scholarly journals Stabilization of Time-Varying System by Controllers with Internal Loop

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yufeng Lu ◽  
Chengkai Shi
Keyword(s):  
Closed Loop ◽  
Time Varying ◽  
Nest Algebra ◽  
Practical Application ◽  
Closed Loop System ◽  
Infinite Dimensional ◽  
Internal Loop ◽  
Stabilizing Controllers ◽  
Strong Stabilization ◽  
Time Varying Systems

We study the concept of stabilization with internal loop for infinite-dimensional discrete time-varying systems in the framework of nest algebra. We originally give a parametrization of all stabilizing controllers with internal loop, and it covers the parametrization of canonical or dual canonical controllers with internal loop obtained before. We show that, in practical application, the controller with internal loop overcomes the awkwardness brought by the extra invertibility condition in the parametrization of the conventional controllers. We also prove that the strong stabilization problem can be completely solved in the closed-loop system with internal loop. Thus the advantage of the controller with internal loop is addressed in the framework of nest algebra.

scholarly journals Stabilization with Internal Loop for Infinite-Dimensional Discrete Time-Varying Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Nai-feng Gan ◽  
Yu-feng LU ◽  
Ting Gong
Keyword(s):  
Transfer Functions ◽  
Necessary Conditions ◽  
Time Varying ◽  
Stabilizing Controller ◽  
Infinite Dimensional ◽  
Internal Loop ◽  
Stabilizing Controllers ◽  
Time Varying Systems ◽  
Sufficient And Necessary Conditions ◽  
Well Posed

The concepts of stabilization with internal loop are analyzed for well-posed transfer functions. We obtain some sufficient and necessary conditions such that a stabilizing controller with internal loop stabilizes plant L. We also analyze two special subclasses of stabilizing controllers with internal loop, called canonical and dual canonical controllers, and show that all stabilizing controllers can be parameterized by a doubly coprime factorization of the original transfer function.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

2012 ◽  
Vol 461 ◽  
pp. 763-767
Author(s):  
Li Fu Wang ◽  
Zhi Kong ◽  
Xin Gang Wang ◽  
Zhao Xia Wu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Closed Loop System ◽  
Overhead Cranes ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Invariant System

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

scholarly journals Learning Input Shaping Technique for Non-LTI Systems

1998 ◽  
Vol 123 (2) ◽  
pp. 288-293 ◽  
Author(s):  
Juyi Park ◽  
Pyung-Hun Chang
Keyword(s):  
Natural Frequency ◽  
Closed Loop ◽  
Industrial Robot ◽  
Loop System ◽  
Input Shaping ◽  
Time Varying ◽  
Closed Loop System ◽  
Shaping Technique ◽  
Time Varying Systems

It is well known that conventional Input Shaping Technique (IST) is not very effective in suppressing residual vibrations for non-LTI systems, such as substantially nonlinear or time-varying systems. In an effort to increase the effectiveness such systems, this paper presents Learning Input Shaping Technique (LIST) which iteratively updates the parameters of IST from previous trials. Simulations are presented for four different cases: (1) when the natural frequency or damping of a system is not estimated well; (2) when a system has time varying vibration; (3) when a system has nonlinear flexibility; and (4) when a closed-loop system includes a saturation element in the loop. LIST is experimented on a six D.O.F industrial robot to evaluate its effectiveness. The results of the simulations and the experiment show that the residual vibrations become considerably smaller as iteration goes on, thereby demonstrating the effectiveness of LIST.

The Implementation of the Minimal Control Synthesis Algorithm on a Web Control Problem

1994 ◽  
Vol 208 (1) ◽  
pp. 53-60 ◽  
Author(s):  
D P Stoten ◽  
M G Dye ◽  
M Webb
Keyword(s):  
Closed Loop ◽  
Control Synthesis ◽  
Time Varying ◽  
Closed Loop System ◽  
Synthesis Algorithm ◽  
Time Varying Parameters ◽  
Transport Control ◽  
Adaptive Control Strategy ◽  
Web Control ◽  
Experimental Comparisons

The minimal control synthesis (MCS) algorithm is an adaptive control strategy that requires no prior knowledge of plant dynamic parameters, and yet is guaranteed to provide global asymptotic stability of the closed-loop system. The purpose of this paper is to present MCS as applied to web tension und transport control a class of plant that has highly non-linear dynamics and time-varying parameters. The plant is difficult to control by conventional methods over its full operating range. A typical example and model of such a plant is presented along with the implementation of MCS. Experimental comparisons of MCS with conventional control benchmarks are provided. It will be seen that MCS significantly outperforms the conventional controller.

Stabilization of Nonlinear Strict-Feedback Systems With Time-Varying Delayed Integrators

2011 ◽  
Author(s):  
Nikolaos Bekiaris-Liberis ◽  
Miroslav Krstic
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Loop System ◽  
Time Varying ◽  
Feedback Systems ◽  
Closed Loop System ◽  
Feedback Form ◽  
Globally Asymptotically Stable ◽  
Strict Feedback

We consider nonlinear systems in the strict-feedback form with simultaneous time-varying input and state delays, for which we design a predictor-based feedback controller. Our design is based on time-varying, infinite-dimensional backstepping transformations that we introduce, to convert the system to a globally asymptotically stable system. The solutions of the closed-loop system in the transformed variables can be found explicitly, which allows us to establish its global asymptotic stability. Based on the invertibility of the backstepping transformation, we prove global asymptotic stability of the closed-loop system in the original variables. Our design is illustrated by a numerical example.

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