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- Herausgeber: Wiley-VCH
- Kategorie: Fachliteratur
- Sprache: Englisch
A detailed introduction to mathematical models for new and established control engineers
Control engineering is a system that helps us understand electrical, physical, chemical, and biochemical systems through the use of mathematical modeling, using inputs, outputs, and simulations. These experimental platforms are implemented in most systems of modern advanced control engineering.
Advanced Control Methods for Industrial Processes provides a solid grounding in traditional control techniques. It emphasizes practical application methods alongside the underlying theory and core instrumentation. Each chapter discusses the full profile of the technology covered, from the field layer and control layer to its implementation. It also includes the interfaces for advanced control systems: between controllers and systems theory, between different layers, and between operators-systems. Through an emphasis on the practical issues of components, devices, and hardware circuits, the book offers working principles and operation mechanisms that allow an engineer to put theory into practice for the advanced control techniques.
Advanced Control Methods for Industrial Processes readers will also find:
- A practical overview on advanced control methods applied to real-time and in-silico systems
- Specific parameters, install procedures, calibration and configuration methodologies necessary to conduct the relevant models
- Clear insights into the necessary mathematical models
- Tutorial material to facilitate the understanding of core concepts
Advanced Control Methods for Industrial Processes is an ideal companion for process engineers, control engineers, and chemists in industry.
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Seitenzahl: 424
Veröffentlichungsjahr: 2025
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Table of Contents
Cover
Table of Contents
Title Page
Copyright
Preface
Acknowledgments
Part I: Classical and Advanced Control Theory: Simulation and Examples
Chapter 1: Field Elements of Classic Control Systems
1.1 The Principles of Control (Industry 5.0)
1.2 Field Elements of Classic and Modern Control Systems
1.3 Process Modeling in Control Systems Design
1.4 Ordinary Differential Equations and Laplace
1.5 Linear Systems
1.6 Nonlinear Dynamical Systems
1.7 Stability Theory
1.8 Systems’ Identification
1.9 General Methodology Based on Recursive Least Squares for Nonlinear Systems
1.10 Optimal Controllers
1.11 Observer-based Controllers
1.12 Examples of Modeling, Simulation, and Practical Platforms for Industrial Processes
1.13 Sensors
1.14 Module MQ
1.15 Sensor Operation
References
Chapter 2: Advanced Control Theory Fundamentals
2.1 Nonlinear Controllers and Advanced Control Theory
2.2 Nonlinear Control
2.3 Accessibility Rank Condition
2.4 Steady-output Controllability
2.5 Controllable and Reachable Subspaces
2.6 Controllable Matrix Test
2.7 Eigenvector Test for Controllability
2.8 Popov–Belevitch–Hautus
2.9 Lyapunov Test for Controllability
2.10 Sliding-mode Control Systems
2.11 Filippov’s
2.12 Lyapunov Method
2.13 Sontag Universal Formula
2.14 Control of Industrial Time-delay Systems
2.15 Linear Time Systems with Delays and the Predictive Control Scheme
References
Part II: Advanced Control Methods for Industrial Process
Chapter 3: Design of a Nonlinear Controller to Regulate Hydrogen Production in a Microbial Electrolysis Cell
3.1 Introduction
3.2 Mathematical Models
3.3 Bioprocess Modeling
3.4 MEC Modeling
3.5 Control Preliminaries
3.6 Methodology
3.7 Results and Discussion
3.8 System Model
3.9 Local Controllability Properties of the MEC Model
3.10 Measuring Hydrogen
3.11 Stability Test of the Proposed Controller
3.12 Conclusions
References
Chapter 4: Comparison of Linear and Nonlinear State Observer Design Algorithms for Monitoring Energy Production in a Microbial Fuel Digester
4.1 Introduction
4.2 Biodigester Operation
4.3 State Estimation
4.4 Luenberger Observer
4.5 Sliding-mode Estimator
4.6 Proposed Nonlinear Estimator
4.7 Estimator Performance Index
