Output‐feedback tracking in causal nonminimum‐phase nonlinear systems using higher‐order sliding modes

Abstract

SUMMARYAsymptotic output-feedback tracking in a class of causal nonminimum phase uncertain nonlinear systems is addressed via sliding mode techniques. Sliding mode control is proposed for robust stabilization of the output tracking error in the presence of a bounded disturbance. The output reference profile and the unknown input/disturbance are supposed to be described by unknown linear exogenous systems of a given order. Local asymptotic stability of the output tracking error dynamics along with the boundedness of the internal states are proven. The unstable internal states are estimated asymptotically via the proposed multistage observer that is based on the method of extended system center. A higher-order sliding mode observer/differentiator is used for the exact estimation of the input-output states in a finite time. The bounded disturbance is reconstructed asymptotically. A numerical example illustrates the efficiency of the proposed output-feedback tracking approach developed for causal nonminimum phase nonlinear systems.

A new generator of causal ideal internal dynamics for a class of unstable linear differential equations

“…Remark The IID can be also given by using the methods in . The forcing ξ can be piecewise modeled by a linear exosystem with known characteristic polynomial: then can be generated by the following: where the numbers c i are chosen to guarantee desirable eigenvalue placement for the convergence and P i all depend on A − 1 .…”

“…Because A S has three different eigenvalues 0, ± j , rank( A S − λ I ) = 2 for λ = 0, ± j . Because A is nonsingular, the dynamic IID generators proposed in are inapplicable to this example. Similar to in Appendix A.1, L 1 is chosen as .…”

“…The IID can be also given by using the methods in [8,9]. The forcing can be piecewise modeled by a linear exosystem with known characteristic polynomial: P .s/ D m P i D0 p i s i ; then O Á can be generated by the following:…”

“…Because A S has three different eigenvalues 0;˙j , rank.A S I / D 2 for D 0;˙j . Because A is nonsingular, the dynamic IID generators proposed in [8,9] IID O Á converges to the desired IID. In the presence of ", as shown in Figure 4, it is easily observed that the estimated IID can also converge to the desired IID with a small error.…”

“…Nonminimum-phase output tracking is a challenging, real-life control problem that has been extensively studied [2][3][4][5][6]. An important solution to this problem is to identify the state references such that the output tracking problem can be converted into a stabilization problem, which can be solved by using conventional control methods, such as sliding mode control [7][8][9]. State references are composed of output references and internal state references.…”