUDOV
Keyword(s):  
Biological Sciences ◽  
Differential Equations ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Impulsive Effects ◽  
Infinite Dimensional ◽  
Infinite Dimensional Dynamical Systems ◽  
Necessary And Sufficient

Many practical systems in physical and biological sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, the approximate controllability of nonlinear second-order stochastic infinite-dimensional dynamical systems with impulsive effects is considered. By using the Holder's inequality, stochastic analysis and fixed point strategy, a new set of necessary and sufficient conditions are formulated which guarantees the approximate controllability of the nonlinear second-order stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable.

Point Control of a One-Link Flexible Manipulator

1986 ◽  
Vol 53 (1) ◽  
pp. 23-27 ◽  
Author(s):  
S. B. Skaar ◽  
D. Tucker
Keyword(s):  
Transfer Functions ◽  
Control Strategies ◽  
Open Loop ◽  
Flexible Manipulator ◽  
Distributed Parameter ◽  
Loop Control ◽  
Control Approach ◽  
Alternative Approach ◽  
Single Link ◽  
Point Control

An alternative approach to the control of nonrigid, distributed parameter systems is presented. Transfer functions that relate the response of points on the system to a controlling force or torque are used in place of ordinary differential equations, which represent an approximation to the system dynamics. The implications of this “point control” approach are discussed with regard to plant modeling accuracy, uncontrolled regions, open-loop and closed-loop control strategies, system identification, and feedback estimation. Sample optimal control histories are illustrated for a single-link manipulator member with end load.

Achieving Passive Integral Control Using Feedback and Output Redefinition

2013 ◽  
Vol 284-287 ◽  
pp. 2199-2204
Author(s):  
Liang Yih Liu ◽  
Hsiung Cheng Lin
Keyword(s):  
Transfer Function ◽  
Contact Force ◽  
Angular Acceleration ◽  
Joint Torque ◽  
Minimum Phase ◽  
Force Output ◽  
Integral Control ◽  
Output Redefinition ◽  
Poles And Zeros ◽  
Necessary And Sufficient

There exist an infinite number of right-half plane zeros in the transfer function relating the joint torque input to the tip contact force output for a constrained single-link flexible arm. Since the non-minimum phase nature is the cause of instability or stability but caused the smaller control bandwidth. In order to overcome the inherent limitations caused by the non-minimum phase nature, a new input induced by the measurement of joint angular acceleration and a output generated using the measurements of contact force and root shear force are defined. A necessary and sufficient condition is derived such that all poles and zeros of the new transfer function lie on the imaginary axis. The passive integral control is designed to accomplish the regulation of the contact force. The excellent performance of the passive integral controller is verified through numerical simulations.

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