4.8 Mathematical Modeling and Steady States
4.9 Conclusions
References
Chapter 5: Optimal Control Approach Applied to a Fed-batch Reactor for Wastewater Treatment Plants
5.1 Introduction
5.2 Metal and Contaminants’ Removal
5.3 Operation Bioreactor
5.4 Dynamic Model
5.5 Proposed Model
5.6 Isolation and Propagation of a Sulfate-reducing Bacteria Consortium
5.7 Analytic Methods
5.8 Results and Discussion
5.9 Conclusion
References
Chapter 6: Experimental Implementation of the Dynamic Predictive-based Control to a Coupled Tank System
6.1 Introduction
6.2 Coupled Tank System Description
6.3 Experimental Results
6.4 Conclusion
References
Chapter 7: Temperature Robust Control Applied to a Tomato Dehydrator with the CLKF Approach
7.1 Introduction
7.2 Dehydrator: Modeling and Description
7.3 Control Synthesis
7.4 System Parameters
7.5 Experimental Results
7.6 Wi-Fi Monitoring System
7.7 Conclusions
References
Chapter 8: Design of an Adaptive Robust Controller: Temperature Regulation of a Heat Exchanger Prototype
8.1 Introduction
8.2 Methodology
8.3 Robust and Adaptive Control Design
8.4 Representation of the Control System
8.5 Robust P and PI Control Law Design
8.6 Adaptative P and PI Control Law Design
8.7 Experimental Results
8.8 MATLAB Code
8.9 Experimental Platform and Identification
8.10 Identification by Least Squares
8.11 Additional Tools
8.12 Robust P and PI Control
8.13 Adaptative Robust P and PI Control
8.14 Conclusions
References
Credits
Acronyms
Index
End User License Agreement
List of Illustrations
Chapter 1
Figure 1.1 The concept of Industry 5.0. Adapted from Borchardt et al. [11].
Figure 1.2 The timeline of industrial revolutions. Adapted from Madsen and Berg...
Figure 1.3 The timeline of industrial revolution’s pyramid of automation. Adapt...
Figure 1.4 Properties’ comparison of classical and modern control methods. Adap...
Figure 1.5 Classical and modern control theory.
Figure 1.6 Dynamic system modules. Adapted from López-Pérez et al. [59, 60], J...
Figure 1.7 Block diagram for the proposed observer.
Figure 1.8 Simulink system’s representation.
Figure 1.9 Recursion scheme.
Figure 1.10 PI control diagram in Simulink.
Figure 1.11 Embedded bioreactor system.
Chapter 2
Figure 2.1 The advanced control methods include adaptive control, optimal contr...
Chapter 3
Figure 3.1 Example of a microbial electrolysis cell.
Figure 3.2 Example of an MFC.
Figure 3.3 System elements.
Figure 3.4 Method for the design of a mathematical model in an MEC.
Figure 3.5 Deduction of the strategy for a continuous system.
Figure 3.6 Implementation of the proposed structure.
Figure 3.7 Substrate literature results.
Figure 3.8 Biomass literature results.
Figure 3.9 Hydrogen literature results.
Figure 3.10 System response with initial conditions equal to (3.9).
Figure 3.11 Nonlinear plant design in software.
Figure 3.12 Control by status feedback .
Figure 3.13 Control by status feedback
Figure 3.14 Control by status feedback .
Figure 3.15 Structure of the proposed controller in an MEC.
Figure 3.16 MEC operated open and closed loops for substrate dynamics comparing ...
Figure 3.17 MEC-operated open and closed loops for biomass dynamics comparing tw...
Figure 3.18 MEC-operated open and closed loops for hydrogen dynamics comparing t...
Figure 3.19 MEC-operated open and closed loops to show valve control effort.
Chapter 4
Figure 4.1 General diagram of a virtual sensor.
Figure 4.2 Biodigester.
Figure 4.3 Substrate consumption and biomass growth.
Figure 4.4 Biogas dynamics.
Figure 4.5 Comparison of the proposed observer for the substrate variable.
Figure 4.6 Comparison of the proposed observer for the biomass variable.
Figure 4.7 Comparison of estimation for the CH
4
production variable.
Figure 4.8 Comparison of estimates for the CO
2
production variable.
Figure 4.9 Simulation of disturbance considering noise in the sensor.
Figure 4.10 Biodigester instrumentation diagram.
Figure 4.11 Proposed sensor design.
Figure 4.12 Probe (Vernier CO
2
-BTA, Millikan Way, Beaverton, U.S.A.)
Chapter 5
Figure 5.1 Discontinuous and fed-batch mode of operation in the bioreactor. Opt...
Figure 5.2 Discontinuous mode of operation in the bioreactor. Comparison of exp...
