Design of Dynamic Nonlinear Control Techniques for Flexible-Link Manipulators

In this paper, we develop robust dynamical controllers for addressing the problems of tracking and regulation of flexible-link manipulators. The design of dynamical controllers is based on construction of a two-time scale dynamical motion of the closed-loop system. The main control objective is to achieve stability of the closed-loop system while ensuring boundedness of all the control signals as well as sufficiently small tip-position tracking requirement. In order to achieve a minimum phase behaviour for utilizing output feedback control strategy, a new redefined output is proposed. Instead of using the joint angles as outputs in the rigid-link case, a new output is chosen for the flexible-link case which will provide and guarantee stability of the closed-loop flexible system. Simulations results are provided for flexible-link manipulators using the proposed control strategies. A comparative analysis is also included to demonstrate and illustrate the advantages and disadvantages of the considered control methodologies.

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Robust and Optimal Output-Feedback Control for Interval State-Space Model: Application to a Two-Degrees-of-Freedom Piezoelectric Tube Actuator

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4040977 ◽

2018 ◽

Vol 141 (2) ◽

Cited By ~ 2

Author(s):

Mounir Hammouche ◽

Philippe Lutz ◽

Micky Rakotondrabe

Keyword(s):

State Space ◽

Output Feedback ◽

Degrees Of Freedom ◽

Closed Loop ◽

State Space Model ◽

Output Feedback Control ◽

Optimal Solution ◽

Loop System ◽

Closed Loop System ◽

Optimal Output

The problem of robust and optimal output feedback design for interval state-space systems is addressed in this paper. Indeed, an algorithm based on set inversion via interval analysis (SIVIA) combined with interval eigenvalues computation and eigenvalues clustering techniques is proposed to seek for a set of robust gains. This recursive SIVIA-based algorithm allows to approximate with subpaving the set solutions [K] that satisfy the inclusion of the eigenvalues of the closed-loop system in a desired region in the complex plane. Moreover, the LQ tracker design is employed to find from the set solutions [K] the optimal solution that minimizes the inputs/outputs energy and ensures the best behaviors of the closed-loop system. Finally, the effectiveness of the algorithm is illustrated by a real experimentation on a piezoelectric tube actuator.

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Robust Piecewise-Linear State Observers for Flexible Link Mechanisms

Volume 3: Dynamic Systems and Controls, Symposium on Design and Analysis of Advanced Structures, and Tribology ◽

10.1115/esda2006-95445 ◽

2006 ◽

Author(s):

Roberto Caracciolo ◽

Dario Richiedei ◽

Alberto Trevisani

Keyword(s):

Nonlinear Model ◽

Closed Loop ◽

Linear Models ◽

Piecewise Linear ◽

Equilibrium Points ◽

Loop System ◽

State Variables ◽

Flexible Link ◽

Closed Loop System ◽

State Observers

This paper tackles the problem of designing state observers for flexible link mechanisms: an investigation is made on the possibility of employing observers making use of suitable piecewise-linear truncated dynamics models. A general approach is proposed, which provides an objective way of synthesizing observers preventing the instability that may arise from using reduced-order linearized models. The approach leads to the identification of the regions of the domain of the state variables where the linear approximations of the nonlinear model can be considered acceptable. To this purpose, first of all, the stability of the equilibrium points of the closed-loop system is assessed by applying the eigenvalue analysis to appropriate piecewise-linear models. Admittedly, the dynamics of such a closed-loop system is affected by the pole perturbation caused by spillover, and by the discrepancies between the linearized models of the plant and the one of the observer. Additionally, when nodal elastic displacements and velocities are not bounded in the infinitesimal neighborhoods of the equilibrium points, the difference between the nonlinear model and the locally-linearized one is expressed in terms of unstructured uncertainty and stability is assessed by H∞ robust analysis. The method is demonstrated by applying it to a closed-chain flexible link mechanism.

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Robust Piecewise-Linear State Observers for Flexible Link Mechanisms

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2909600 ◽

2008 ◽

Vol 130 (3) ◽

Cited By ~ 12

Author(s):

Roberto Caracciolo ◽

Dario Richiedei ◽

Alberto Trevisani

Keyword(s):

Nonlinear Model ◽

Closed Loop ◽

Linear Models ◽

Piecewise Linear ◽

Equilibrium Points ◽

Loop System ◽

State Variables ◽

Flexible Link ◽

Closed Loop System ◽

State Observers

This paper tackles the problem of designing state observers for flexible link mechanisms: An investigation is made on the possibility of employing observers making use of suitable piecewise-linear truncated dynamics models. A general and novel approach is proposed, which provides an objective way of synthesizing observers preventing the instability that may arise from using reduced-order linearized models. The approach leads to the identification of the regions of the domain of the state variables where the linear approximations of the nonlinear model can be considered acceptable. To this purpose, first of all, the stability of the equilibrium points of the closed-loop system is assessed by applying the eigenvalue analysis to appropriate piecewise-linear models. Admittedly, the dynamics of such a closed-loop system is affected by the perturbation of the poles caused by spillover and by the discrepancies between the linearized models of the plant and the one of the observer. Additionally, when nodal elastic displacements and velocities are not bounded in the infinitesimal neighborhoods of the equilibrium points, the difference between the nonlinear model and the locally linearized one is expressed in terms of unstructured uncertainty and stability is assessed through H∞ robust analysis. The method is demonstrated by applying it to a closed-chain flexible link mechanism.

