Dynamic Analysis of Noncollocated Flexible Arms and Design of Torque Transmission Mechanisms

1994 ◽  
Vol 116 (2) ◽  
pp. 201-207 ◽  
Author(s):  
Jahng-Hyon Park ◽  
Haruhiko Asada
Keyword(s):  
Closed Loop ◽  
Open Loop ◽  
Design Guidelines ◽  
Phase System ◽  
Nonminimum Phase ◽  
Transmission Mechanisms ◽  
Flexible Arm ◽  
Torque Transmission ◽  
Endpoint Control ◽  
Flexible Arms

A new actuation method for one-link flexible arms is presented. The endpoint control of a flexible arm has been known as a nonminimum phase system due to the noncollocated sensor and actuator. By relocating the actuator near the endpoint, the system can be modified to approximate a minimum phase system. In order to implement this, transmission mechanisms are developed which transform the actuator torque to a combination of force and torque and transmit them to an appropriate point on the arm link. Exact pole-zero configurations are analyzed with regard to the location of the actuation point and the type of actuator used. Guidelines for design of the transmission mechanisms and the actuation points are developed with respect to the operation bandwidth, stability and controllability. A prototype flexible arm is designed based on the design guidelines and open-loop and closed-loop tests are performed to verify the effectiveness.

Passive optimal feedback control of an articulated flexible arm

2020 ◽  
pp. 107754632095676
Author(s):  
Raja Tebbikh ◽  
Hicham Tebbikh ◽  
Sihem Kechida
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Closed Loop ◽  
Open Loop ◽  
Optimal Feedback Control ◽  
Convolution Operators ◽  
High Frequencies ◽  
Zero Initial Condition ◽  
Flexible Arm ◽  
Euler Bernoulli Beam

This article deals with stabilization and optimal control of an articulated flexible arm by a passive approach. This approach is based on the boundary control of the Euler–Bernoulli beam by means of wave-absorbing feedback. Due to the specific propagative properties of the beam, such controls involve long-memory, non-rational convolution operators. Diffusive realizations of these operators are introduced and used for elaborating an original and efficient wave-absorbing feedback control. The globally passive nature of the closed-loop system gives it the unconditional robustness property, even with the parameters uncertainties of the system. This is not the case in active control, where the system is unstable, because the energy of high frequencies is practically uncontrollable. Our contribution comes in the achievement of optimal control by the diffusion equation. The proposed approach is original in considering a non-zero initial condition of the diffusion as an optimization variable. The optimal arm evolution, in a closed loop, is fixed in an open loop by optimizing a criterion whose variable is the initial diffusion condition. The obtained simulation results clearly illustrate the effectiveness and robustness of the optimal diffusive control.

Design of an Actuated Flexible Arm for Improved Vibration Properties

2003 ◽  
Vol 9 (9) ◽  
pp. 1041-1056 ◽  
Author(s):  
M. Moallem ◽  
R. V. Patel ◽  
K. Khorasani
Keyword(s):  
Cost Function ◽  
Dynamic Behavior ◽  
Closed Loop ◽  
Open Loop ◽  
Loop System ◽  
Shape Design ◽  
Closed Loop System ◽  
Structural Shape ◽  
Flexural Mode ◽  
Flexible Arm

In this paper, a multi-objective optimization index is introduced for improving the dynamic behavior of an actuated structurally flexible arm through geometric shape design. The improvement in the dynamic behavior is achieved by defining a vector optimization cost function. This cost function is associated with the frequency of the lowest system zero when joint angles are taken as outputs, the gain sensitivity of open-loop system modes, and the gain sensitivity of the closed-loop system modes at its transmission zeros. Moreover, a general relationship is obtained between the system pole and zero locations. In particular, it is shown that the magnitude of each system zero is smaller than a corresponding flexural mode and thus the smallest zero always occurs before the smallest pole and should therefore be considered in structural shape design. The design method is applied for finding an optimized structural shape for a single-link flexible arm. The optimized link is shown to yield superior robustness and performance characteristics in a closed-loop system when compared to the non-optimized uniform link. Thus, simpler control schemes can be utilized for the optimized flexible-link system compared to the non-optimized case.

Analytical Statistical Study of Linear Parallel Feedforward Compensators for Nonminimum-Phase Systems

2019 ◽  
Author(s):  
Keyvan Noury ◽  
Bingen Yang
Keyword(s):  
Feedback Loop ◽  
Closed Loop ◽  
Controller Design ◽  
Phase System ◽  
Main Concern ◽  
Nonminimum Phase ◽  
Loop Design ◽  
Nonminimum Phase Systems ◽  
Phase Systems ◽  
Feedforward Compensators

Abstract In this work, a new parallel feedforward compensator for the feedback loop of a linear nonminimum-phase system is introduced. Then, analytical statistical arguments between the existing developed methods and the innovated method are brought. The compelling arguments suggest the parallel feedforward compensation with derivative (PFCD) method is a strong method even though at its first survey it seems to be optimistic and not pragmatic. While most of the existing methods offer an optimal integral of squared errors (ISE) for the closed-loop response of the nominal plant, the PFCD offers a finite ISE; in reality, typically, the nominal plant is not of main concern in the controller design and the performance in the presence of mismatch model, noise, and disturbance has priority. In this work, there are several arguments brought to bold the importance of the innovated PFCD design. Also, there is a closed-loop design example to show the PFCD effectiveness in action.