Figure 5.3 Discontinuous mode of operation in the bioreactor. Comparison of exp...
Figure 5.4 Discontinuous mode of operation in the bioreactor. Comparison of exp...
Figure 5.5 Discontinuous mode of operation in the bioreactor. Comparison of exp...
Figure 5.6 Discontinuous mode of operation in the bioreactor. Comparison of exp...
Figure 5.7 Fed-batch mode of operation in the reactor. Optimal control approach...
Figure 5.8 Fed-batch mode of operation in the reactor. Optimal control approach...
Figure 5.9 Fed-batch mode of operation in the reactor. Optimal control approach...
Figure 5.10 Fed-batch mode of operation in chemical reactor (CR). Optimal contro...
Figure 5.11 Fed-batch mode of operation in the bioreactor. Reactor volume contro...
Figure 5.12 Fed-batch mode of operation in the bioreactor. Time response of the ...
Figure 5.13 Schematic of the experimental setup in fed-batch operation in real t...
Figure 5.14 Percent of cadmium removal during hybrid systems for WWTP.
Chapter 6
Figure 6.1 Instrumentation diagram of the coupled tank system.
Figure 6.2 Sketch of the RLS algorithm on LabVIEW.
Figure 6.3 Validation of the identified model via RLS.
Figure 6.4 Poles of the closed-loop system.
Figure 6.5 Sketch of the implementation of the predictive-based control on LabV...
Figure 6.6 Front panel on LabVIEW running the predictive control.
Figure 6.7 System response.
Chapter 7
Figure 7.1 Tomato dehydration plant prototype.
Figure 7.2 Instrumentation diagram Martínez et al. [35] / John Wiley & Sons.
Figure 7.3 Temperature system block diagram, as a first-order plant.
Figure 7.4 Nozzle, within the system, with a to diameter change.
Figure 7.5 RLS offline algorithm with a sine.
Figure 7.6 Control program and data acquisition in LabVIEW.
Figure 7.7 Programming logic.
Figure 7.8 System state.
Figure 7.9 DC control signal.
Figure 7.10 Error graph.
Figure 7.11 3NH-NR110 colorimeter.
Figure 7.12 Optimal PI control tomato slices.
Figure 7.13 Advanced nonlinear control tomato slices.
Figure 7.14 Colorimeter measurement: optimal PI control.
Figure 7.15 Colorimeter measurement: advanced nonlinear control.
Figure 7.16 Wi-Fi monitoring system structure.
Figure 7.17 Wi-Fi monitoring system structure.
Figure 7.18 Wi-Fi monitored tomato slices.
Figure 7.19 Colorimeter measurement: Wi-Fi-monitored advanced nonlinear control.
Figure 7.20 Process diagram.
Chapter 8
Figure 8.1 Thermal system output response.
Figure 8.2 Solid works design by specialized software.
Figure 8.3 Main sections of the thermal plant.
Figure 8.4 MAX6675 module for thermocouple type K.
Figure 8.5 Zero-crossing edge dimmer.
Figure 8.6 Arduino Uno.
Figure 8.7 Prototype plant.
Figure 8.8 Schematic diagram.
Figure 8.9 Input signal for identification.
Figure 8.10 Experimental plant status.
Figure 8.11 Parameters identified.
Figure 8.12 Simulation of the identified system.
Figure 8.13 Robust P system status.
Figure 8.14 Robust P control signal.
Figure 8.15 Robust PI system status.
Figure 8.16 Robust PI control signal.
Figure 8.17 Robust adaptive P system status.
Figure 8.18 System parameters.
Figure 8.19 Robust adaptive P control signal.
Figure 8.20 Robust adaptive PI system status.
Figure 8.21 Robust adaptive PI control signal.
List of Tables
Chapter 1
Table 1.1 Test data.
Table 1.2 Parameters obtained from LSA.
Chapter 3
Table 3.1 Hydrogen energy.
Table 3.2 Energy comparison of hydrogen versus gasoline.
Table 3.3 Inhibition kinetic models.
Table 3.4 Inhibition kinetic models.
Table 3.5 Simulators and properties for intracellular and extracellular modeli...
Table 3.6 Kinetic models.
Table 3.7 Control strategies.
Table 3.8 Criteria for validating the MEC model.
