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.

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.

Force Control of a Distributed-Parameter Flexible Arm via Parallel Compensation

2011 ◽  
Vol 201-203 ◽  
pp. 1898-1906
Author(s):  
Liang Yih Liu ◽  
Hsiung Cheng Lin
Keyword(s):  
Contact Force ◽  
Force Control ◽  
Stable Condition ◽  
Joint Torque ◽  
Distributed Parameter ◽  
Dimensional System ◽  
Minimum Phase ◽  
Force Output ◽  
Integral Control ◽  
Flexible Arm

In this paper, the force control of a constrained one-link flexible arm is fully studied based on a linear distributed parameter model, including the internal damping of Kelvin-Voight type. A new input induced by the joint angular acceleration and a virtual contact force output generated by a parallel compensator are defined. The inherent limitations due to the non-minimum phase nature of the noncollocation from the joint torque input and the tip contact force output can be thus resolved. Therefore, the transfer function from the new input to the virtual contact force is not only driven to a strictly minimum phase but also stable condition. The integral control is then used to improve the performance of the overall closed loop system. Also, the asymptotic tracking of a desired contact force trajectory can be achieved with the internal stability. On the other hand, the exact solutions in the infinite-dimensional system are reached using the infinite product formulation. Numerical performance results are provided to verify the effectiveness of the proposed approach in term of fast, stable and robust performance.

Tip-contact force control of a single-link flexible arm using feedback and parallel compensation approach

Robotica ◽  
2013 ◽  
Vol 31 (5) ◽  
pp. 825-835 ◽  
Author(s):  
Liang-Yih Liu ◽  
Hsiung-Cheng Lin
Keyword(s):  
Contact Force ◽  
Force Control ◽  
Infinite Product ◽  
Stable Condition ◽  
Joint Torque ◽  
Dimensional System ◽  
Minimum Phase ◽  
Force Output ◽  
Parameter Uncertainties ◽  
Flexible Arm

SUMMARYIn this paper, the force control of a constrained one-link flexible arm is investigated using a feedback parallel compensation algorithm based on a linear distributed parameter model with internal damping of Kelvin–Voigt type. Generally, the non-collocation of the joint torque input and the tip contact force output comes along with the non-minimum phase in nature. To overcome this inherent limitation, a new input induced by the measurement of root-bending moment and its derivative, and a virtual contact force output generated by a parallel compensator are defined. Therefore, the transfer function from the new input to the virtual contact force output is proved not only strictly minimum phase but also in a stable condition. A PD controller then improves the performance of the overall closed-loop system. Furthermore, the perfect asymptotic tracking of a desired contact force trajectory with internal stability can be achieved accurately. The exact solutions of the infinite-dimensional system are obtained using the infinite product formulation. The proposed system promises stability robustness to parameter uncertainties, also free of spillover problems. Numerical simulations are provided to verify the effectiveness of the proposed approach.

Force Control of a Constrained One-Link Flexible Arm with Internal Damping

2011 ◽  
Vol 199-200 ◽  
pp. 147-155
Author(s):  
Liang Yih Liu ◽  
Hsiung Cheng Lin
Keyword(s):  
Contact Force ◽  
Force Control ◽  
Phase Transfer ◽  
Infinite Product ◽  
Joint Torque ◽  
Minimum Phase ◽  
Internal Damping ◽  
Force Output ◽  
Parameter Uncertainties ◽  
Flexible Arm

In this paper, the contact force control of a constrained one-link flexible arm is fully investigated using a linear distributed parameter model including the internal damping of Kelvin-Voight type. To overcome the inherent limitations caused by the non-minimum phase nature of the noncollocation of the joint torque input and the contact force output, a minimum phase transfer function is deduced by using the feedback and the output redefinition. A PD controller is then designed to accomplish the regulation of the contact force. Therefore, asymptotic tracking of a desired contact force trajectory with internal stability can be achieved. With the infinite product of transcendental functions, exact solutions of the noncollocated infinite-dimensional closed-loop force control system can be obtained so that it is free from spillover problems with stability robustness to parameter uncertainties. Numerical simulations are provided to verify the effectiveness of the proposed approach.

A Class of Transfer Functions With Non-Negative Impulse Response

1991 ◽  
Vol 113 (2) ◽  
pp. 313-315 ◽  
Author(s):  
S. Jayasuriya ◽  
M. A. Franchek
Keyword(s):  
Transfer Function ◽  
Impulse Response ◽  
Closed Loop ◽  
Transfer Functions ◽  
Phase Transfer ◽  
Minimum Phase ◽  
Step Input ◽  
Input Disturbance ◽  
Negative Impulse ◽  
Poles And Zeros

Presented in this note is a class of stable, minimum phase transfer functions whose impulse response is non-negative. A simple sufficiency criterion based on the relative locations of the poles and zeros characterizes the class. When the transfer function is in a factored form the sign of its impulse response may either be obtained by inspection or is inconclusive. A need for identifying such transfer functions was recently established by Jayasuriya (1989) who showed that a controller designed on the basis of maximizing a step input disturbance will reject a persistent disturbance bounded by the size of the maximized step if and only if the closed-loop system’s impulse response is of one sign.

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.

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.

Robust Feedback Control of a Baffled Plate via Open-Loop Optimization

2001 ◽  
Vol 124 (1) ◽  
pp. 154-157 ◽  
Author(s):  
P. De Man ◽  
A. Franc¸ois ◽  
A. Preumont
Keyword(s):  
Genetic Algorithm ◽  
Control System ◽  
Transfer Function ◽  
Open Loop ◽  
Displacement Sensor ◽  
Search Procedure ◽  
Loop Optimization ◽  
Loop Transfer Function ◽  
Poles And Zeros ◽  
Siso System

A SISO control system is built by using a volume displacement sensor and a set of actuators driven in parallel with a single amplifier. The actuators location is optimized to achieve an open-loop transfer function which exhibits alternating poles and zeros, as for systems with collocated actuators and sensors; the search procedure uses a genetic algorithm. The ability of a simple lead compensator to control this SISO system is numerically demonstrated.

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