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Output Feedback Control for a Class of Switched Fuzzy Systems

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.536-537.1170 ◽

2014 ◽

Vol 536-537 ◽

pp. 1170-1173

Author(s):

Hong Yang ◽

Huan Huan Lü ◽

Le Zhang

Keyword(s):

Feedback Control ◽

Output Feedback ◽

Fuzzy Systems ◽

Closed Loop ◽

Sufficient Conditions ◽

Output Feedback Control ◽

Loop System ◽

Asymptotically Stable ◽

Closed Loop System ◽

Switching Law

The output feedback control problem is addressed for a class of switched fuzzy Systems. Using multiple Lyapunov function method and switching law, the relevant closed-loop system is asymptotically stable, with the switching law designed to implement the global asymptotic stability. The sufficient conditions to ensure the output feedback asymptotically stable output feedback control of closed-loop system are studied. The sufficient condition is transformed into Linear Matrix Inequality (LMI) problem which are more solvable. Finally, a numerical simulation example is employed to illustrate the effectiveness and the convergence of the design methodologies.

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Accounting for Out-of-Bandwidth Modes in the Assumed Modes Approach: Implications on Colocated Output Feedback Control

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2801270 ◽

1997 ◽

Vol 119 (3) ◽

pp. 390-395 ◽

Cited By ~ 63

Author(s):

R. L. Clark

Keyword(s):

Output Feedback ◽

Closed Loop ◽

Output Feedback Control ◽

Open Loop ◽

Loop System ◽

Closed Loop System ◽

Open Loop System ◽

Low Frequencies ◽

Poles And Zeros ◽

Admissible Functions

Colocated, output feedback is commonly used in the control of reverberant systems. More often than not, the system to be controlled displays high modal density at a moderate frequency, and thus the compliance of the out-of-bandwidth modes significantly influences the performance of the closed-loop system at low frequencies. In the assumed modes approach, the inclusion principle is used to demonstrate that the poles of the dynamic system converge from above when additional admissible functions are used to expand the solution. However, one can also interpret the convergence of the poles in terms of the zeros of the open-loop system. Since colocated inputs and outputs are known to have interlaced poles and zeros, the effect of a modification to the structural impedance locally serves to couple the modes of the system through feedback. The poles of the modified system follow loci defined by the relative location of the open-loop poles and zeros. Thus, as the number of admissible functions used in the series expansion is increased, the interlaced zeros of the colocated plant tend toward the open-loop poles, causing the closed-loop poles to converge from above as predicted by the inclusion principle. The analysis and results presented in this work indicate that the cumulative compliance of the out-of-bandwidth modes and not the modes themselves is required to converge the zeros of the open-loop system and the poles of the closed-loop system.

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Disturbance Observer-Based Control for Trajectory Tracking of a Quadrotor

Electronics ◽

10.3390/electronics9101624 ◽

2020 ◽

Vol 9 (10) ◽

pp. 1624

Author(s):

Sang Wook Ha ◽

Bong Seok Park

Keyword(s):

Trajectory Tracking ◽

Closed Loop ◽

Control Method ◽

Control Strategies ◽

Hierarchical Control ◽

Loop System ◽

Nonlinear Controller ◽

Closed Loop System ◽

External Disturbances ◽

Dynamic Surface

This paper presents a new control approach for the trajectory tracking of a quadrotor in the presence of external disturbances. Unlike in previous studies using hierarchical control strategies, a nonlinear controller is designed by introducing new state transformations that can use Euler angles as virtual control inputs. Thus, the proposed method can eliminate the timescale separation assumption of hierarchical control strategies. To estimate the external disturbances involved in the translational and rotational dynamics of the quadrotor, disturbance observers are developed. Using state transformations and estimates of external disturbances, we design a robust nonlinear controller based on the dynamic surface control method. The stability of the closed-loop system is analyzed without separation into two subsystems. From the Lyapunov stability theory, it is proven that all error signals in the closed-loop system are uniformly ultimately bounded and can be made arbitrarily small. Finally, simulation results are presented to demonstrate the performance of the proposed controller.

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Passive Feedforward Approach to Bilateral Teleoperated Manipulators

10.1115/imece2000-2425 ◽

2000 ◽

Author(s):

Perry Y. Li ◽

Dongjun Lee

Keyword(s):

Work Environment ◽

Internal Energy ◽

Closed Loop ◽

Internal State ◽

Loop System ◽

Closed Loop System ◽

Control Scheme ◽

Control Objective

Abstract A control scheme for linear dynamically similar bilateral teleoperated manipulator system which ensures that the closed loop system is energetically passive is proposed. Energetic passivity implies that the teleoperated manipulator system is safe to interact with, and that the coupling between the system and any strictly passive environment is stable. The control objective is for the two manipulators in the system to behave in unison under the influence of both the operator and the work environment, while maintaining energetic passivity. The dynamics of the system in unison and its response to the operator and work environment can be specified as kinematic and power scalings. To maintain energetic passivity with feedback and feedforward actions, the proposed control makes use of two fictitious internal energy storages. The result is that when the internal state of the storage elements are suitably initialized, the teleoperated manipulator system achieves asymptotic locking even in the presence of external (bounded) forcing from the operator and work environment.

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