Date of final exam: 02/2001

E-mail: pisano@diee.unica.it

Tutor: Prof.  G. Bartolini, Università di Cagliari

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Second Order Sliding Modes: Theory and Applications   ___________________________________________________________________________________________________________

Advisor:

Prof.  G. Bartolini, Università di Cagliari

Summary of the thesis

This work analyzes a recent development of sliding mode control theory, referred to as the "second order sliding mode approach". The objective of the present thesis is to survey the theoretical background of the second order sliding mode control, mainly developed in the last years, to present several new results, and to show that the second order sliding mode approach may constitute a good alternative. or a possible complement to, other methodologies, developed in other research areas, for solving a wide range of important theoretical and practical problems (stabilization/tracking for nonlinear uncertain systems, control of underactuated systems etc.)

The thesis is divided in two parts, namely, the Part I (Theory) and Part II (Applications).

More specifically, as for the Part I, in Chapter 1 the fundamentals regarding the variable structure control approach are recalled. In the subsequent Chapter 2 the attention is focused on the second order sliding mode (2-SMC) approach, and its main features are described. In Chapter 3 the so-called "Sub-Optimal 2-SMC algorithm" is presented in its original formulation, and a novel continuous-time version, enjoying some better properties, is proposed. Chapter 4 refers to the problem of the discrete-time implementation of 2-SMC control, while in Chapter 5 a new 2-SMC control algorithm is proposed, which enjoys convergence features similar to those of the conventional first-order sliding mode approach and which allows us to solve the global stabilization problem for a class of nonlinear uncertain single-input plants with unmodelled dynamic actuator and which may exhibit, with zero input, finite escape-time phenomena.

In the Second Part, the control of robotic manipulators, induction motors and overhead container cranes is addressed, using the proposed methodologies, in Chapters 6, 7 and 8 respectively. While Chapters 6 and 7 (as well as the Chapters of Part I) contain simulation results only, Chapter 8 contains also some experimental results on a laboratory-sized crane prototype.
 

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