This dissertation presents the analysis and control of water treatment plants using robust control techniques. Simulations show that all controllers can effectively deal with large uncertainties, disturbances and noises in water treatment plants.
Introduction
Reverse osmosis process
Two of the most important technologies are multi-stage flash distillation (MSF) and the RO process (Alatiqi et al., 1999). PID can be used as a standard PID controller or redesigned into a multiple single-input and single-output structure for a more effective control strategy (Alatiqi et al. 1989).
Activated sludge process
The ASM3 model is expected to become the new standard model, correcting many errors that occurred during the use of the ASM1 model (Gujer et al., 1999). Until now, existing ASP regulators have not addressed large variations in influent flow and concentration.
Robust H ∞ and gain scheduling control
Gain planning is one of the most commonly used controller design approaches for nonlinear systems and is widely adopted in industrial applications. With the large variation of the ASP influent flow and the availability of the measurement of this parameter, the robust gain scheduling controller is applied to control the DO concentration in the system.
Robust H ∞ controller
Introduction
Uncertainty modelling
- Unstructured uncertainties
- Parametric uncertainties
- Structured uncertainties
- Linear fractional transformation
Parametric uncertainty is sometimes called "structured uncertainty" since it models uncertainty in a structured way. The total uncertainty block Δ now has two types of uncertainty: s is repeated scalar blocks and f is full blocks.
Stability criterion
- Small gain theorem
- Structured singular value ( ) synthesis brief definition
Note that the small theorem considers the norm of the closed loop system and is therefore independent of the sign of feedback. 7 you can see that |1+L| is the distance from point -1 to the center of the disk representing Lp, which is |WML| is the radius of the disk.
Robustness analysis and controller design
- Forming generalised plant and N - ˆ structure
- Robustness analysis
Ny u is the transfer matrix from u∆ to y∆, Ny w the transfer matrix from w to y∆,Nzu the transfer matrix from u∆ toz and Nzw the transfer matrix from w to z. A system is internally stable if all the transfer functions of the closed-loop system are stable, i.e.
Reduced controller
- Truncation
- Residualization
- Balanced realization
- Optimal Hankel norm approximation
Therefore, it is safe to implement the 7-order controller instead of the full-order one. 15 Closed-loop time responses of the full-order and reduced-order controller: (a) and (b) closed-loop time responses of the full-order and 7th-order controller; (c) and. d) closed-loop time responses of the full-order and 6th-order controller.
Robust gain scheduling controller
- Introduction
- Linear parameter varying (LPV) system
- Matrix Polytope
- Polytope and affine parameter-dependent representation
- Polytope representation
- Affine parameter-dependent representation
- Quadratic stability of LPV systems and quadratic (robust) H ∞ performance
- Robust gain scheduling
- LPV system linearization
- Polytope-based gain scheduling
- LFT-based gain scheduling
The stability of the LTI system can be checked through linear fraction transform (LFT) or linear matrix inequality (LMI). The LPV properties are global, as they concern the behavior of the system along all possible trajectories of (t). In this framework, the parameter is treated as real and must enter the state-space matrices of the LPV plant in an affine way.
Then the closed-loop connection of the resulting LFTs is transformed, again using a lower LFT.
Mixed robust H ∞ and µ-synthesis controller applied for a reverse
RO principles
- Osmosis and reverse osmosis
- Dead-end filtration and cross-flow filtration
Dead-end technique is used in simple filtration processes, where the flow of liquid to be filtered is directed perpendicular to the membrane surface. Some common examples of dead end filtration are home water filters, vacuum cleaners and oil filters in cars. In contrast, there are many processes whose fluids have a high concentration of particles or macromolecules, such as cells, proteins, and precipitates that compact rapidly on the membrane surface when dead-end filtration is used.
In these cases, a cross-flow membrane system provides the means to maintain stable filtration rates and reduce cleaning.
Membranes
- Structure and material
- Hollow fine fiber membrane module
- Spiral wound membrane module
Typically, a single hollow fiber permeator can be used with up to 50 percent recovery and meet the minimum ejection current required to limit concentration polarization. The hollow fiber unit allows a large membrane surface area per unit volume of permeator, resulting in a compact structure. Due to their compact structures, hollow fiber modules require feed water at a lower concentration than the spiral wound module configuration.
Compared to the hollow fiber membrane, the spiral wound membrane works under lower pressure while the recoveries are equal.
Nonlinear RO modelling and analysis
- RO system introduction
- Modelling
- Nonlinear analysis
- Concentration polarization
This model is based on a macroscopic kinetic energy balance and is one of the irreversible thermodynamic models. From the graph of the zero lines it can be deduced whether a system will be bistable or not. It will result in increasing the osmotic pressure, the velocities through two valves and the product water concentration, as well as decreasing the product water flow.
31 illustrates the effects of CP and feed concentration on concentrate flow rate and system performance ratio at steady-state values of the two control inputs.
Water hammer phenomenon
- Water hammer, column separation and vaporous cavitation
- Water hammer analysis and simulation
- Prevention of water hammer effect
The Q2 term is changed to Q|Q| so that the sign of the velocity can be considered. Provided that there is a valve at the end of the permeate tube of an RO system. However, the permeate water in the membrane sheet still flows with velocity up(x,y) at each point of the membrane.
One of the simpler and more effective methods of minimizing water hammer damage is to install the bypass pipe in the current model.
