Advanced Sliding Mode Control for Mechanical Systems: Design, Analysis and MATLAB Simulation
2
(VSC) with sliding mode control. During the past decades, VSC and SMC have
generated significant interest in the control research community.
SMC has been applied into general design method being examined for wide
spectrum of system types including nonlinear system, multi-input multi-output
(MIMO) systems, discrete-time models, large-scale and infinite-dimension systems,
and stochastic systems. The most eminent feature of SMC is it is completely
insensitive to parametric uncertainty and external disturbances during sliding
mode
[2]
.
VSC utilizes a high-speed switching control law to achieve two objectives.
Firstly, it drives the nonlinear plant’s state trajectory onto a specified and user-
chosen surface in the state space which is called the sliding or switching surface.
This surface is called the switching surface because a control path has one gain if
the state trajectory of the plant is “above” the surface and a different gain if the
trajectory drops “below” the surface. Secondly, it maintains the plant’s state
trajectory on this surface for all subsequent times. During the process, the control
system’s structure varies from one to another and thereby earning the name
variable structure control. The control is also called as the sliding mode control
[3]
to emphasize the importance of the sliding mode.
Under sliding mode control, the system is designed to drive and then constrain
the system state to lie within a neighborhood of the switching function. Its two
main advantages are (1) the dynamic behavior of the system may be tailored by
the particular choice of switching function, and (2) the closed-loop response
becomes totally insensitive to a particular class of uncertainty. Also, the ability to
specify performance directly makes sliding mode control attractive from the
design perspective.
Trajectory of a system can be stabilized by a sliding mode controller. The
system states “slides” along the line
0s after the initial reaching phase. The
particular 0s surface is chosen because it has desirable reduced-order dynamics
when constrained to it. In this case, the
11
,
s
cx x
0c !
surface corresponds to
the first-order LTI system
11
,
x
cx
which has an exponentially stable origin. Now,
we consider a simple example of the sliding mode controller design as under.
Consider a plant as
() ()Jt ut
T
(1.1)
where
J
is the inertia moment, ()t
T
is the angle signal, and ( )ut is the control
input.
Firstly, we design the sliding mode function as
() () ()
s
tcetet
(1.2)
where
c
must satisfy the Hurwitz condition,
0.c !
The tracking error and its derivative value are
d
() () (),et t t
TT
d
() () ()et t t
TT
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