On the Control of Linear Systems With Pure Time Delay

1965 ◽  
Vol 87 (1) ◽  
pp. 74-80 ◽  
Author(s):  
R. W. Koepcke
Keyword(s):  
Time Delay ◽  
Difference Equation ◽  
Control Systems ◽  
Matrix Elements ◽  
Infinite Dimensional ◽  
Slight Extension ◽  
Recursive Formulas ◽  
Linear Differential ◽  
Control Of Linear Systems ◽  
Stable Control

A synthesis technique is developed for control systems governed by linear differential-difference equations. It is shown that such a system is equivalent to an infinite-dimensional difference equation whose matrix elements can be calculated readily by recursive formulas. From this it takes but a slight extension of present-day procedures to calculate a stable control.

scholarly journals On the Lyapunov equation in Banach spaces and applications to control problems

2002 ◽  
Vol 29 (3) ◽  
pp. 155-166 ◽  
Author(s):  
Vu Ngoc Phat ◽  
Tran Tin Kiet
Keyword(s):  
Control Systems ◽  
Banach Spaces ◽  
Sufficient Conditions ◽  
Lyapunov Equation ◽  
Null Controllability ◽  
Control Problems ◽  
Infinite Dimensional ◽  
Infinite Dimensional Banach Space ◽  
Linear Differential Systems ◽  
Linear Differential

By extending the Lyapunov equationA*Q+QA=−Pto an arbitrary infinite-dimensional Banach space, we give stability conditions for a class of linear differential systems. Relationship between stabilizability and exact null-controllability is established. The result is applied to obtain new sufficient conditions for the stabilizability of a class of nonlinear control systems in Banach spaces.

scholarly journals The Application of an Impedance-Passivity Controller in Haptic Stability Analysis

2021 ◽  
Vol 11 (4) ◽  
pp. 1618
Author(s):  
Ping-Nan Chen ◽  
Yung-Te Chen ◽  
Hsin Hsiu ◽  
Ruei-Jia Chen
Keyword(s):  
Control Systems ◽  
Force Feedback ◽  
Training System ◽  
Considerable Time ◽  
Virtual Training ◽  
Control Gain ◽  
Negative Damping ◽  
The Stability ◽  
Time Required ◽  
Stable Control

This paper proposes a passivity theorem on the basis of energy concepts to study the stability of force feedback in a virtual haptic system. An impedance-passivity controller (IPC) was designed from the two-port network perspective to improve the chief drawback of haptic systems, namely the considerable time required to reach stability if the equipment consumes energy slowly. The proposed IPC can be used to achieve stability through model parameter selection and to obtain control gain. In particular, haptic performance can be improved for extreme cases of high stiffness and negative damping. Furthermore, a virtual training system for one-degree-of-freedom sticking was developed to validate the experimental platform of our IPC. To ensure consistency in the experiment, we designed a specialized mechanical robot to replace human operation. Finally, compared with basic passivity control systems, our IPC could achieve stable control rapidly.

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