Chapter 4
Table 4.1 Comparison of estimators used in bioprocesses. Adapted from Iratni e...
Table 4.2 Biochemical methane potential models. Adapted from Ali Mahmoud et al...
Table 4.3 Cumulative methane production models. Adapted from Ali Mahmoud et al...
Table 4.4 Validation of kinetic parameters of the mathematical model.
Table 4.5 Validation of operating ranges of biodigester status variables.
Table 4.6 Equilibrium states and eigenvalues.
Table 4.7 Comparison of estimable variables for .
Table 4.8 Comparison of estimable variables for .
Table 4.9 Comparison of estimable variables for .
Table 4.10 Comparison of estimators applied in bioprocesses. Adapted from Orteg...
Table 4.11 Application of soft sensors.
Table 4.12 Measuring devices used by soft sensors. Adapted from Luttmann et al....
Chapter 5
Table 5.1 Batch, semibatch, and continuous regimens of operation in bio-photor...
Table 5.2 Parametric identification of the SRP is presented in batch culture [...
Table 5.3 Fit statistic for the mathematical model.
Table 5.4 Sensitivity of the variables.
Chapter 6
Table 6.1 Coupled tank features.
Chapter 7
Table 7.1 Control comparison.
Chapter 8
Table 8.1 Comparison of system trajectories.
Guide
Cover
Table of Contents
Title Page
Copyright
Preface
Acknowledgments
Begin Reading
Credits
Acronyms
Index
End User License Agreement
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Advanced Control Methods for Industrial Processes
Modeling, Design, and Simulation of Emerging Systems in Real Time
Edited by
Pablo Antonio López-Pérez
Omar Jacobo Santos Sánchez
Liliam Rodríguez Guerrero
Patricio Ordaz
Authors
Prof. Pablo Antonio López-Pérez
UAEH, Escuela Superior de Apan
Carretera Apan-Calpulalpan
s/n Colonia Chimalpa, CP.
Apan, Hidalgo
MX, 43900
Prof. Omar Jacobo Santos Sánchez
UAEH - Research Center on Technology
Electr./Control Academic Group
Mineral de la Reforma 42184,
Hidalgo, MX
Prof. Liliam Rodríguez Guerrero
UAEH - Research Center on Technology
Electr./Control Academic Group
Mineral de la Reforma 42184,
Hidalgo, MX
Prof. Patricio Ordaz
UAEH - Research Center on Technology
Electr./Control Academic Group
Mineral de la Reforma 42184,
Hidalgo, MX
Cover Design: Wiley
Cover Image: © Oleksiy Mark/Shutterstock
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Print ISBN 9783527352814
ePDF ISBN 9783527844173
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oBook ISBN 9783527844197
Preface
This book presents recent research advances in emerging topics for the application of advanced control to real-time system. The book includes robust solutions to important theoretical issues and also applied contributions to the design of complex systems. The book’s novel structure completely describes the most important advanced control optimization algorithms at the theoretical and experimental level.
Specifically, we focus on optimizing unit operations used in different processes in emerging areas through advanced control techniques. Furthermore, the book’s approach is based on understanding electrical, physical, chemical, industrial food dehydrator and biochemical systems, using mathematical modeling, in terms of inputs, outputs and simulation and experimental platforms that are implemented in most systems of modern advanced control engineering. Furthermore, this book has been developed from the perspective of advanced control engineering theories that can be applied to experimental platforms. A solid grounding is provided in traditional control techniques, followed by detailed studies of modern control techniques such as real-time and in silico systems.
This book also has several practical exercises. MATLAB, LabVIEW toolbox, and other open-source software is integrated as complementary material, which allows readers to quickly move from a simulation environment to an experimental one. The book also includes interfaces for the advanced control systems: between controllers and systems theory, between different levels, and between operators and systems. In addition to working principles and operation mechanisms, this book emphasizes the practical issues of components, devices and hardware circuits, providing specification parameters, installation procedures, calibration and configuration methodologies necessary for engineers when putting theory into practice for the advanced control techniques.
