By Rama K. Yedavalli
This textbook goals to supply a transparent figuring out of some of the instruments of study and layout for strong balance and function of doubtful dynamic structures. In model-based keep watch over layout and research, mathematical types can by no means thoroughly signify the “real global” process that's being modeled, and therefore it's vital to include and accommodate a degree of uncertainty into the types. This ebook without delay addresses those concerns from a deterministic uncertainty point of view and specializes in the period parameter characterization of doubtful platforms. numerous instruments of research and layout are provided in a consolidated demeanour. This quantity fills a present hole in released works by way of explicitly addressing the topic of keep watch over of dynamic structures from linear kingdom house framework, particularly utilizing a time-domain, matrix-theory established approach.
This ebook also:
Presents and formulates the robustness challenge in a linear nation area version framework.
Illustrates a variety of platforms point methodologies with examples and purposes drawn from aerospace, electric and mechanical engineering.
Provides connections among lyapunov-based matrix process and the move functionality dependent polynomial approaches.
Robust keep an eye on of doubtful Dynamic structures: A Linear nation area Approach is a perfect e-book for first 12 months graduate scholars taking a path in strong keep watch over in aerospace, mechanical, or electric engineering.
Read or Download Robust Control of Uncertain Dynamic Systems: A Linear State Space Approach PDF
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Additional info for Robust Control of Uncertain Dynamic Systems: A Linear State Space Approach
In the matrix approach, the stability of interval parameter matrix family is analyzed directly in the matrix domain using approaches such as Lyapunov theory or other matrix theory-based techniques. In this connection, in what follows we provide a brief review of the literature on the robust stability check of polynomial families. s; q/. i D 1; 2; : : : r/. 4 Problem B Formulation: Given Perturbation Bounds, Checking for Robust Stability 49 Category P1. Independent Coefficients In this case, the coefficients vary independently of each other.
It is also possible to give slightly different conditions for other shapes of parameter space. 28) where Pe D ŒP1 P2 : : : Pr . Reduction in Conservatism by State Transformation The proposed stability robustness measures presented in the previous section were basically derived using the Lyapunov stability theorem, which is known to yield conservative results. One novel feature of the above bounds is that the proposed bound exploits the “structural” information about the perturbation. Clearly, one avenue available to reduce the conservatism of these bounds is to exploit the flexibility available in the construction of the Lyapunov function used in the analysis.
As P will P P . 2 we chose that factorization to be 1P 2 P 0 Ä ˛ Ä 1. i / . One could also allow ˛ to be an arbitrary real number or choose a different value of ˛ for each diagonal element P of . However, our simple factorization seemed to be adequate for the examples considered. The presence of free “balance” parameters in Lyapunov bounds is a common feature of robustness theory [35,36]. p D 1/, all four of the regions (i)–(iv) coincide. Examples. q1 ; q2 / W q1 < 1:75 and q2 < 3 }. Note that the nominal parameter values q1 D q2 D 0 are close to the boundary of the stability region.