VSC of the third order systems with state and input signal constraints

In this paper the design of a time-varying switching plane for the sliding mode control of the third order system subject to velocity, acceleration and input signal constraints is considered. Initially, the plane passes through the system representative point in the error state space and then it moves with a constant velocity to the origin of the space. Having reached the origin the plane stops moving and remains fixed. The plane parameters (determining angles of inclination and the velocity of its motion) are selected to ensure the minimum integral absolute error (IAE) without violating velocity, acceleration and input signal constraints simultaneously. The switching plane is chosen in such a way that the reaching phase is eliminated, insensitivity of the system with reference to the external disturbances and the model uncertainty is guaranteed from the very beginning of the proposed control action and fast, monotonic error convergence to zero is achieved.

[1]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[2]  R. Decarlo,et al.  Variable structure control of nonlinear multivariable systems: a tutorial , 1988, Proc. IEEE.

[3]  Seung-Bok Choi,et al.  Moving switching surfaces for robust control of second-order variable structure systems , 1993 .

[4]  John Y. Hung,et al.  Variable structure control: a survey , 1993, IEEE Trans. Ind. Electron..

[5]  Seung-Bok Choi,et al.  A time-varying sliding surface for fast and robust tracking control of second-order uncertain systems , 1994, Autom..

[6]  Andrzej Bartoszewicz,et al.  A comment on 'A time-varying sliding surface for fast and robust tracking control of second-order uncertain systems' , 1995, Autom..

[7]  Andrzej Bartoszewicz,et al.  Time-varying sliding modes for second-order systems , 1996 .

[8]  H. Temeltas.  A fuzzy adaptation technique for sliding mode controllers , 1998, IEEE International Symposium on Industrial Electronics. Proceedings. ISIE'98 (Cat. No.98TH8357).

[9]  Hugh F. Durrant-Whyte,et al.  Fuzzy moving sliding mode control with application to robotic manipulators , 1999, Autom..

[10]  M Güzelkaya,et al.  A new design method for sliding mode controllers using a linear time-varying sliding surface , 2002 .

[11]  Gérard-André Capolino,et al.  A time-varying sliding surface for robust position control of a DC motor drive , 2002, IEEE Trans. Ind. Electron..

[12]  Müjde Güzelkaya,et al.  Design of a sliding mode controller with a nonlinear time-varying sliding surface , 2003 .

[13]  Andrzej Bartoszewicz,et al.  Switching Plane Design for the Sliding Mode Control of Systems with Elastic Input Constraints , 2005 .

[14]  Andrzej Bartoszewicz,et al.  Reaching phase elimination in variable structure control of the third order system with state constraints , 2006, Kybernetika.