This book develops advanced discrete-time and, in some cases, continuous control techniques that require real-time execution when connected to a real experimental plant, that is, the controller task must be activated at fixed points in time and finished within a certain time. Therefore, we propose that the control engineer should be aware of the effects resulting from the finite processing power of the hardware controller and I/O units. Computational delays and jitter must be carefully considered when designing a real-time system because they introduce variable time delays into the system, leading to loss of control quality or even instability and severe physical damage to the system controlled. Part I of this book describes basic implementation techniques for such simple systems, including a discussion of numerical integration algorithms suitable for real-time execution and a stability-convergence test of the controller proposal. Part II complements the theoretical part via practical cases with real-time application. In general, we organized the book with interesting structures that include a complete description of the most important advanced control optimization algorithms to level theoretical and experimental, as well as several practical exercises. Finally, it integrates the development of new sensor technology that provides strong technical support for the optimal operation and coordinated control of an integrated energy system (IES). The book is divided into two parts with eight chapters in total.
Part I
(
Chapters 1
and
2
) includes a general overview of the comparative study of different classical theories for process control. This part focuses on control theory and the behavior of dynamical systems. When one or more output variables of a system need to follow a certain reference over time, a controller manipulates the inputs of a system to obtain the desired effect on the system’s output. The above is based on an input and output approach. The overall aim is to present sensors, instrumentation, and control and their uses within measurement systems as an integrated and coherent subject applied to advanced control theories. The advances in systems’ technology have radically altered the control design options mainly in implementation, and low-cost design capability can be obtained because of the widespread availability of inexpensive and powerful digital processing platforms and high-speed analog I/O devices. We focus on systems described with ordinary differential equations for linear and nonlinear processes. In addition, we emphasize that most ideas, methods, and results presented here extend to a more general setting, which leads to very important technical developments.
Part II
(
Chapters 3
to
8
) introduces the theory of linear and nonlinear control applied to industrial processes and research. In practice, the development of process control engineers generally apply control tools to their processes focuses on the dynamics of bioprocesses, which are often complex and slow. For mechanical or electrical systems and because of the above, new advanced control strategies are rarely modeled and implemented in real time necessary in the processes.
Part II
focuses on modelling and controlling different types of processes, as well as designing and monitoring different types of sensors, valves, feedback loops, sequences, and constraints that work together to automate a given process. An approach based on in silico systems, modeling, and simulations, combined with real-time applications, is developed. For example:
A new control strategy is applied and designed based on a theoretical framework of Lyapunov stability.
Prediction-based control delay systems are designed with one state delay and two delayed inputs.
Nonlinear stabilization for a class of time delay systems based on the well-known control Lyapunov-Krasovskii functional using Sontag’s universal formula.
Robust and adaptive proportional-integral (PI) control schemes are designed.
A discrete optimal control law for an input variable is executed in real time.
The examples are implemented in experimental platforms such as Arduino and academic MATLAB communication between LabVIEW and hardware devices (reactors, valves, and sensors) through an online interface design in LabVIEW. Data acquisition and control is performed in cRIO-9030-NI from actuators and a coupled connection, via digital implementation in LabVIEW and MATLAB. In addition, a PI controller optimally was tuned into a Honeywell DC10440 industrial PID. finally, monitoring is based on IoT that analyzes the system in real time based on related IoT security sensors to detect risk factors. The above is applied to the emerging topics such as the following:
Design of a nonlinear controller to regulate hydrogen production in a microbial electrolysis cell (MEC) and monitoring energy production in a microbial fuel digester (MFD)
Optimal control approach applied to a fed-batch reactor for wastewater treatment plants
A coupled tank process modeled as a two-in-two-out (TITO) system with inherent delay due to the tube length, from actuators and coupled connection
Control applied to a tomato dehydrator with the CLKF approach
Control implemented in a heat exchanger to regulate the temperature of a fluid (distilled water) by transferring heat between a thermal resistance and a spiral-shaped metal conduit through which the fluid circulates
Acknowledgments
D. A. Meneses Gonzalez, The Autonomous University of the State of Hidalgo, México
B. Cervantes Santamaria, The Autonomous University of the State of Hidalgo, México
C. A. Rodríguez Castro, The Autonomous University of the State of Hidalgo, México
E. Cornejo Velazquez, The Autonomous University of the State of Hidalgo, México
O. Lopez Arias, The Autonomous University of the State of Hidalgo, México
C. Cuvas Castillo, The Autonomous University of the State of Hidalgo, México
C. A. Lucho Constantino, The Autonomous University of the State of Hidalgo, México
Iraiz González Viveros, The Autonomous University of the State of Hidalgo, México
Part IClassical and Advanced Control Theory: Simulation and Examples
Chapter 1Field Elements of Classic Control Systems
After reading this chapter, you should be able to understand that:
The chapter mainly compares different classical theories regarding process control.