RO linearization
- Nominal linearization
- Uncertainty modeling
- Parametric uncertainty linearization
By applying a Taylor expansion of the right-hand side of Eq. 103), and ignores all higher order terms. The variation of the parameters in Table 2 can be lumped into the WM∆ structure and shown as an input multiplicative uncertainty as in the dashed block in Fig. 40 The Bode plots of uncertainty weighting function WM and lM: (a) WM11 and the set of lM11 in the first channel; (b) WM22 and the set of lM22 in the second channel.
Using the uncertain model of Cm as in Eqs. 112) and (113), the components of the uncertainty matrix are calculated and given in appendix B.
Robust H ∞ controller design for RO system
- Control of uncertain RO system
- Robustness analysis and H ∞ controller design
This type of uncertainty can be modeled at the input (as in this study), output or in parallel of the system. A performance weighting function WP is added to the output of the system to output the performance requirement level. The controller is successfully designed if it can withstand water hammer, noise and uncertainties while meeting robust performance and stability requirements.
In order to apply μ-synthesis to structured uncertainty, a closed-loop transfer matrix connecting a generalized device P to a controller K via a lower linear fractional transform.
Simulation result and discussion
It means that regardless of the values of the parameters in Table 2, the controlled system still functions properly. 46B shows that the system pressure response is less than 0.2 s, which is very fast. As discussed, this transient pressure has a damping wave profile and the magnitude of the first pressure wave is very high.
It happens as a result of the regulator alternately closing and opening the bypass valve in a manner opposite to the value of the transient pressure.
Conclusion
48 it can be observed that although the transient pressure has the wave profile with positive and negative values, the system is effectively regulated. The safest way is to include a pressure reducing valve (PRV) and a check valve in the exhaust pipe. The PRV should be combined with the controlled bypass valve to optimally reduce transient pressure.
The non-return valve allows air to be sucked into the tube under vacuum.
Robust gain scheduling control of activated sludge process
Introduction about activated sludge process
- State variables
- ASM1 processes
- The control problem of activated sludge process
The activated sludge consists of a mixed community of micro-organisms, approximately 59% bacteria and 5% higher organisms such as protozoa, rotifers... The most predominant micro-organisms are aerobic bacteria, which require oxygen for their function. This liquid is then mixed in the aeration system including aeration basin and diffuser to provide the microorganisms with oxygen. At the bottom of the settling tank, the cell mass settles and forms a blanket of activated sludge, separated from clearer water.
The real-time control of the activated sludge faces some complex problems due to the changing nature of the microbiological processes taking place in the bioreactor.
System modelling
The measurement of efficiency is expressed as standard aeration efficiency (SAE), which takes into account the pressure and efficiency of the mechanical equipment required to achieve an oxygen transfer factor. The DO concentrations in the input flow and sludge recirculated flow are considered constant: ci = 2 mg/L and cr = 0. The aeration factor Dfb is normalized varying between 0 and 1, which represents the percentage of the maximum effect of the fine bubble diffused system .
The dynamics of the biomass x and the substrate s in the bioreactor can be described by Cristea et al.
Model linearization
To linearize the process as a controllable system, the recycle stream flow rate is chosen as the second manipulated variable. It is clear that the dynamics of the system changes depending on the parameter qi in the matrix A.
Robust gain-schedule controller design for activated sludge process
From the state-space equation it can be seen that changing the dynamics of the system depends on the variation of qi. In order to formulate the robust criterion for controller design, the clustering of the generalized plant and the controller K is performed by a lower linear fractional transform (LFT) as depicted in Fig. The problem is equal to solving the LFT of the generalized system P and the controller K (see Fig. 57) s.t.
Then, the selected weighting functions are applied in the final stage to synthesize a planned gain controller K, which is optimized for each value of the planned parameter qi, and can be automatically tuned whenever qi changes in the range of his.
Simulation result and discussion
Air flow and RAS flow are controlled by a gain scheduling controller so that the DO concentration remains stable at 2 mg/l under large variations in inlet water flow. It demonstrates that the designed controller can handle feedwater variations over large distances. The first is the response of the DO system without the controller and the second is the one controlled by the designed controller.
Being controlled by the scheduled gain controller, the DO concentration is kept stable at exactly 2 mg/l and the rise time is very short with a slight overshoot.
Conclusion
In the high frequency ranges where measurement noise occurs, the controller is designed so that the value of KS is small to reduce the effects of noise. Therefore, in addition to the ability to eliminate disturbances caused by parameter uncertainty, the controller can also mitigate sensor noises. The simulation result shows that the response is fluctuating, but in very light magnitudes compared to the noise magnitudes.
It can be concluded that most sounds are muted and the operating system is insensitive to sounds.
Observer-based loop-shaping control of anaerobic digestion
- Introduction
- Control problem in anaerobic digestion
- System modelling
- Controller design
- H∞ loop-shaping controller
- Coprime factor uncertainty
- Control synthesis
- Simulation result
- Conclusion
The feed rate can be represented as the dilution rate, which is the ratio between the substrate flow rate and the liquid volume of the digester. This can be explained by the complexity of operation and maintenance of the advanced analyzers or sensors. Robust stability bounds in terms of the H∞ norm are conservative when there are many disturbance blocks at different positions in the AD system.
Assuming that the initial value of real VFA is 60 mmol/l and that of estimated VFA is 30 mmol/l.
Conclusion
Process improvement and energy saving in a full-scale wastewater treatment plant: Air supply regulation by a fuzzy logic system. Mathematical modeling of perfect decoupled control system and its application: An industrial scale reverse osmosis desalination unit. A supervisory control system for optimizing nitrogen removal and aeration energy consumption in wastewater treatment plants.
Total cost minimization control system for the biological wastewater treatment process and its evaluation based on the COST benchmark process.
