By Alexander Leonessa
This e-book offers a basic nonlinear keep an eye on layout technique for nonlinear doubtful dynamical platforms. in particular, a hierarchical nonlinear switching keep an eye on framework is constructed that gives a rigorous replacement to achieve scheduling regulate for common nonlinear doubtful structures. The proposed switching keep an eye on layout framework debts for actuator saturation constraints in addition to process modeling uncertainty. The efficacy of the keep an eye on layout strategy is generally proven on aeroengine propulsion structures. particularly, dynamic types for rotating stall and surge in axial and centrifugal circulation compression structures that lend themselves to the applying of nonlinear keep an eye on layout are built and the hierarchical switching regulate 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 strong keep an eye on this publication presents a plethora of latest examine instructions. then again, for researchers already energetic within the box of hierarchical keep watch over and hybrid structures, this booklet can be utilized as a connection with an important physique of modern paintings. in addition, keep watch over practitioners concerned with nonlinear keep an eye on layout can immensely enjoy the novel nonlinear stabilization concepts awarded within the book.
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Additional info for Hierarchical nonlinear switching control design with applications to propulsion systems
1. To construct the hierarchical switching feedback control dpXs(x(t))(x(t)) , t > O, perform the following steps: Step 1. ) is an arbitrary function of A E Ao. 1} corresponding to the parameter value A. We note that the above parameterization can be constructed using the approaches given in [81, 64, 107]. 6 Inverse Optimal Nonlinear Switching Control 39 Step 2. ). Here, the controllers Ca('), A E As, can be obtained using any appropriate standard linear or nonlinear stabilization scheme. Step 3.
Each robust subcontroller can be nonlinear and thus local set point designs can be nonlinear. Furthermore, for each nominally parameterized equilibrium manifold, the collection of the robust subcontrollers provide guaranteed domains of attraction with nonempty intersections that cover the region of operation over the prescribed range of system uncertainty of the nonlinear uncertain system in the state space. A hierarchical robust switching nonlinear controller architecture is developed based on a generalized lower semicontinuous Lyapunov function obtained by minimizing a potential function, associated with each domain of attraction, over a given switching set induced by the parameterized nominal system equilibria.
Finally, for all t 9 Ix o such that As(x(t)) r O, there exists a finite time T > 0 such that V(x(t + T)) < V(x(t)). Finally, we present the main result of this chapter. 15) guarantees that the closed-loop system trajectories converge to a union of largest invariant sets contained on the boundary of intersections over finite intervals of the closure of the generalized Lyapunov level surfaces. In addition, if the scheduling set S is homeomorphic to an interval on the real line and/or consists of only isolated points, then the hierarchical switching nonlinear controller establishes robust asymptotic stability of the compact positively invariant set A;o.