The paper presents a dynamic surface fixed-time prescribed performance trajectory tracking control scheme for ball and plate system with input saturation, coupling terms in the system and bounded disturbances. First, a novel fixed-time prescribed performance function is introduced to ensure the output error remains within prescribed performance bounds within a predetermined time. Subsequently, an adaptive neural network approximates the coupling terms and bounded disturbances, ensuring the estimation error of the adaptive law converges within a fixed time. A new dynamic surface fixed-time control scheme without fractional power terms is then designed to ensure fixed-time convergence of the tracking error. Finally, a fixed-time anti-saturation compensator is designed to mitigate the input saturation effects on performance. Lyapunov stability analysis demonstrates that the proposed scheme ensures practical fixed-time stability and guarantees all the upper bound of convergence time are estimated. Simulation results validate the effectiveness of the proposed control scheme.
BechlioulisCPRovithakisGA (2008) Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance. IEEE transactions on Automatic Control53(9): 2090–2099.
2.
CaiTDongZLiuX (2021) On disturbance rejection control for nonlinear three-revolute prismatic spherical ball and plate systems. Advanced Control for Applications: Engineering and Industrial Systems3(2): e62.
3.
CaoSSunLJiangJ, et al. (2021) Reinforcement learning-based fixed-time trajectory tracking control for uncertain robotic manipulators with input saturation. IEEE Transactions on Neural Networks and Learning Systems34(8): 4584–4595.
4.
DengHKrstićM (1997) Stochastic nonlinear stabilization—I: A backstepping design. Systems & Control Letters32(3): 143–150.
5.
FanXZhangNTengS (2004) Trajectory planning and tracking of ball and plate system using hierarchical fuzzy control scheme. Fuzzy Sets and Systems144(2): 297–312.
6.
Gonzalez VillarrealOJRossiterJATsourdosA (2022) An efficient condensing algorithm for fast closed loop dual-mode nonlinear model predictive control. IET Control Theory & Applications16(9): 872–888.
7.
HoráčekP (2000) Laboratory experiments for control theory courses: A survey. Annual Reviews in Control24: 151–162.
8.
JinX (2018) Adaptive fixed-time control for MIMO nonlinear systems with asymmetric output constraints using universal barrier functions. IEEE Transactions on Automatic Control64(7): 3046–3053.
9.
LiGChenXYuJ, et al. (2021) Adaptive neural network-based finite-time impedance control of constrained robotic manipulators with disturbance observer. IEEE Transactions on Circuits and Systems II: Express Briefs69(3): 1412–1416.
10.
LiJYangYHuaC, et al. (2017) Fixed-time backstepping control design for high-order strict-feedback non-linear systems via terminal sliding mode. IET Control Theory & Applications11(8): 1184–1193.
11.
MaQXieY (2024) Adaptive event-triggered fixed-time practical tracking control for uncertain nonlinear systems. IEEE Transactions on Automatic Control69: 5678–5685.
12.
MijaS, et al. (2024) Multiswitching surface based sliding mode controller for a class of underactuated nonlinear systems: With application to ball and plate system. IEEE Transactions on Industrial Electronics71(9): 11326–11337.
13.
PolyakovA (2011) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE transactions on Automatic Control57(8): 2106–2110.
14.
PolyakovA (2012) Fixed-time stabilization of linear systems via sliding mode control. In: 2012 12th international workshop on variable structure systems, Mumbai, India, 12–14 January, pp. 1–6. New York: IEEE.
15.
PolycarpouMM (2002) Stable adaptive neural control scheme for nonlinear systems. IEEE Transactions on Automatic control41(3): 447–451.
16.
QianCLinW (2001) Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Systems & Control Letters42(3): 185–200.
17.
SuiSChenCPTongS (2021) Finite-time adaptive fuzzy prescribed performance control for high-order stochastic nonlinear systems. IEEE Transactions on Fuzzy Systems30(7): 2227–2240.
18.
SunWWuYQSunZY (2020) Command filter-based finite-time adaptive fuzzy control for uncertain nonlinear systems with prescribed performance. IEEE Transactions on Fuzzy Systems28(12): 3161–3170.
19.
SunYChenBLinC, et al. (2016) Adaptive neural control for a class of stochastic nonlinear systems by backstepping approach. Information Sciences369: 748–764.
20.
SwaroopDHedrickJKYipPP, et al. (2000) Dynamic surface control for a class of nonlinear systems. IEEE transactions on automatic control45(10): 1893–1899.
21.
TianYBaiMSuJ (2006) A non-linear switching controller for ball and plate system. International Journal of Modelling, Identification and Control1(3): 177–182.
22.
UdekweDAjayiOoUbadikeO, et al. (2024) Comparing actor-critic deep reinforcement learning controllers for enhanced performance on a ball-and-plate system. Expert systems with applications245: 123055.
23.
WangALiXHeS, et al. (2020) Command-filtering-based adaptive finite-time tracking control for ball and plate system. IFAC-PapersOnLine53(2): 6165–6170.
24.
WangFLaiG (2020) Fixed-time control design for nonlinear uncertain systems via adaptive method. Systems & Control Letters140: 104704.
25.
WangHShiPLiH, et al. (2016) Adaptive neural tracking control for a class of nonlinear systems with dynamic uncertainties. IEEE Transactions on Cybernetics47(10): 3075–3087.
26.
WangWWenC (2010) Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance. Automatica46(12): 2082–2091.
27.
WangYShenZWangQ, et al. (2022) Predictor-based practical fixed-time adaptive sliding mode formation control of a time-varying delayed uncertain fully-actuated surface vessel using RBFNN. ISA transactions125: 166–178.
28.
XuPXiangFLiJ (2022) Design of fixed time backstepping controller for ball and plate system. In: 6th international conference on mechatronics and intelligent robotics (ICMIR2022), Kunming, China, 10 November, pp. 58–67. Bellingham, WA: SPIE.
29.
YangPSuY (2021) Proximate fixed-time prescribed performance tracking control of uncertain robot manipulators. IEEE/ASME Transactions on Mechatronics27(5): 3275–3285.
30.
ZhangZWuY (2019) Further results on fixed-time stabilization and tracking control of a marine surface ship subjected to output constraints. IEEE Transactions on Systems, Man, and Cybernetics: Systems51(9): 5300–5310.
31.
ZhouYYUJLiuJ, et al. (2024) Fixed time impedance control for uncertain manipulator systems with input saturation. Control and Decision39(12): 3919.
32.
ZhuZXiaYFuM (2011) Attitude stabilization of rigid spacecraft with finite-time convergence. International Journal of Robust and Nonlinear Control21(6): 686–702.
