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.

Observer and Controller Design Using Time-Varying Gains: Duality and Distinctions

2004 ◽  
Vol 127 (2) ◽  
pp. 267-274
Author(s):  
Vladimir Polotski
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Dual Problem ◽  
Controller Design ◽  
Time Varying ◽  
Feedback Controllers ◽  
Observer Error ◽  
Time Varying Systems ◽  
Error Dynamics ◽  
Time Invariant

Stabilization of linear systems by state feedback is an important problem of the controller design. The design of observers with appropriate error dynamics is a dual problem. This duality leads, at first glance, to the equivalence of the responses in the synthesized systems. This is true for the time-invariant case, but may not hold for time-varying systems. We limit ourselves in this work by the situation when the system itself is time invariant, and only the gains are time varying. The possibility of assigning a rapidly decaying response without peaking is analyzed. The solution of this problem for observers using time-varying gains is presented. Then we show that this result cannot be obtained for state feedback controllers. We also analyze the conditions under which the observer error dynamics and the response of the closed loop time-varying controllers are equivalent. Finally we compare our results to recently proposed observer converging in finite time and Riccati-based continuous observer with limited overshoots.

Floquet Experimental Modal Analysis for System Identification of Linear Time-Periodic Systems

2007 ◽  
Author(s):  
Matthew S. Allen
Keyword(s):  
System Identification ◽  
Linear Time ◽  
Time Varying ◽  
Response Model ◽  
State Matrix ◽  
Linear Time Invariant ◽  
Response Data ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Periodic

A variety of systems can be faithfully modeled as linear with coefficients that vary periodically with time or Linear Time-Periodic (LTP). Examples include anisotropic rotorbearing systems, wind turbines, satellite systems, etc… A number of powerful techniques have been presented in the past few decades, so that one might expect to model or control an LTP system with relative ease compared to time varying systems in general. However, few, if any, methods exist for experimentally characterizing LTP systems. This work seeks to produce a set of tools that can be used to characterize LTP systems completely through experiment. While such an approach is commonplace for LTI systems, all current methods for time varying systems require either that the system parameters vary slowly with time or else simply identify a few parameters of a pre-defined model to response data. A previous work presented two methods by which system identification techniques for linear time invariant (LTI) systems could be used to identify a response model for an LTP system from free response data. One of these allows the system’s model order to be determined exactly as if the system were linear time-invariant. This work presents a means whereby the response model identified in the previous work can be used to generate the full state transition matrix and the underlying time varying state matrix from an identified LTP response model and illustrates the entire system-identification process using simulated response data for a Jeffcott rotor in anisotropic bearings.

Robust Adaptive Controllers for Interconnected Mechanical Systems: Influence of Types of Interconnections on Time-Invariant and Time-Varying Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 456-473 ◽  
Author(s):  
Sunil K. Singh ◽  
Lin Shi
Keyword(s):  
State Space ◽  
High Speed ◽  
Linear Time ◽  
Direct Method ◽  
Time Varying ◽  
Adaptive Controllers ◽  
First Order ◽  
Time Varying Systems ◽  
Robust Adaptive ◽  
Time Invariant

We investigate robust adaptive controller designs for interconnected systems when no exact knowledge about the structure of the nonlinear interconnections between various subsystems is available. In this study, we concentrate on several different types of systems. We deal with both linear time-invariant (LTI) and linear time-varying (LTV) systems with nonlinear interconnections. For LTI systems, we examine the following types of interconnections: • interconnections that are bounded by first order polynomials in state space; • slowly time varying interconnections; • interconnections bounded by higher-order polynomials in state-space together with input channel interconnections. For LTV systems we deal with interconnections bounded by first-order polynomials in state space. We show that the nature of the nonlinear interactions influences the adaptation laws. We use the direct method of Lyapunov for the design of adaptive controllers for tracking in such systems. We investigate issues such as stability, transient performance and steady-state errors, and derive quantitative estimates and analytical bounds for various different adaptive controllers. For time-varying systems, we analyze the effect of the time variations of parameters and interactions and propose a modified adaptive control scheme with better performance. Simulation results are presented to validate our conclusions. We also investigate these results experimentally on a two-link robot manipulator. Experimental results validate theoretical conclusions and demonstrate the usefulness of such robust adaptive controllers for high-speed motions in uncertain systems.

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