Performance Analysis of Second-Order Sliding-Mode Control Systems With Fast Actuators

The robustness of the second-order sliding-mode control (2-SMC) algorithm known as the "generalized sub-optimal" algorithm is analyzed with respect to the cascade introduction of a linear fast actuator. It is shown that if the actuator dynamics are sufficiently fast then the system trajectories converge to an invariant set that includes the second-order sliding domain s = s' = 0. It is also shown that the size of the invariant set has quadratic dependence with respect to the actuator "small parameter" mu for the sliding variable s, and linear dependence for its derivative s. This means that in the steady state the system trajectories converge to an invariant domain described by the following conditions: |s| les O(mu2) and |s| les O(mu). A simulation example is given to confirm the proposed.

[1]  Leonid Fridman.  Chattering analysis in sliding mode systems with inertial sensors , 2003 .

[2]  I︠a︡. Z. T︠S︡ypkin.  Relay Control Systems , 1985 .

[3]  Gabriele Pannocchia,et al.  Disturbance models for offset‐free model‐predictive control , 2003 .

[4]  Wilfrid Perruquetti,et al.  Higher-order sliding mode stabilization for a class of nonholonomic perturbed systems , 2003, Autom..

[5]  I. Boiko.  Analysis of sliding modes in the frequency domain , 2005 .

[6]  Gabriele Pannocchia,et al.  How to Use Simplified Dynamics in Model Predictive Control of Superfractionators , 2005 .

[7]  Y. ORLOV,et al.  Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems , 2004, SIAM J. Control. Optim..

[8]  Yuri B. Shtessel,et al.  AN ASYMPTOTIC SECOND‐ORDER SMOOTH SLIDING MODE CONTROL , 2003 .

[9]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[10]  A. Levant.  Sliding order and sliding accuracy in sliding mode control , 1993 .

[11]  L. Fridman,et al.  Parameter tuning of second-order sliding mode controllers for linear plants with dynamic actuators , 2006, Autom..

[12]  Leonid M. Fridman,et al.  An averaging approach to chattering , 2001, IEEE Trans. Autom. Control..

[13]  James B. Rawlings,et al.  Constrained linear quadratic regulation , 1998, IEEE Trans. Autom. Control..

[14]  Leonid M. Fridman,et al.  Singularly perturbed analysis of chattering in relay control systems , 2002, IEEE Trans. Autom. Control..

[15]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[16]  James B. Rawlings,et al.  Nonlinear Model Predictive Control: A Tutorial and Survey , 1994 .

[17]  J. Rawlings,et al.  Feasibility issues in linear model predictive control , 1999 .

[18]  Sigurd Skogestad,et al.  Limitations of dynamic matrix control , 1995 .

[19]  Giorgio Bartolini,et al.  Digital second-order sliding mode control for uncertain nonlinear systems , 2001, Autom..

[20]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[21]  James B. Rawlings,et al.  Model predictive control with linear models , 1993 .

[22]  Gabriele Pannocchia,et al.  Robust Disturbance Modeling for Model Predictive Control with Application to Multivariable Ill-conditioned Processes , 2003 .

[23]  Leonid M. Fridman,et al.  Analysis of chattering in continuous sliding-mode controllers , 2005, IEEE Transactions on Automatic Control.

[24]  Yury Orlov,et al.  Switched chattering control vs. backlash/friction phenomena in electrical servo-motors , 2003 .

[25]  Leonid M. Fridman,et al.  Analysis of second-order sliding-mode algorithms in the frequency domain , 2004, IEEE Transactions on Automatic Control.

[26]  Arie Levant,et al.  Homogeneity approach to high-order sliding mode design , 2005, Autom..

[27]  Alessandro Pisano,et al.  Output-feedback control of an underwater vehicle prototype by higher-order sliding modes , 2004, Autom..

[28]  Giorgio Bartolini,et al.  A survey of applications of second-order sliding mode control to mechanical systems , 2003 .

[29]  Antonella Ferrara,et al.  On the convergence properties of a 2-sliding control algorithm for non-linear uncertain systems , 2001 .

[30]  C. R. Cutler,et al.  Dynamic matrix control¿A computer control algorithm , 1979 .

[31]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .