H∞ control of periodic piecewise vibration systems with actuator saturation

In this paper, an H∞ controller with actuator saturation consideration is proposed to attenuate the vibration of periodic piecewise vibration systems. Based on a continuous Lyapunov function with a time-varying Lyapunov matrix, the H∞ performance index of periodic piecewise vibration systems is studied first. On the basis of the obtained H∞ criterion, the conditions of designing a state-feedback active vibration controller are proposed in matrix inequality form with actuator saturation taken into account. Because of the nonconvexity of the conditions, a corresponding algorithm to compute the controller gain is developed as well. A representative numerical example is used to verify the effectiveness of the proposed method.

[1]  Emiliano Rustighi,et al.  Active Control of the Longitudinal-Lateral Vibration of a Shaft-Plate Coupled System , 2012 .

[2]  D. Swanson,et al.  A linear independence method for system identification/secondary path modeling for active control , 2004 .

[3]  Ashok Midha,et al.  Steady-State Response of Periodically Time-Varying Linear Systems, With Application to an Elastic Mechanism , 1995 .

[4]  Kambiz Farhang,et al.  On Efficient Computation of the Steady-State Response of Linear Systems With Periodic Coefficients , 1996 .

[5]  Dierk Schröder,et al.  Control of vibrations in multi-mass systems with locally controlled absorbers , 2001, Autom..

[6]  Bo Hu,et al.  Disturbance attenuation properties of time-controlled switched systems , 2001, J. Frankl. Inst..

[7]  Cheuk Ming Mak,et al.  An active vibration control system with decoupling scheme for linear periodically time-varying systems , 2016 .

[8]  B. Ravindra,et al.  A General Approach in the Design of Active controllers for nonlinear Systems exhibiting Chaos , 2000, Int. J. Bifurc. Chaos.

[9]  Peng Shi,et al.  Stability, ${l}_{2}$ -Gain and Asynchronous ${H}_{{\infty}}$ Control of Discrete-Time Switched Systems With Average Dwell Time , 2009, IEEE Transactions on Automatic Control.

[10]  Zhang Zhi-yi,et al.  Multi-channel Active Vibration Isolation for the Control of Underwater Sound Radiation From A Stiffened Cylindrical Structure: A Numerical Study , 2012 .

[11]  Faryar Jabbari,et al.  Disturbance Attenuation of LPV Systems with Bounded Inputs , 1998 .

[12]  V. Deshmukh,et al.  Control of Dynamic Systems with Time-Periodic Coefficients via the Lyapunov-Floquet Transformation and Backstepping Technique , 2004 .

[13]  James Lam,et al.  Stability, stabilization and L2-gain analysis of periodic piecewise linear systems , 2015, Autom..

[14]  Faryar Jabbari,et al.  Disturbance attenuation for systems with input saturation: An LMI approach , 1999, IEEE Trans. Autom. Control..

[15]  V. Deshmukh,et al.  Order Reduction and Control of Parametrically Excited Dynamical Systems , 2000 .

[16]  S. C. Sinha,et al.  Control of General Dynamic Systems With Periodically Varying Parameters Via Liapunov-Floquet Transformation , 1994 .

[17]  Oleg A. Bobrenkov,et al.  Optimal feedback control strategies for periodic delayed systems , 2014 .

[18]  Faryar Jabbari,et al.  Output feedback controllers for disturbance attenuation with actuator amplitude and rate saturation , 2000, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[19]  James Lam,et al.  Energy-to-peak performance controller design for building via static output feedback under consideration of actuator saturation , 2006 .

[20]  Marco Lovera,et al.  Periodic control of helicopter rotors for attenuation of vibrations in forward flight , 2000, IEEE Trans. Control. Syst. Technol..