Direct controller designs from plant data

In PID design, an open-loop experiment using pulse input signal is first conducted to generate the process input and output data.. Subsequently, Discrete Fourier Transform is applied to

DIRECT CONTROLLER DESIGNS FROM PLANT DATA

XU BU

B.Sc., BUCT

A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING

DEPARTMENT OF CHEMICAL & BIOMOLECULAR

ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2007

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ACKNOWLEDGMENT

The completion of this thesis is primarily attributed to the keen supervision and constructive direction of my supervisor, Dr Chiu Min-Sen, to whom I feel most grateful His academic excellence and meticulous attitude set an exemplar for my future life

Next I would like to pay thankfulness to my labmates, Mr Yasuki Kansha and Mr Martin Hermanto Mr Kansha provides valuable suggestions on my project, Matlab simulations and the usage of Latex, and Mr Hermanto helps me with my thesis editing Also my thanks to Dr Jia Li (who initiated my originally assigned research), Mr Ye Myint Hlaing and Ankush Ganeshreddy Kalmukale and Ms Yang Xin (who helps finalize the submission) and Imma Nuella

The whole bunch of my friends in Singapore contributed to this project with their encouraging friendship, and thus deserves to be listed here with gratitude Besides those mentioned above, they are: Liu Xiao, Khew Shih Tak, Yin Xiangning, Wang Ke, Wang Likui, Li Jianguo, Tian Xiaoning, Zhou Weihua, Zhang Yi, Dai Taofang, Yao Kexin, Dai Xuexin, Liu Hongyu, Xie Yi, Tan Jing, Zhang Xinhui, Ma Hua, Malik, Sadesh, Ricky Tan, Maxine Lee, Zhang Xingui, Shen Zhigang, etc Lastly, this research was sponsored by NUS Research Scholarship for nine months and by NUS Graduate Student Tutorship for fifteen months The generosity of National University of Singapore and its Department of Chemical and Biomolecular Engineering is appreciated

2.1 Data-based Controller Design Methods 8

CHAPTER 3 DATA-BASED PID CONTROLLER DESIGN 18

3.2 Data-based Design of PID Controller 20

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CHAPTER 4 DATA-BASED INTERNAL MODEL CONTROL DESIGN 58

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SUMMARY

In this study, data-based approaches derived from VRFT framework are developed for PID and IMC controller designs In PID design, an open-loop experiment using pulse input signal is first conducted to generate the process input and output data Subsequently, Discrete Fourier Transform is applied to the process input and output data to obtain their respective frequency responses The frequency responses data thus obtained are then used to approximate a specified reference model

by using an adjustable parameter in the reference model, which is to be determined to provide the best approximation After determination of the optimal parameter in reference model, the PID controller parameters are subsequently obtained through the least square solution Though this method requires less design effort than the conventional two-step model-based PID design methods, extensive simulation results show that the resulting PID controller designed off-line by the proposed method gives comparable or better control performance compared to its model-based counterparts, i.e IMC-PID and Maclaurin-PID controllers, that have been tuned on-line to achieve their respective best control performances

In the proposed data-based IMC design, by using the frequency responses data

as mentioned above, a one-step design procedure for IMC controller is developed Specifically, the parameters of both IMC controller and model are determined simultaneously by solving an optimization problem derived from model-reference problem formulated in the frequency domain Thus, a distinct feature of the proposed IMC design is that a detailed IMC model is not required to design the IMC controller Simulation results show that the proposed IMC controller performs as good as or

T Complementary sensitivity function

W Column vector in Eq (3.10)

X Column vector in Eq (4.13)

~ ~ Matrices used in Eq (3.10)

Adjustable parameter in reference model

m Time delay in IMC process model

Adjustable parameter in IMC-PID and Maclaurin-PID designs

c IMC filter constant

IMC

~ Matrix used in Eq (4.13)

Frequency

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B Bandwidth frequency

Abbreviations

DFT Discrete Fourier Transform

FOPDT First-order-plus-dead-time model IAE Integral absolute error

IFT Iterative feedback tuning

IMC Internal model control

PID Proportional-integral-derivative SOPDT Second-order-plus-dead-time model VRFT Virtual reference feedback tuning

2 s M

4

Figure 2.2 Discrete time feedback system 11

Figure 3.3 Input and output signals from the open-loop test (example

1)

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Figure 3.4 Effect of  on J() (example 1) 28 Figure 3.5 Step responses of the process and two models (example 1) 29 Figure 3.6 Set-point responses of the proposed design and model-

based designs based on a FOPDT model (example 1)

30

Figure 3.7 Set-point responses of the proposed design and

model-based designs model-based on a SOPDT model (example 1)

 (bottom) process noise (example 1)

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Figure 3.11 Output signal from the open-loop test (example 2) 34 Figure 3.12 Effect of  on J() (example 2) 35

Figure 3.15 Set-point responses of the proposed design and

model-based designs model-based on a SOPDT model (example 2)

 (bottom) process noise (example 2)

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Figure 3.19 Output signal from the open-loop test (example 3) 40 Figure 3.20 Effect of  on J() (example 3) 41 Figure 3.21 Step responses of the process and two models (example 3) 42 Figure 3.22 Set-point responses of the proposed design and model-

based designs based on a FOPDT model (example 3)

42

Figure 3.23 Set-point responses of the proposed design and

model-based designs model-based on a SOPDT model (example 3)

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Figure 3.24 Set-point responses of the proposed design and

model-based design by Huang (example 3)

 (bottom) process noise (example 3)

46

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Figure 3.28 Set-point responses of the proposed design and

model-based designs model-based on a FOPDT model (example 4)

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Figure 3.29 Set-point responses of the proposed design and

model-based designs model-based on a SOPDT model (example 4)

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Figure 3.30 Set-point responses of the proposed design and

model-based designs model-based on a FOPDT model (example 5)

48

Figure 3.31 Set-point responses of the proposed design and

model-based designs model-based on a SOPDT model (example 5)

49

Figure 3.32 Set-point responses of the proposed design and

model-based designs model-based on a FOPDT model (example 6)

49

Figure 3.33 Set-point responses of the proposed design and

model-based designs model-based on a SOPDT model (example 6)

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Figure 3.34 Set-point responses of the proposed design and

model-based designs model-based on a FOPDT model (example 7)

50

Figure 3.35 Set-point responses of the proposed design and

model-based designs model-based on a SOPDT model (example 7)

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Figure 3.36 Set-point responses of the proposed design and

model-based designs model-based on a FOPDT model (example 8)

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Figure 3.37 Set-point responses of the proposed design and

model-based designs model-based on a SOPDT model (example 8)

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Figure 3.38 Set-point responses of the proposed design and

model-based designs model-based on a FOPDT model (example 9)

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Figure 3.39 Set-point responses of the proposed design and

model-based designs model-based on a SOPDT model (example 9)

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Figure 4.3 Set-point responses of two IMC designs (example 1) 66 Figure 4.4 T(j) for the reference model and IMC system (example

1)

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Figure 4.5 Set-point responses of the proposed design under 5%and

%2

 (bottom) process noise (example 1)

 (bottom) process noise (example 2)

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Figure 4.9 Output signal from the open-loop test (example 3) 72 Figure 4.10 Set-point responses of two IMC designs (example 3) 73 Figure 4.11 T(j) for the reference model and IMC system (example

 (bottom) process noise (example 3)

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Table 4.3 IMC controllers obtained by two design methods (example

3)

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