Physical systems are often affected by nonlinearities, such as saturation, which leads to the degradation of performance and stability. However, it is lacking of compensation design methods to improve transient performance for finite-time control under input saturation. To address the issue, we propose a new dynamic adjustment compensation (DAC) method for finite-time sliding mode control of linear systems with input saturation. It constructs a dynamic function where a time-varying parameter can be adjusted to enhance transient performance. The method that is applied to modify fast terminal sliding mode control designs yields a new controller that guarantees finite-time stability. An estimate of region of attraction for linear systems with input saturation is obtained by using the induced matrix norm. The advantages of the proposed method are evaluated through some simulation results of the closed loop control system of a Bernoulli air suspension gripper such that the closed-loop system is finite-time stable within the estimated region of attraction with the improved transient performance.
HuQShaoXZhangY, et al. Nussbaum-type function–based attitude control of spacecraft with actuator saturation. Int J Robust Nonlinear Control2018; 28(8): 2927–2949.
3.
ZhaoTLiuYLiZ, et al. Adaptive control and optimization of mobile manipulation subject to input saturation and switching constraints. IEEE Trans Autom Sci Eng2019; 16(4): 1543–1555.
4.
TeelAR.Global stabilization and restricted tracking for multiple integrators with bounded controls. Syst Control Lett1992; 18(3): 165–171.
5.
BhatSPBernsteinDS.Finite-time stability of continuous autonomous systems. SIAM J Control Optim2000; 38(3): 751–766.
6.
DoyleJCFrancisBATannenbaumAR.Feedback control theory. Macmillan Publishing Company, 1992.
NarendraKSTaylorJ.Neural networks for control. Springer, 1990.
9.
SussmannHJSontagEDYangY.A general result on the stabilization of linear systems using bounded controls. IEEE Trans Automat Contr1994; 39(12): 2411–2425.
10.
GaleaniSTarbouriechSTurnerM, et al. A tutorial on modern anti-windup design. Eur J Control2009; 15(3-4): 418–440.
11.
ZaccarianLTeelAR.Modern anti-windup synthesis: control augmentation for actuator saturation. Princeton University Press, 2011.
12.
TarbouriechSTurnerM.Anti-windup design: an overview of some recent advances and open problems. IET Control Theory Appl2009; 3(1): 1–19.
13.
GilbertEGKolmanovskyITanKT.Discrete-time reference governors and the nonlinear control of systems with state and control constraints. Int J Robust Nonlinear Control1995; 5(5): 487–504.
14.
LiYLinZ.Design of saturation-based switching anti-windup gains for the enlargement of the domain of attraction. IEEE Trans Automat Contr2013; 58(7): 1810–1816.
15.
da SilvaJMGOliveiraMZCoutinhoD, et al. Static anti-windup design for a class of nonlinear systems. Int J Robust Nonlinear Control2014; 24(5): 793–810.
16.
Gomes da SilvaJMLonghiMBOliveiraMZ.Dynamic anti-windup design for a class of nonlinear systems. Int J Control2016; 89(12): 2406–2419.
17.
GrimmGHatfieldJPostlethwaiteI, et al. Antiwindup for stable linear systems with input saturation: an LMI-based synthesis. IEEE Trans Automat Contr2003; 48(9): 1509–1525.
18.
us SaqibNRehanMIqbalN, et al. Static antiwindup design for nonlinear parameter varying systems with application to DC motor speed control under nonlinearities and load variations. IEEE Trans Control Syst Technol2018; 26(3): 1091–1098.
FuCTianYHuangH, et al. Finite-time trajectory tracking control for a 12-rotor unmanned aerial vehicle with input saturation. ISA Trans2018; 81(1): 52–62.
21.
HuangDHuangTQinN, et al. Finite-time control for a UAV system based on finite-time disturbance observer. Aerosp Sci Technol2022; 129: 107825.
22.
ShenYHuangY.Uniformly observable and globally lipschitzian nonlinear systems admit global finite-time observers. IEEE Trans Automat Contr2009; 54(11): 2621–2625.
23.
XuH.Finite-time stability analysis: a tutorial survey. Complexity2020; 2020: 1–12.
24.
LiuYLiHLuR, et al. An overview of finite/fixed-time control and its application in engineering systems. IEEE/CAA J Automat Sin2022; 9(12): 2106–2120.
25.
HuangXLinWYangB.Global finite-time stabilization of a class of uncertain nonlinear systems. Automatica2005; 41(5): 881–888.
26.
WangHShiLManZ, et al. Continuous fast nonsingular terminal sliding mode control of automotive electronic throttle systems using finite-time exact observer. IEEE Trans Ind Electron2018; 65(9): 7160–7172.
27.
LiuCLiuY.Adaptive finite-time stabilization for uncertain nonlinear systems with unknown control coefficients. Automatica2023; 149: 110845.
28.
SunZYShaoYChenCC.Fast finite-time stability and its application in adaptive control of high-order nonlinear system. Automatica2019; 106: 339–348.
29.
TianBZuoZYanX, et al. A fixed-time output feedback control scheme for double integrator systems. Automatica2017; 80: 17–24.
30.
ZekraouiSEspitiaNPerruquettiW.Finite/fixed-time stabilization of a chain of integrators with input delay via PDE-based nonlinear backstepping approach. Automatica2023; 155: 111095.
31.
ZhouB.Finite-time stabilization of linear systems by bounded linear time-varying feedback. Automatica2020; 113: 1–11.
32.
ZuoZLiXNingB, et al. Global finite-time stabilization of first-order systems with bounded controls. IEEE Trans Circuits Syst II Express Briefs2023; 70(7): 2440–2444.
33.
SeeberRReichhartingerM.Conditioned super-twisting algorithm for systems with saturated control action. Automatica2020; 116: 108921.
34.
RussoAIncremonaGPCavalloA.Higher-order sliding mode design with bounded integral control generation. Automatica2022; 143: 110430.
35.
ShenHYuXYanH, et al. Robust fixed-time sliding mode attitude control for a 2-DOF helicopter subject to input saturation and prescribed performance. IEEE Trans Transp Electrific2025; 11(1): 1223–1233.
36.
WardDGLinZWardD.An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation. IEEE Trans Automat Contr2002; 47(1): 140–145.
37.
LiYX.Finite time command filtered adaptive fault tolerant control for a class of uncertain nonlinear systems. Automatica2019; 106: 117–123.
