Systems, Man & Cybernetics - April 2017 - 31
by Xinghuo Yu and Okyay Kaynak
Sliding
Mode Control
Made Smarter
A Computational Intelligence
Perspective
©ISTOCKPHOTO.COM/PIXTUM
S
liding mode control (SMC) is a well-known
control method that has been widely studied
and applied for more than 50 years since its
inception in the late 1950s [1], [2]. While its
simplicity in methodology and robustness
against certain uncertainties and disturbances are celebrated, its shortcomings, such as chattering and brutalness
of control forces, are also well documented. Computational
intelligence (CI) techniques, such as neural networks
(NNs), fuzzy systems (FSs), and evolutionary computation
(EC), can provide means to help overcome the shortcomings. This article introduces the basic concepts and principles of SMC, shows how CI techniques can be tailored to
make SMC smarter (in the sense of reducing chattering and
control brutalness), and speculates on the future of SMC.
SMC's key design steps are as follows:
1) choose an appropriate sliding manifold representing the
desired control
2) design a discontinuous control to force the system state
to reach the manifold and stay in it thereafter.
The consequence of following this design is that the
controlled system goes through two modes: the reaching
phase before the system state enters the sliding manifold
and the sliding mode phase, where the system state is
forced to stay in the sliding mode after the reaching phase.
Digital Object Identifier 10.1109/MSMC.2017.2663559
Date of publication: 18 April 2017
2333-942X/17©2017IEEE
There is another kind of discontinuous control, called
the switched control system, which should not be confused
with SMC [3]. In this control, the switching manifold is not
intended to become the sliding manifold in that the system
state will leave the manifold immediately after reaching it
under another control.
To illustrate the SMC design philosophy, let us consider
the following controllable single-input and single-output
control system:
xo = f ^ x h + b (x) u + z (x, t) + d (t)
y = g ^ x h,
(1)
where x ! R n is the system state, u ! R 1 is the control,
y ! R 1 is the output, f ^ x h, b ^ x h, and g ^ x h are continuous, b ^ x h ! 0 b ^ x h ! 0, z ^ x, t h represents system un certainties, and d ^ t h stands for external disturbances.
Here, Rn and R1 stand for state spaces of n and 1 dimensions, respectively.
The simplicity lies in the discontinuous control
structure. Let us consider a binary switching control:
u=(
u + ^ x, t h s ^ x h 2 0
,
u - ^ x, t h s ^ x h # 0
(2)
where u + ^ x, t h ! u - ^ x, t h . In this case, we can see that
system (1) becomes
Ap ri l 2017
IEEE SyStEmS, man, & CybErnEtICS magazInE
31
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Table of Contents for the Digital Edition of Systems, Man & Cybernetics - April 2017
Systems, Man & Cybernetics - April 2017 - Cover1
Systems, Man & Cybernetics - April 2017 - Cover2
Systems, Man & Cybernetics - April 2017 - 1
Systems, Man & Cybernetics - April 2017 - 2
Systems, Man & Cybernetics - April 2017 - 3
Systems, Man & Cybernetics - April 2017 - 4
Systems, Man & Cybernetics - April 2017 - 5
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Systems, Man & Cybernetics - April 2017 - Cover3
Systems, Man & Cybernetics - April 2017 - Cover4
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