Robust output feedback regulation of minimum-phase nonlinear systems using conditional integrators☆

Sliding mode control of F-16 longitudinal dynamics

“…Our approach to control design for α is based (see [17]) on minimumphase systems transformable to the normal formη = φ(η, ξ), ξ = A c ξ+B c γ(x) [u−α(x)], y = C c ξ, where x ∈ R n is the state, u the input, ρ is the system's relative degree, ξ ∈ R ρ the output and its derivatives up to order ρ − 1, η ∈ R n−ρ the part of the state corresponding to the internal dynamics, and the triple (A c , B c , C c ) a canonical form representation of a chain of ρ integrators. A SMC design for such a system was carried out in [17], with the assumption that the internal dynamicsη = φ(η, ξ) are input-to-state stable (ISS) with ξ as the driving input.…”

“…Our approach to control design for α is based (see [17]) on minimumphase systems transformable to the normal formη = φ(η, ξ), ξ = A c ξ+B c γ(x) [u−α(x)], y = C c ξ, where x ∈ R n is the state, u the input, ρ is the system's relative degree, ξ ∈ R ρ the output and its derivatives up to order ρ − 1, η ∈ R n−ρ the part of the state corresponding to the internal dynamics, and the triple (A c , B c , C c ) a canonical form representation of a chain of ρ integrators. A SMC design for such a system was carried out in [17], with the assumption that the internal dynamicsη = φ(η, ξ) are input-to-state stable (ISS) with ξ as the driving input. For such systems, it is shown in [17] that a continuous sliding mode controller of the form u = −ksign(γ(x)) sat k 0 σ + k 1 e 1 + k 2 e 2 + · · · + e ρ µ (3) can be designed to achieve robust regulation, where e 1 , ..., e ρ are the tracking error and its derivatives up to order ρ, the positive constants k i , i = 1, · · · , ρ − 1 in the sliding surface function…”

“…The application of SMC to flight control has been pursued by several others authors, see, for example, [5], [6], [19]. Our work differs from earlier ones in that it is based on a recent technique in [17] for introducing integral action in SMC. While we design a nonlinear controller, it is still designed based upon plant linearization.…”

“…It is simply a high-gain PI/PID controller with an "antiwindup" integrator, followed by saturation. This controller structure is a special case of a general design for robust output regulation for multiple-input multiple-output (MIMO) nonlinear systems transformable to the normal form, with analytical results for stability and performance described in [17]. Through simulations, we show the efficacy of the design and that it outperforms a traditional gain-scheduled controller design based on the polynomial approach to model-following design.…”

Time‐scale separation redesign for stabilisation and performance recovery of sampled‐data non‐linear systems

“…Performance recovery of non-linear systems has been studied in [1][2][3][4][5] and references therein. In the series of works by Khalil and co-workers, for example, [1][2][3], an output-feedback controller recovering the performance of a state-feedback controller was designed. Chakrabortty and Arcak [4] provided two different redesign techniques via time-scale separation.…”