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INTEGRATION OF SC METHODOLOGIES
WITH SLIDING MODE CONTROL
RING
Ms. RINU ALICE KOSHY,
ASST.PROFESSOR, DEE
Fundamentals of SMC
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 singleoutput
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