Presentation 1 for Project

8/8/2019 Presentation 1 for Project

1/23

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


2/23

Outline

Introduction

Sliding mode control

Integral Sliding Mode Control Problem statement

Work done

Simulation results


3/23

Introduction

Position servo system

Tracking control system

Rotary inverted pendulum


4/23

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.


23/23

Thank You

Presentation 1 for Project

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