In this article, a kind of time-varying H∞ controller, which could be easily obtained by solving linear matrix inequalities, is proposed to attenuate the vibration of periodic piecewise vibration systems. The Lyapunov function with continuous time-varying Lyapunov matrix is adopted to develop a general condition of H∞ performance index for periodic piecewise vibration systems. An H∞ controller with continuous time-varying controller gain is designed to attenuate the system vibration. A numerical example is used to verify the merit of the proposed controller.
BittantiSColaneriP.Periodic systems: filtering and control. New York: Springer, 2008.
2.
KaranamKCSivalingamSAmbatiSR.Modified smith predictor design for unstable processes with step and periodic disturbances. Proc IMechE, Part I: J Systems & Control Engineering2013; 227(2): 146–160.
3.
LiuXCaoJ.Exponential stability of anti-periodic solutions for neural networks with multiple discrete and distributed delays. Proc IMechE, Part I: J Systems & Control Engineering2009; 223(3): 299–308.
4.
WangCChenZSunQet al. Design of PID and ADRC based quadrotor helicopter control system. In: Proceedings of control and decision conference, Yinchuan, China, 28–30 May 2016, pp.5860–5865. New York: IEEE.
5.
RaffoGVOrtegaMGRubioFR. An integral predictive/nonlinear H∞ control structure for a quadrotor helicopter. Oxford: Pergamon Press.
6.
SvobodnyTPRussellDL.Phase identification in linear time-periodic systems. IEEE T Automat Contr1989; 34(2): 218–220.
7.
LiPLamJChenYet al. Stability and -gain analysis of periodic piecewise linear systems. In: Proceedings of American control conference, Chicago, IL, 1–3 July 2015, pp.3509–3514. New York: IEEE.
8.
LiPLamJCheungKC. Generalized performance analysis of periodic piecewise systems. In: Proceedings of Chinese control conference, Hangzhou, China, 28–30 July 2015, pp.77–82. New York: IEEE.
9.
LiPLamJCheungKC.Stability, stabilization and -gain analysis of periodic piecewise linear systems. Automatica2015; 61: 218–226.
10.
XieXLamJLiP.Finite-time H∞ control of periodic piecewise linear systems. Int J Syst Sci2017; 48: 1–12.
11.
SessaVIannelliLVascaFet al. A complementarity approach for the computation of periodic oscillations in piecewise linear systems. Nonlinear Dynam2016; 85(2): 1–19.
12.
AskariHEsmailzadehE. Chaotic and periodic vibration of a carbon nanotube supported by nonlinear foundation. In: Proceedings of IEEE international conference on nanotechnology, Toronto, ON, Canada, 18–21 August 2014, pp.632–635. New York: IEEE.
13.
LiYChenS.Periodic solution and bifurcation of a suspension vibration system by incremental harmonic balance and continuation method. Nonlinear Dynam2016; 83(1–2): 941–950.
14.
KhotSMYelveNPKumarPet al. Implementation of H-infinity controller in experimental active vibration control of a cantilever beam. In: Proceedings of international conference on nascent technologies in engineering (ICNTE), Mumbai, India, 27–28 January 2017, pp.1–5. New York: IEEE.
15.
DeshmukhVS.Control of dynamic systems with time-periodic coefficients via the Lyapunov-Floquet transformation and backstepping technique. J Vib Control2004; 10(10): 1517–1533.
16.
IsidoriAMarconiLSerraniA. Robust nonlinear motion control of a helicopter. In: Proceedings of IEEE conference on decision and control2003; 48: 413–426.
17.
MadaniTBenallegueA. Backstepping control for a quadrotor helicopter. In: Proceedings of IEEE/RSJ international conference on intelligent robots and systems, Beijing, China, 9–15 October 2007, pp.3255–3260. New York: IEEE.
18.
SelstadTJFarhangK.On efficient computation of the steady-state response of linear systems with periodic coefficients. J Vib Acoust1996; 118(3): 522–526.
19.
LiPLamJCheungKC.H∞ control of periodic piecewise vibration systems with actuator saturation. J Vib Control2017; 23(20): 3377–3391.
20.
LiPLamJKwokKWet al. Stability and stabilization of periodic piecewise systems: a polynomial matrix approach. Atutomatica2018; 94: 1–8.
21.
LordN. Theory of differentiation: a unified theory of differentiation via new derivate theorems and new derivatives by Krishna M. Garg. Math Gazette1998; 84(499): 183–184.
