presentation 1 for project
TRANSCRIPT
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Tracking control of position
servo and stabilization of
Rotary Inverted PendulumUsing ISM
Presented by
Jalkote S S
Under the guidance of
Dr. S R Kurode
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Outline
Introduction
Sliding mode control
Integral Sliding Mode Control Problem statement
Work done
Simulation results
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Introduction
Position servo system
Tracking control system
Rotary inverted pendulum
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Sliding mode control
Introduction
Fig. Sliding Mode control
X
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Advantages
oRobust Control
oReduction in order of state equation
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Integral Sliding Mode Control
Above problem can be solved by using ISMC.
To design control law we use the sum of continues
and discontinues control
Consider a system of the form,
Sliding surface is considered as
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Advantages
o In ISMC, the system trajectory always starts from
the sliding surface.
o The order of the motion equation in ISMC is equalto the order of the state space.
o
Robustness of system can be guaranteedthroughout an entire response of the system.
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Problem statement
1. Model of position servo
The plant consists of a D.C. motor.
Fig DC Motor Model
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Transfer Function is
Substituting all constants value
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By using state space representation following
matrices are obtained
,
,
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2. Tracking control problem Tracking control using SM:-
Consider xd as the desired reference such that
Let the sliding surface be
Control u is,
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Tracking control using ISM:-Consider a system of the form,
Sliding surface is considered as
The Integral sliding mode control is of the form
Control u is,
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Work done
In this performance of the controller is tested in
simulation.
For this following are the simulation parameters
o
C
T
matrix chosen wasCT = [-2.2900 -1.0000];
o LQR gain matrix K = [2.9580 0.0868];
o = 0.05 (sigmoid function was used to alleviate chattering);
o Closed loop pole for LQR are-2.2906 + 3.9090i, -2.2906 - 3.9090i;
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o Closed loop pole for SMC is -2.2906;
o Sliding surface matrix G is
G = [0 0.0179];
Figure 1.1 to 1.6 shows simulation results for
stabilisation control with and without disturbance.
Figure 2.1 to 2.6 shows simulation results fortracking control with and without disturbance.
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0 1 2 3 4 5 6 7 8 9 1 0 0
1
2
Time t (sec)
U
(rad/s
ec) U
U-reqd
0 1 2 3 4 5 6 7 8 9 1 0 -5
0
5
Time t (sec)
d
U
/dt(rad/sec)
dU/dt
dU/dt-reqd
0 1 2 3 4 5 6 7 8 9 1 0 -2
0
2
4
Time t (sec)
Control(u)
0 1 2 3 4 5 6 7 8 9 10 0
1
2
Time t (sec)
U
(rad/s
ec) U
U-reqd
0 1 2 3 4 5 6 7 8 9 10 -5
0
5
Time t (sec)
d
U
/dt(rad/sec)
dU/dt
dU/dt-reqd
0 1 2 3 4 5 6 7 8 9 10 -2
0
2
4
Time t (sec)
Control(u)
1. Stabilisation control
1.1 Stabilisation control Using LOR
without disturbance.
1.2 Stabilisation control Using LOR with
disturbance.
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0 5 10 0
0. 5
1
1. 5
Time t (sec)
U
(rad/sec
)
U
U-reqd
0 5 10 -1
0
1
2
Time t (sec)
d
U
/dt(rad/s
ec)
dU/dt
dU/dt-reqd
0 5 10 -0.5
0
0. 5
1
1. 5
Time t (sec)
Control(u)
0 5 10 -0.05
-0.04
-0.03
-0.02
-0.01
0
Time t (sec)
Surface
s
0 5 10 0
0. 5
1
1. 5
Time t (sec)
U
(rad/sec
)
U
U-reqd
0 5 10 -1
0
1
2
3
Time t (sec)
d
U
/dt(rad/s
ec)
dU/dt
dU/dt-reqd
0 5 10 -0.5
0
0. 5
1
1. 5
Time t (sec)
Control(u)
0 5 10 -0.04
-0.02
0
0 .02
Time t (sec)
Surface
s
1.3 Stabilisation control Using SM without
disturbance.
1.4 Stabilisation control Using SM with
disturbance.
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0 1 2 3 4 5 6 7 8 9 10 0
5
10
Time t (sec)
U
(rad/se
c) U
U-reqd
0 1 2 3 4 5 6 7 8 9 10 0
1
2
Time t (sec)
d
U
/dt(rad/sec) dU/dt
dU/dt-reqd
0 1 2 3 4 5 6 7 8 9 10 0
0. 5
1
Time t (sec)
Control(u)
0 1 2 3 4 5 6 7 8 9 10 0
5
10
Time t (sec)
U
(rad/sec
) U
U-reqd
0 1 2 3 4 5 6 7 8 9 10 0
1
2
Time t (sec)
d
U
/dt
(rad/sec)
dU/dt
dU/dt-reqd
0 1 2 3 4 5 6 7 8 9 10 0
0 .5
1
Time t (sec)
Control(u)
2. Tracking control
2.1 Tracking control using LQR without
disturbance
2.2 Tracking control using LQR with
disturbance
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0 5 10 0
5
10
Time t (sec)
U
(rad/sec
)
U
U-reqd
0 5 10 0
0. 5
1
1. 5
Time t (sec)
d
U
/dt(rad/s
ec
)
dU/dt
dU/dt-reqd
0 5 10 0 .55
0. 6
0 .65
0. 7
0 .75
Time t (sec)
Control(u)
0 5 10 0
0 .005
0 .01
0.015
0 .02
Time t (sec)
Surface
s
0 5 10 0
5
10
Time t (sec )
U
(rad/sec
)
U
U-reqd
0 5 10 0
0. 5
1
1. 5
Time t (sec)
d
U
/dt(rad/s
ec
)
dU/dt
dU/dt-reqd
0 5 10 0
0. 2
0. 4
0. 6
0. 8
Time t (sec )
Control(u)
0 5 10 0
0.01
0.02
0.03
0.04
Time t (sec )
Surface
s
2.4 Tracking control using SM with
disturbance.
2.3 Tracking control using SM without
disturbance.
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0 5 10 0
5
10
Time t (sec)
U
(rad/sec)
U
U-reqd
0 5 10 0
0. 5
1
1. 5
Time t (sec)
d
U
/dt(rad/sec)
dU/dt
dU/dt-reqd
0 5 10 0
0. 2
0. 4
0. 6
0. 8
Time t (sec)
Control(u)
0 5 10 -1
-0.5
0
0. 5
1
Time t (sec)
Surface
s
0 5 10 0
5
10
Time t (sec)
U
(rad/sec)
U
U-reqd
0 5 10 0
0. 5
1
1. 5
Time t (sec)
d
U
/dt(rad/se
c)
dU/dt
dU/dt-reqd
0 5 10 0
0. 2
0. 4
0. 6
0. 8
Time t (sec)
Control(u)
0 5 10 0
0 .005
0 .01
0.015
Time t (sec)
Surface
s
2.5 Tracking control using ISM without
disturbance.
2.6 Tracking control using ISM with
disturbance.
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Conclusion
LQR based control gives good results but it requiredmore control efforts than SM control and SMC ismore robust.
It is found from the simulation results that SM isrobust however ISM yields the robustness in theentire state space.
Both stabilisation and tracking control using ISM arebetter in terms of performance and control.
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Future Scope
Real time implementation of the designed controller.
Design and implementation of control for RIP using
ISM.
Validation in simulation and experiment.
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Thank You