Final report intelligent control system

Chapter 1 Controlling Water Level Using Fuzzy PI...3I Modelling of The System...3II Simulation in Matlab...3Chapter 2 Fuzzy Sliding Mode Control of Container Cranes...6I Dynamic Model...

111Equation Chapter 1 Section 1HCMC UNIVERSITY

OF TECHNOLOGY AND EDUCATION

FINAL REPORT INTELLIGENT CONTROL SYSTEM

Mentor: M.Eng Nguyễn Trần Minh Nguyệt

Students: 19101054 – Vũ Đức Hải

19151057 – Trần Vũ Hùng

Ho Chi Minh City, 15/06/2022

Chapter 1 Controlling Water Level Using Fuzzy PI 3

I) Modelling of The System 3

II) Simulation in Matlab 3

Chapter 2 Fuzzy Sliding Mode Control of Container Cranes 6

I) Dynamic Model 6

II) Fuzzy Sliding Mode Controller 7

III) Simulation in Matlab 9

IV) References 12

Chapter 1 Controlling Water Level Using Fuzzy PI I) Modelling of The System

Figure 1 Water Tank

The water tank has the cross section change overtime (depends on the water level) Differential Equation of the system show as 12 and 13

212\* MERGEFORMAT (.)

313\* MERGEFORMAT (.)

h(t) – Water level (cm)

k – ration of pump motor power

CD – hệ số xả

II) Simulation in Matlab

k=300cm3/sec, C = 0.6D

Design Fuzzy PI controller

By using the sugeno interface system The controller has 1 input (setpoint) and 2 outputs (Kp and Ki)

Figure 3 Membership function of input Table 1 Fuzzy rules

PI Parameters

Set point

If (DIEM_LAM_VIEC is RAT_THAP) then (Kp is RAT_THAP)(Ki is RAT_THAP) (1)

If (DIEM_LAM_VIEC is THAP) then (Kp is THAP)(Ki is THAP) (1)

If (DIEM_LAM_VIEC is TRUNG_BINH) then (Kp is TB)(Ki is TB) (1)

If (DIEM_LAM_VIEC is CAO) then (Kp is CAO)(Ki is CAO) (1)

0 100 200 300 400 500 600 0

5

10

15

20

25

30

35

Water Level Set point

Figure 4 Water Level of the tank

In Figure 4, the output of the system (water level) is almost the same as the set point The rise time and settling time is extremely small Although the steady state error is zero, there are a small overshoot at the beginning of each state

0

5

10

15

20

Voltage

Figure 5 The voltage of the pump motor

Chapter 2 Fuzzy Sliding Mode Control of Container Cranes I) Dynamic Model

Figure 6 Container Crane Model

The container crane is physically modelled as Figure 6 in which x is the trolley position along

is the control force applied into the trolley; g is the gravitational acceleration

Assumptions:

The rope for suspending the container from the trolley is massless

The length of the rope is constant during the operation

All frictional elements in the trolley motion can be eliminated

The kinetic energy T and the potential energy U of the two-dimensional system are give as follows:

422Equation Chapter 2 Section 2

525\* MERGEFORMAT (.)

626\* MERGEFORMAT (.)

f = (f , 0) The following Lagrange’s equation is

727\* MERGEFORMAT (.)

Then, the equations of motion are derived as follows:

828\* MERGEFORMAT (.)

929\* MERGEFORMAT (.)

This equation (2.4) and (2.5) can be rewritten as:

10210\* MERGEFORMAT (.) 11211\* MERGEFORMAT (.) Where

II) Fuzzy Sliding Mode Controller

Make an assumption that the first and second derivatives of the trolley reference input are bounded The sliding surface s that combines the trolley motion and the swing dynamics is defined as follows (despite the uncertainly parameters)

12212\* MERGEFORMAT (.)

where k and k are positive constants Finally, the following fuzzy SMC law is given by1 2

13213\* MERGEFORMAT (.)

saturation function sat(s) is defined:

Where sigma is a small positive constant

Fuzzy rule for control gain

Figure 7 Membership function of position error.

Figure 8 Membership function of derivative of position error.

Table 2 Fuzzy rule of gain tunning.

Derivative of Position Error

Position Error

III) Simulation in Matlab

Figure 10 Overall of the system.

Setpoint is 0.5 is the desired distance, another output of the system is the sway angle These 2 outputs are shown in figure 11 and figure 12

0 1 2 3 4 5 6 7 8 9 10

0

0.1

0.2

0.3

0.4

0.5

Position Setpoint

Figure 11 Position of Crane

From figure 11, the output signal (position of crane) do not have overshoot and steady state error is zero Rising time is 3 seconds and settling time is 3.5 seconds

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

Sway Angle

Figure 12 Sway Angle of the crane.

From figure 12, sway angle of the crane has overshoot (6,2%), steady state error is zero Though the settling time is quite long (5 seconds)

0 1 2 3 4 5 6 7 8 9 10 -0.5

-0.4

-0.3

-0.2

-0.1

Sliding Variable

Figure 13 Sliding Variable

IV) References

[1] Fuzzy Sliding Mode Control of Container Cranes - Quang Hieu Ngo*, Ngo Phong Nguyen, Chi Ngon Nguyen, Thanh Hung Tran, and Keum-Shik Hong