Homogeneous High Order Sliding Mode design: A Lyapunov approach

168

154

Summary In this paper, we provide a new nonconservative upper bound for the settling time of a class of fixed‐time stable systems. To expose the value and the applicability of this result, we present four main contributions. First, we revisit the well‐known class of fixed‐time stable systems, to show the conservatism of the classical upper estimate of its settling time. Second, we provide the smallest constant that the uniformly upper bounds the settling time of any trajectory of the system under consideration. Third, introducing a slight modification of the previous class of fixed‐time systems, we propose a new predefined‐time convergent algorithm where the least upper bound of the settling time is set a priori as a parameter of the system. At last, we design a class of predefined‐time controllers for first‐ and second‐order systems based on the exposed stability analysis. Simulation results highlight the performance of the proposed scheme regarding settling time estimation compared to existing methods.

Section: Resultsmentioning

confidence: 99%

Enhancing the settling time estimation of a class of fixed‐time stable systems

Aldana‐López

Gómez‐Gutiérrez

Jiménez‐Rodríguez

et al. 2019

168

154

“…It means states q e and ω e can converge to a certain residual set D 1 in a fixed time T 2 . D 1 and T 2 , which are independent of initial values of q e or ω e , are related to the control parameters , and will be given in the proof of this theorem . Proof See Appendix B. Remark The sign function sign(·) is explicitly introduced in some adaptive attitude controllers and some finite‐time controllers, which results in the chattering problem inevitably. Although a saturation function or a boundary layer can be applied to weaken the effect of chattering in the practical engineering, its proof of finite‐time stability is difficult.…”

Section: New Fixed‐time Attitude Controllers Design Based On Adding‐amentioning

confidence: 99%

“…▪ Remark 3. The sign function sign(⋅) is explicitly introduced in some adaptive attitude controllers 24,26 and some finite-time controllers, [34][35][36][37] which results in the chattering problem inevitably. Although a saturation function or a boundary layer can be applied to weaken the effect of chattering in the practical engineering, its proof of finite-time stability is difficult.…”

Section: Adaptive Fixed-time Attitude Controller Design With Externalmentioning

confidence: 99%

“…Compared with most of the existing fixed‐time attitude controllers that are designed based on the TSMC, such as those in References , the two proposed fixed‐time controllers are designed based on the AAPIC. In comparison with the research results related to finite‐time attitude control, such as those in , this study further considers the case where external disturbance and thruster faults exist. Moreover, compared with many discontinuous finite‐time controllers, the two proposed controllers are continuous.…”

Section: Introductionmentioning

confidence: 99%

“…(3) In comparison with the research results related to finite-time attitude control, such as those in 12,13,28-31, this study further considers the case where external disturbance and thruster faults exist. Moreover, compared with many discontinuous finite-time controllers, [34][35][36][37] the two proposed controllers are continuous.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Fixed‐time attitude tracking control for spacecraft based on adding power integrator technique

Jiang

Hou

et al. 2020

Summary In this article, the fixed‐time attitude tracking problem for rigid spacecraft is investigated based on the adding‐a‐power‐integrator control technique. First, a fixed‐time attitude tracking controller is designed to guarantee fixed‐time convergence of tracking errors. Then, by considering the presence of random disturbance and actuator faults, an adaptive fault‐tolerant attitude tracking controller is designed to guarantee tracking errors converge to a residual set of zero in a fixed time. The complete bounds on settling time are derived independently of initial conditions. The simulation results illustrate the highly precise and robust attitude control performance obtained by using the proposed controllers.

When is it reasonable to implement the discontinuous sliding‐mode controllers instead of the continuous ones? Frequency domain criteria

Pérez‐Ventura

Fridman

2018

Summary Professor Utkin proposed an example showing that the amplitude of chattering caused by the presence of parasitic dynamics (stable actuators) in some systems governed by the First‐Order Sliding‐Mode Controller is lower than that produced by the Super‐Twisting Algorithm. This example served to motivate this paper reconsidering the problem of comparison of chattering in systems with stable actuators, and driven by Discontinuous Sliding‐Mode Controllers (DSMCs) and Continuous Sliding‐Mode Controllers (CSMCs). Comparison of chattering produced by DSMC and CSMC taking into account their amplitudes, frequencies, and average power (AP) needed to maintain the system into real‐sliding modes, allowing to conclude the following: (i) for systems with slow actuators, the amplitude of oscillations and AP produced by DSMC be smaller than those caused by CSMC; (ii) for bounded disturbances with fixed Lipschitz constant, there exist sufficiently fast actuators for which the amplitude of oscillations and AP produced by CSMC be smaller than those caused by DSMC.