SLIDING MODE CONTROL AND ITS APPLICATION

SLIDING MODE CONTROL AND ITS
APPLICATION
Mr.BINDUTESH V SANER
Guided by Prof. B.J PARVAT
Pravara Rural Engineering College, Loni
11/11/2015
Mr.BINDUTESH V SANER SLIDING MODE CONTROL AND ITS APPLICATION

CONTENTS
1. INTRODUCTION
2. SLIDING MODE CONTROL
3. CONCEPT OF SLIDING MODE CONTROL
4. CHATTERING MAIN DRAWBACK
5. CHATTERING REDUCTION METHOD
6. MERITS & DEMERITS
7. DRAWBACK OF SMC
8. SMC IN TRANSLATIONAL TRAJECTOY OF QUADROTOR
9. CONCLUSION
10. REFERENCE

INTRODUCTION
◮ An ideal sliding mode exists only when the system state
satisfies the dynamic equation that governs the sliding mode
for all time. This requires an infinite switching, in general, to
ensure the sliding motion.
◮ The sliding mode control approach is recognized as one of the
efficient tools to design robust controllers for complex
high-order nonlinear dynamic plant operating under
uncertainty conditions.
◮ sliding controller design provides a systematic approach to the
problem of maintaining stability and consistent performance.

CONCEPT OF SLIDING MODE CONTROLLER
Advantage of sliding mode controllers is their insensitivity to
parameter variations and disturbances once in the sliding mode,
there by eliminating the necessity of exact modeling.
The SMC design is composed of two steps.
◮ In the ﬁrst step, a custom-made surface should be designed.
While on the sliding surface, the plants dynamics is restricted
to the equations of the surface and is robust to match plant
uncertainties and external disturbances.
◮ In the second step, a feedback control law should be designed
to provide convergence of a systems trajectory to the sliding
surface; thus, the sliding surface should be obtained in a ﬁnite
time. The systems motion on the sliding surface is called the
sliding mode.

◮ First Step: The first step in SMC is to define the sliding
surface, S(t),
which represents a desired global behavior, such as stability
and tracking performance.
s(t) = (
d
dt
+ λ)
n
t
0
e(t)dt
◮ Second step: once the sliding surface has been selected,
attention must be turned to designing the control law that
drives the controlled variable to its reference value and
satisfies equation
U(t) = Uc(t) + Ud(t)
where
Ud = b−1
[−a1x1 − (c + a2)x2 − n sin(σ)]
◮ The continuous part is given by
Uc(t) = f (x(t), r(t))

Cont...
◮ The continuous part of the controller is obtained by
combining the process model and sliding condition.
The discontinuous part is nonlinear and represents the
switching element of the control law.
◮ The aggressiveness to reach the sliding surface depends on the
control gain but if the controller is too aggressive it can
collaborate with the chattering.
UD(t) = KD
s(t)
| s(t) | +δ

Cont...
sliding mode can be clearly understood by the below ﬁgure

◮ Reaching phase:In this phase a trajectory, starting from a
nonzero initial condition and reach to sliding surface.
◮ Sliding surface:In which the trajectory on reaching the sliding
surface, remains there for all further times and thus evolves
according to the dynamics speciﬁed by the sliding surface.

CHATTERING main drawback of SMC
◮ In theory, the trajectories slide along the switching function.
◮ In practice, there is high frequency switching.
◮ A high-frequency motion called chattering (the states are
repeatedly crossing the surface rather than remaining on it),
so that no ideal sliding mode can occur in practice.
◮ Yet, solutions have been developed to reduce the chattering
and so that the trajectories remain in a small neighborhood
(boundary) of the surface.
Called as chattering because of the sound made by old
mechanical switches.