On the Accuracy of End-Point Trajectory Tracking for Flexible Arms by Noncausal Inverse Dynamic Solutions

1991 ◽  
Vol 113 (2) ◽  
pp. 320-324 ◽  
Author(s):  
H. Moulin ◽  
E. Bayo
Keyword(s):  
Flexible Structures ◽  
Open Loop ◽  
Open Loop Control ◽  
Inverse Dynamic ◽  
Element Discretization ◽  
Loop Control ◽  
End Point ◽  
Flexible Arm ◽  
Single Link ◽  
Flexible Arms

The problem of open-loop control of the end-point trajectory of a single-link flexible arm by an inverse dynamic solution is addressed in this paper. A finite element discretization of the system is used to obtain a set of ordinary differential equations describing the motion. Theoretical difficulties pertaining to the inverse problem for flexible structures are exposed, and it is shown that a noncausal solution for the actuating torque enables a tracking of an arbitrary tip displacement with any desired accuracy.

A Neural Network Controller for a Class of Nonlinear Non-Minimum Phase Systems with Application to a Flexible-Link Manipulator

2004 ◽  
Vol 127 (2) ◽  
pp. 289-294 ◽  
Author(s):  
H. A. Talebi ◽  
R. V. Patel ◽  
K. Khorasani
Keyword(s):  
Neural Network ◽  
Explicit Knowledge ◽  
Open Loop ◽  
Flexible Manipulator ◽  
Phase System ◽  
Zero Dynamics ◽  
Practical Case ◽  
Nonminimum Phase ◽  
Neural Network Controller ◽  
Improved Performance

This paper investigates the problem of controlling a nonlinear nonminimum phase system. An output re-definition strategy is first introduced to guarantee stable zero dynamics. This output re-definition scheme is applicable to a class of open-loop stable nonlinear systems whose input–output maps contain nonlinear terms in the output and linear terms in the input. No explicit knowledge about the nonlinearities of the system is required. The nonlinearities of the system are identified by a neural network. The identified neural network model is then used in modifying the zero dynamics of the system. A stable∕anti-stable factorization is performed on the zero dynamics of the system. The new output is re-defined using the neural identifier and the stable part of the zero dynamics. A controller is then designed based on the new output whose zero dynamics are stable and can be inverted. An experimental setup of a single-link flexible manipulator is considered as a practical case study of a nonlinear nonminimum phase system. Experimental results are presented to illustrate the advantages and improved performance of the proposed tracking controller over both linear and nonlinear conventional controllers in the presence of unmodeled dynamics and parameter variations.

Stable Controller Interpolation and Controller Switching for LPV Systems

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Bryan P. Rasmussen ◽  
Young Joon Chang
Keyword(s):  
Closed Loop ◽  
A Priori ◽  
Gain Scheduling ◽  
Phase System ◽  
Closed Loop System ◽  
Linear Parameter Varying ◽  
Nonminimum Phase ◽  
Quadratic Stability ◽  
Critical Design ◽  
Guaranteed Stability

This paper examines the gain-scheduling problem with a particular focus on controller interpolation with guaranteed stability of the nonlinear closed-loop system. For linear parameter varying model representations, a method of interpolating between controllers utilizing the Youla parametrization is proposed. Quadratic stability despite fast scheduling is guaranteed by construction, while the characteristics of individual controllers designed a priori are recovered at critical design points. Methods for reducing the state dimension of the interpolated controller are also given. The capability of the proposed approach to guarantee stability despite arbitrarily fast transitions leads naturally to application to switched linear systems. The efficacy of the method is demonstrated in simulation using a multi-input, multi-output, nonminimum-phase system, while interpolating between two controllers of different sizes and structures.

Electromagnetic Coupling in a dc Motor and Tachometer Assembly

2004 ◽  
Vol 126 (3) ◽  
pp. 684-691 ◽  
Author(s):  
Shorya Awtar ◽  
Kevin C. Craig
Keyword(s):  
Disturbance Rejection ◽  
Closed Loop ◽  
Electromagnetic Coupling ◽  
Dc Motor ◽  
Open Loop ◽  
Conventional Model ◽  
Open Loop System ◽  
Nonminimum Phase ◽  
Motion System ◽  
Loop Bandwidth

This paper presents an enhanced tachometer model that takes into account the effect of electromagnetic coupling that can exist between the actuator and sensor in an integrated dc motor-tachometer assembly, where the conventional model is found to be inadequate. The tachometer dynamics identified in this paper is experimentally verified, and incorporated in the modeling and parameter identification of a motion system that has multiple flexible elements. It is shown that the tachometer dynamics contributes additional nonminimum phase zeros that degrade the servo system performance in terms of closed-loop bandwidth, disturbance rejection and sensitivity to modeling uncertainty. The zeros of the open loop system are found to vary with the geometric parameters of the motor-tachometer assembly. Based on the insight gained by modeling the electromagnetic coupling, methods for eliminating it and its resulting detrimental effects are also suggested.

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