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Stabilization Control Design for Some Nonlinear Systems Based on Block Diagram

Author: XuZhiMing
Tutor: WangYinHe
School: Shantou University
Course: Applied Mathematics
Keywords: nonlinear systems global stability system block diagram Linear Matrix Inequality input-output coupling absolute stabilization
CLC: O231
Type: Master's thesis
Year: 2007
Downloads: 23
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In the control engineering, a system is usually constituted by many components. And eachcomponent often is described as block diagram to express its function in the system. At thesame time, linearization processing is made to each component in practical engineering tosimplify system analysis and controller design; as a result backlog a series of system transferfunction model block diagrams. But there is a big problem to design controller by the modelafter linearization: the robustness of the close-loop system is not strong enough usually. For thesake of the exaltation of system control quality and keeping the block diagram research result inengineering, consider the neglected nonlinearity and uncertainty as a new block piece to jointhe primitive linear block diagram. Is it possible to look for some more effective controlstrategy to achieve that goal? In such method, in fact, the nonlinear system is decomposed intoa linear part and a nonlinear part. Currently the research in this aspect has already had abundantof results, and the control design about nonlinear systems with nonlinear block is an importantresearch topic of control theories too.As for the study about nonlinear systems with nonlinear block, mainly focus on the system’slinear part is described by state space equation; however, the research results of the systemswhich possess the linear part represented by transfer function block diagram are few.This paper discusses the global stabilize problem on some nonlinear systems, which base onblock diagram, according to Lyapunov stability theory method. The main work shown in thispaper is as follows:First, aim at a class of single-input single-output systems; the global stabilize controllerwhich base on system state variable and output is proposed, and that controller illustrated bydiagram for more detail. Meanwhile, some sufficient conditions about the existence of thesecontrollers are proposed for the system’s nonlinear part placed in a different Cape arearespectively. Finally, made use of the Linear Matrix Inequality method to resolve the algorithmproblem.Second, the research method for single-input single-output systems is expanded to a class of multi-input multi-output coupling systems, and the LMI method is used to present a sufficientcondition to globally stabilize the given system. Finally, one simulation example is provided todemonstrate the influence of nonlinear item upon the system and effectiveness of the proposedmethod.Third, for a class of Lurie control systems which do not satisfy conditions of absolutestability, discuss how to design the feedback matrix or absolute stabilize control law in brief tomake the close-loop system absolutely stable. Finally, the result is giving in the format of LMIvia variable displace method, which can be easily deal with Matlab LMI Toolbox.

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