CHATTERING- REDUCTION
Chattering could be reduced or suppressed using diﬀerent
technique such as,
◮ Non-linear gains
◮ Dynamic extension
◮ Higher order sliding mode control

MERITS & DEMERITS
MERIT
◮ Controller design provides a systematic approach to the
problem of maintaining stability & consistent performance in
the face of modeling imprecision.
◮ Possibility of stabilizing some nonlinear systems which are not
stabilizable by continuous state feedback laws.
◮ Robustness property that is once the system is on sliding
surface then it produced bounded parameter variation and
bounded disturbances.
DEMERITS
◮ The main obstacle to the success of these techniques in the
industrial community is the implementation had an important
drawback that is the actuators had to cope with the high
frequency control actions that could produce premature
wear or even breaking.

What SMC does in quadrotor vehicles?
◮ Sliding mode control was chosen for its ability to stabilize the
platform in the face of unknown modeling errors.
◮ The control scheme operates by forcing an error vector toward
a sliding surface in the state space .
◮ Once on the sliding surface, the vehicles dynamics are deﬁned
by the dynamics of the surface. These dynamics
converge(move towards one point ie. towards sliding surface)
the error vector towards zero.
◮ Sliding modes to control the quadrotor, but computed desired
roll and pitch angles as the controller output instead of
calculating motor speeds.

Depicting the Euler angles of roll (φ), pitch(θ), and yaw(ψ) and
the cartesian co-ordinate frame.
◮ The motors operate in pairs with motors 1 and 3 operating
together and motors 2 and 4 operating together. By varying
the speed of a motor, it is possible to manipulate the
generalized lift force.
◮ Changing the relative speeds of motors 1 and 3 controls the
pitch angle, and consequently creates motion in the x-axis.
◮ Varying the speeds of motors 2 and 4 creates a roll angle
which creates translational motion in the y-axis.
◮ Altitude is controlled by the sum of the forces of all the
motors.
◮ Yaw moment is created from the diﬀerence in the
counter-torques between each pair of motors.

Figure: Quadrotor vehicle(non-linear system)

Model assumption for Quadrotor
For translational motion, the inputs become a desired roll, pitch
and yaw value to create an attitude that translates the quadrotor
to the desired position.
To verify the validity of those assumptions, an estimated model
was computed from groundtruth data to determine the accuracy
and bounds of the parameters in the estimated model.
The estimated model is shown in equation with the calculated
parameters.
ˆx = 10.84(CφSθCψ + SφSψ) − 0.37ˆx + 0.16 (1)
ˆy = −10.49(CφSθCψ − SφCψ) − 0.18ˆy − 0.28 (2)

Chattering eﬀect
When the system is operating near the manifold(s ≈ 0), noise in
the observed quantities causes chatter to result from the function
sign(s). The function is smoothed using the approximation sign(s).
control chatter is evident as shown in Figure.
Figure: Control Response with Chattering

Simulation result
Figure shows where the red line is the desired position/attitude
and the blue line is the simulated position/attitude.

Conclusion
◮ SMC has been an important theoretical research ﬁeld. Today,
it is becoming a good source of solutions to real-world
problems. Its potential is limited only by the imagination of
the people working in process control. Therefore, the
prospects for the application for SMC in the processing
industries are immense.
◮ Main beneﬁts of sliding mode control are the invariance and
quality properties and the ability to minimize the problems
into sub-tasks of lower in balance.
◮ However, it has been shown that imperfections in switching
devices and delays were inducing.

REFERENCES
◮ H. Bouadi, M. Bouchoucha, and M. Tadjine, Sliding mode
control based on backstepping approach for an uav
typequadrotor, International Journal of Applied Mathematics
and Computer Sciences, vol. 4, no. 1, pp. 1217, 2008.
◮ William selby paper on sliding mode control for translational
trajectory following for a quadrotor vehicle 2012
◮ Slotine, J. J., and Li, W., Applied Nonlinear Control,
Englewood Cliﬀs, NJ: Prentice Hall, 1991.

Thank you...!

SLIDING MODE CONTROL AND ITS APPLICATION

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