OPTIMAL REAL-TIME CONTROL OF SEWER NETWORKS

ABSTRACT

During the last decades an increased interest for the protection of the environment from everything that could lead to its downgrading and destruction is observed. The development of a control system for combined sewer networks has as a goal the protection of the quality of waters that receive the outflows of the networks. A multilayer control structure that consists of three control layers (adaptation, optimization and direct control) may be used for the control of a combined sewer network. With regard to the optimization layer, several approaches have been proposed in the past. This thesis is focused on the development and comparison of two methods for the optimization layer, namely the nonlinear optimal control and the multivariable feedback control method. The main goal of this thesis is the development, application and simulation testing of a control system for central sewer network flow control.

In nonlinear optimal control the main control objectives and the secondary operational objectives of sewer network control are considered directly via formulation of a nonlinear cost function that is minimized taking into account the state equation and the constraints. The application of the rolling horizon method is used for the real-time application of the optimal control algorithm with updated inflow predictions and updated initial conditions. The linear multivariable feedback regulator with and without feedforward terms (for the predictions of external inflows) is developed via a systematic design procedure. This linear-quadratic design procedure includes precise specifications on model structure, model equations, nominal steady-state choice, and quadratic criterion choice.

A comparison between both control methods, that was made on the basis of their respective control results for the real large-scale sewer network located at the river Obere Iller in Bavaria (Germany), indicated that optimization with rolling horizon and multivariable regulators with and without feedforward terms deliver almost equivalent control results for the particular sewer network control problem and the investigated scenarios. This study was the basis for the implementation of these control strategies to the particular sewer network.

TABLE OF CONTENTS

ACKNOWLEDGEMENTS
CURRICULUM VITAE
ABSTRACT
CHAPTER 1. INTRODUCTION
CHAPTER 2. MODELING OF SEWER NETWORKS
   2.1 Introduction
   2.2 Accurate model of sewer networks
     2.2.1 Link elements
     2.2.2 Reservoirs
     2.2.3 Control gates
     2.2.4 Nodes
     2.2.5 External inflows
     2.2.6 Treatment plants
   2.3 Simulation program - KANSIM
     2.3.1 Link elements
     2.3.2 Reservoirs
     2.3.3 Control gates
     2.3.4 Nodes
     2.3.5 External inflows
     2.3.6 Treatment plants
   2.4 Simplified model of sewer networks
     2.4.1 Link elements
     2.4.2 Reservoirs
     2.4.3 Nodes
     2.4.4 External inflows
     2.4.5 Treatment plants
     2.4.6 Integrated simplified model of the sewer network

CHAPTER 3. FLOW CONTROL IN SEWER NETWORKS
   3.1 Control objectives
   3.2 Multilayer control system
   3.3 Bibliographic references
   3.4 The pursued approach

CHAPTER 4. NONLINEAR OPTIMAL CONTROL
   4.1 Performance criterion
   4.2 Mathematical problem formulation
   4.3 Solution algorithm
     4.3.1 General problem formulation
     4.3.2 Necessary optimality conditions
     4.3.3 Structure of the solution algorithm
     4.3.4 Specification of a search direction
     4.3.5 Line search algorithm
     4.3.6 Restart
     4.3.7 General remarks
     4.3.8 RPROP algorithm
   4.4 Rolling horizon

CHAPTER 5. MULTIVARIABLE FEEDBACK CONTROL
   5.1 General problem consideration
   5.2 Linear-quadratic formulation
   5.3 Multivariable control law without feedforward terms
   5.4 Multivariable control law with feedforward terms
   5.5 Computational effort

CHAPTER 6. APPLICATION EXAMPLE
   6.1 Application network
   6.2 External inflows
   6.3 Nonlinear optimal control
   6.4 Linear-quadratic formulation
   6.5 Simulation

CHAPTER 7. SIMULATION RESULTS
   7.1 No-control case
   7.2 Nonlinear optimal control
     7.2.1 Optimal control tool
     7.2.2 Open-loop application
     7.2.3 Rolling horizon application
       7.2.3.1 Investigated cases
       7.2.3.2 Rolling horizon with complete inflow information
       7.2.3.3 Rolling horizon with incomplete inflow information
     7.2.4 General observations
   7.3 Multivariable regulator
     7.3.1 Multivariable regulator without feedforward terms
     7.3.2 Multivariable regulator with feedforward terms
       7.3.2.1 Multivariable regulator with feedforward terms and accurate inflow predictions
       7.3.2.2 Multivariable regulator with feedforward terms and inaccurate inflow predictions
   7.4 Comparison between nonlinear optimal control and multivariable feedback control
   7.5 Concluding remarks

CHAPTER 8. CONCLUSIONS AND FUTURE RESEARCH

REFERENCES