The document discusses anaerobic wastewater treatment and control systems for maintaining optimal pH levels. It describes anaerobic wastewater treatment using bacteria and the importance of pH for bacterial activity. Proportional-Integral-Derivative (PID) control and Active Disturbance Rejection Control (ADRC) are examined for controlling pH, with ADRC found to provide better performance with faster settling times and less overshoot than PID control. The document presents mathematical models, control system designs, and analyses for pH control of an anaerobic wastewater treatment system.

1. Anaerobic Waste Water
Treatment System
Mrunalini Kannan
2539239
Department of Electrical and Computer Engineering
Cleveland State University
Cleveland, Ohio-44114

2. Anaerobic Waste Water Treatment System
 Anaerobic wastewater treatment is a method for degradation
of organic compounds by utilizing the action of anaerobic
bacterial flora, which grows in wastewater, at an oxygen-free
environment.
 For an anaerobic treatment system, pH is an important
environmental factor that can influence the activity of
anaerobic bacteria.
 In the final anaerobic stage process the methane bacteria need
optimal pH range from 6.8-7.2
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3. pH Control System
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4. Mathematical Model
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5. Frequency Response
Analysis
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6. Frequency Response Analysis
 Methods
 Bode Plot
 Nyquist Plot
 This gives a non-parametric, and model independent
characterization of arbitrary order stabilizing controllers.
 The result shows the frequency response of any stabilizing
controller that must satisfy constraints on its magnitude phase
and rate of change of phase at certain frequencies that are
imposed by the frequency response .
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7. Continuation
Bode Plot Nyquist Plot
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8. Stability Analysis
 The gain margin is 40.0632 and
the phase margin is 91.7172.
 For a system if both gain margin
and phase margin are positive
then the system is said to be
stable.
 The gain margin and phase
margin of the anaerobic
wastewater treatment system is
positive.
 Hence the anaerobic wastewater
treatment system is stable.
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9. Time Response Analysis
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10. PID Control
 Proportional-Integral-Derivative (PID) control offers the simplest yet most
efficient solution to real world control problems.
 A proportional-integral-derivative controller is a generic control loop
feed-back mechanism widely used in industrial control systems.
 PID controller calculates an error value as the difference between a
measured process variable and a desired set-point.
 The proportional, integral and derivative values can be can be interpreted in
terms of time that is P depends on present error, I depend on
accumulation of past errors and D is a prediction of future errors based
on current rate of change.
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11. Continuation
 The popularity of PID controllers is due to their functional simplicity and
reliability.
 They provide robust and reliable performance for most systems if the
PID parameters are determined or tuned to ensure a satisfactory closed-
loop performance.
 The individual effects of these three terms on the closed-loop performance
are summarized.
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12. PID Control
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13. PID Response
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14. Active Disturbance Rejection Control
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15. Estimated Mathematical Model
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17. Estimated Plant-ADRC Response
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18. Estimated Plant-Observer output
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19. Anaerobic Waste Water Treatment System-
Mathematical Model, Parameters
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20. ADRC Design
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21. ADRC Response
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22. Stability Analysis
 The stability is given by closed loop transfer function.
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23. Continuation
 The characteristic Polynomial is
 Coefficients in C(s) and H(s)
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24. Parameters and Transfer Function
 The parameters and the transfer function to see the stability of
the system is shown
 The stability is checked using the bode plot and nyquist plot
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25. Responses/Plots
Bode Nyquist
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26. Stability Analysis
Since the gain margin is positive the
Gm =4.3420
system is stable. The gain cross-over
Pm =97.7024
frequency and the phase crossover
⍵gc =142.8642
frequency are also positive. Hence the
⍵pc =37.7915
system is said to be stable.
From the nyquist plot it could be said that the system is stable.
Hence from the frequency response analysis it
could be said that the system is stable and robust.
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27. ADRC
WHY?
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28. Comparison of PID and ADRC
PID ADRC
 Simplicity  Simple
 Robustness  Robustness against dynamic
variations and external
 Not inherent disturbances
 Covers treatment to both transient  Inherent due to the fact that
and steady state response controller is not dependent on
accurate mathematical model
 Applies to linear systems  Applies generally to non-linear
 Tuning of three values is difficult and time varying systems with
SISO or MIMO
 Has Maximum overshoot  Tuning a single value is easy
 Settles after a long time.  Has comparatively less overshoot
 Settles immediately and has good
settling time
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29. Comparison of PID and ADRC
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30. Conclusion
From the comparative response it
is noted that ADRC has less
overshoot and good settling time
than PID control.
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31. References
 Cascade Control of the PH in an Anaerobic Wastewater Treatment System Kang
Jiayu Wang Mengxiao Mi Linan and Xiao Zhongjun Shannxi University of
Science & Technology Xi’an, China.
 Implementation of Matlab-SIMULINK Based Real Time Temperature Control for
Set Point Changes, Emine Dogru Bolat 5/11/2011
 PID Control System Analysis, Design, and Technology, Kiam Heong Ang, Gregory
Chong, Student Member, IEEE, and Yun Li, Member, IEEE
 16th IEEE International Conference on Control Applications Part of IEEE Multi-
conference on Systems and Control Singapore, 1-3 October 2007, Frequency
Response Analysis of Active Disturbance Rejection Based Control System Gang
Tian1 and Zhiqiang Gao1,2
 Scaling and Bandwidth-Parameterization Based Controller Tuning Zhiqiang Gao
Dept. of Electrical and Computer Engineering Cleveland State University,
Cleveland, Ohio 44115
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