By Alexander Leonessa
This e-book provides a common nonlinear keep watch over layout method for nonlinear doubtful dynamical structures. in particular, a hierarchical nonlinear switching keep an eye on framework is constructed that offers a rigorous replacement to achieve scheduling keep watch over for normal nonlinear doubtful structures. The proposed switching regulate layout framework debts for actuator saturation constraints in addition to process modeling uncertainty. The efficacy of the regulate layout process is largely proven on aeroengine propulsion structures. particularly, dynamic types for rotating stall and surge in axial and centrifugal stream compression structures that lend themselves to the applying of nonlinear keep an eye on layout are built and the hierarchical switching keep an eye on framework is then utilized to regulate the aerodynamic instabilities of rotating stall and surge.
For the researcher who's coming into the sphere of hierarchical switching powerful regulate this ebook offers a plethora of recent learn instructions. however, for researchers already energetic within the box of hierarchical regulate and hybrid platforms, this publication can be utilized as a connection with an important physique of contemporary paintings. in addition, keep watch over practitioners concerned with nonlinear keep an eye on layout can immensely enjoy the novel nonlinear stabilization suggestions provided within the book.
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Extra resources for Hierarchical nonlinear switching control design with applications to propulsion systems
Specifically, constraining the rate at which the dynamics of the switching function A(t) can evolve on the equilibrium manifold, it is possible to address input rate saturation constraints. 24) that a constraint on the rate at which the dynamics of the parameter A(t) can evolve on the equilibrium manifold can be enforced effectively placing a rate constraint on the control u(t). 4, we present an algorithm that outlines the key steps in constructing the hierarchical switching feedback controller.
4a. If no solution exists, )~s(x(t)) is unchanged. 4b. If one solution ~1 exists and p(~l) < p(,~) then switch )~s(x(t)) to )~1. 4c. ). Note that multiple solutions can be avoided by modifying the ca 's. Step 5. 11) holds. ) such that Step 3 is satisfied, can be guaranteed by modifying the first part Step 4 as follows: Step 4'. , search for the solutions of V~(x(tk)) < c~, )~ 9 As. In this case, the switching set S C_ As need not be explicitly defined and is computed online. Furthermore, the case where AT ~ 0 recovers the continuous framework described in this section.
34), ~ x x x=Xs(x) = q(z)vxscz)(z)' it follows that ~'(x) - dp(A)dA As(x) = q(x)vxs(x)~s(x). 41) is immediate. 33). 5. 43) where c : De --~ R l• is an arbitrary row vector such that c(x)vT(x) # O, x E De, A E S. 33). Proof. 43). 33). 43), with c(x) = Vxs(z)(x)M;sl(z)(x, q(x)), x E 7)c, implicitly characterizes the Lagrange multiplier q(x), x E De, since q(x) appears in M;ls(x)(x, q(x)). The next result provides an explicit characterization for the Lagrange multiplier q(x), x E I)c. 6. 45) where ck (x, q(x) ), x E 7)c, k = O, 1,...