In this paper, we consider a class of affine control systems and propose a new structural feedback linearization technique. This relatively simple approach involves a generic linear-type control scheme and follows the classic failure detection methodology. The robust linearization idea proposed in this contribution makes it possible an effective rejection of nonlinearities that belong to a specific class of functions. The nonlinearities under consideration are interpreted here as specific signals that affect the initially given systems dynamics. The implementability and efficiency of the proposed robust control methodology is illustrated via the attitude control of a PVTOL.
AbstractIn this paper, we consider a class of affine control systems and propose a new structural feedback linearization technique. This relatively simple approach involves a generic linear-type control scheme and follows the classic failure detection methodology. The robust linearization idea proposed in this contribution makes it possible an effective rejection of nonlinearities that belong to a specific class of functions. The nonlinearities under consideration are interpreted here as specific signals that affect the initially given systems dynamics. The implementability and efficiency of the proposed robust control methodology is illustrated via the attitude control of a Planar Vertical Take Off Landing (PV-TOL) system. Notation. The following notation is used through this paper.• Script capitals V , W , . . . denote finite dimensional linear spaces with elements v, w, . . .. The expression V ≈ W stands for dim (V ) = dim (W ). Moreover, when V ⊂ W , W V or W /V stands for the quotient space W modulo V . Next, V κ denotes the Cartesian product V × · · · × V (κ times). By X : V → W , we denote a linear transformation operating from V to W . As usually, Im X = X V denotes the image of X and ker X is its kernel. Moreover, X −1 T stands for the inverse image of T ⊂ W . The special subspaces Im B and ker C are denoted by B, and K , respectively. The zero dimension subspace is indicated as 0 and σ {A} denotes the spectrum of the linear transformation A. The identity operator is denoted by I: Ix = x; A 0 is the identity operator, for any given linear transformation A. The matrix of a given linear transformation A : X → X in a given basis is noted as A ∈ R n×n . Additionally, for the elements v, w, . . . ∈
In this paper, we show in detail a synthesis procedure of the control scheme recently proposed in [3]. This control scheme has the advantage of combining the classical linear control techniques with the sophisticated robust control techniques. This control scheme is specially ad hoc for unmanned aircraft vehicles, where it is important not only to reject the actual nonlinearities and the unexpected changes of the structure, but also to look for the simplicity and effectiveness of the control scheme.
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