impulse-ed 2-060417

IMPULSE 2017
DEE, RSET
INTEGRATION OF SC METHODOLOGIES WITH
Fundamentals of SMC
SLIDING MODE CONTROL
The SMC theory was originated in late 1950s in the former USSR, led by Prof. V. I. Utkin and
Prof. S. V. Emelyanov [2] to address specific problems associated with a special class of VSSs,
which are the control systems involving discontinuous control actions.
In the early days of VSS, the research was focused on single-input and single-output systems, and
various well-known methodologies were developed, e.g., the eigen value assignment approach [2],
the Fillipov approach [5], etc. In recent years, the majority of research in SMC has been done with
regard to multiinput and multioutput systems (MIMO), so we will use MIMO system framework
as a platform for discussing the integration of SC methodologies in SMC. Commonly, the MIMO
SMC systems considered are of the form
ẋ˙ = f(x, t) + B(x, t)u + ξ(x, t)
where
x ∈ R n u is the system state vector and ξ(x, t) ∈ Rn represents all the factors that affect the
performance of the control system, such as disturbances and uncertainties in the parameters of the
system.
.It is well known that when this condition (the matching condition) is satisfied, the celebrated
invariance property of SMC stands.
The design procedure of SMC includes two major steps encompassing two main phases of SMC:
1) Reaching phase: where the system state is driven from any initial state to reach the switching
manifolds (the anticipated sliding modes) in finite time;
2) Sliding-mode phase: where the system is induced into the sliding motion on the switching
manifolds, i.e., the switching manifolds become an attractor. These two phases correspond to the
following two main design steps.
1) Switching manifold selection: A set of switching manifolds are selected with prescribed
desirable dynamical characteristics. Common candidates are linear hyper-planes.
2) Discontinuous control design: A discontinuous control strategy is formed to ensure the finite
time reachability of the switching manifolds. The controller may be either local or global,
depending upon specific control requirements.
In the context of the system (1), following the main SMC design steps, the switching manifolds
can be denoted as
s(x) = 0 ∈ Rm, where s = (s1, . . . , sm)T
is characterized by the control structure defined by