We will focus on systems described in terms of ordinary differential equations for linear and nonlinear processes.
In addition, it must be emphasized that most ideas, methods, and results presented here do extend to this more general setting, which leads to very important technical developments.
1.1 The Principles of Control (Industry 5.0)
Industry 5.0 is a continuation of Industry 4.0 with the objective of introducing humans (human intelligence) as the main axis of industrial production processes. Furthermore, innovation in production processes is human-oriented and highly customizable based on technological advances and high productivity of systems. However, the concept of Industry 5.0 is not accepted so far by corporations and industries but is promoted by researchers because, today, the industrial situation challenges are still congenital to Industry 4.0 and the era of digitalization. Industry 4.0 encourages high manufacturing efficiency and quality, and focuses on near novelty, techno-economic development, and industrial technology progress [1, 2]. Thus, Industry 5.0 is a prolongation and chronological extension of Industry 4.0 [3]. Industry 4.0 has restrictions with regard to industrial sustainability security, as it emphasizes on the productivity and flexibility of manufacturing through digitalization and technologies and integration of data from operations and business activity. The present manufacturing toward evolution of Industry 4.0 operations allows for better-quality productivity through information-driven automation, not only by infrastructure, but also by introducing more advanced monitoring, modeling, sensors, measurements, and control strategies in real time [4, 5]. One of the main advantages of Industry 4.0 is big data, which relates to large sets of processes and manufacturing data collected by sensors and greater visibility of process analytical technologies in the manufacturing operations. The improvements obtained from such a proactive, predictive feed-forward control approach can exceed the incremental yield progresses that corporations seek [6–9]. Furthermore, these data can be used for optimization purposes by applying innovative big data analytics. Machine learning (ML), a branch of artificial intelligence, is one of the ways to accomplish this [10] (see Figure 1.1).
Figure 1.1 The concept of Industry 5.0. Adapted from Borchardt et al. [11].
Technological processes consist of handling, working, refining, combining, and manipulating materials and fluids to produce cost-effective end products. These processes can be precise, demanding, and potentially hazardous. Small changes in a process can have a large impact on the end result [14, 15]. Variations in proportions, temperature, flow, turbulence, and many other parameters are to be carefully and consistently controlled to consistently produce the end product of the desired quality with a minimum of raw materials and energy. Instrumentation provides various indications used to operate a technological process [16–18]. In some cases, the operator records these indications for use in the operation of the process. The information recorded helps the operator evaluate the current condition of the process and take action if the conditions are not as expected. Requiring the operator to take all of the necessary corrective actions is impractical, or sometimes impossible, especially if a large number of indications are to be monitored. For this reason, most technological processes are controlled automatically once they are operating under normal conditions [19, 20]. The main role of process control was to contribute to safety, minimize external perturbation influence, and optimize processes by preserving process variables near the desired values. As the processes become larger in scale-up or behavior complex, the role of process automation has become more important. Today automation has taken over process control purposes, which means that operatives are assisted by a distributed control system, which communicates with the instruments in the real process. Process control is a combination of the statistics and engineering areas that deal with the sensors, designs, and algorithms for controlling a process. The aim of process control is to have it behave in a desired value. This includes the processes that are appealing, more accurate, more reliable, or more economical [21, 22] (see Figure 1.2).
Figure 1.2 The timeline of industrial revolutions. Adapted from Madsen and Berg [12] & Cohen and Singer [13].
In different manufacturing industries, advanced process control systems (APC) have become a nonnegotiable necessity for any manufacturing operation, which allows progress in the automation, understanding, and use of complex systems. APC incorporates a variety of model-based software system technologies, as well as stochastic and metaheuristic systems (see Figure 1.3). Currently, APCs provide supervisory control, bridging the gap between basic controls and overall process improvement, allowing the process to be cost-effective and of sustainable quality and operational safety aligned with Industry 4.0 and 5.0 [26–28].
Figure 1.3 The timeline of industrial revolution’s pyramid of automation. Adapted from López-Pérez et al. [7], Lucizano et al. [23], Wollschlaeger et al. [24], Martinez et al. [25].
1.2 Field Elements of Classic and Modern Control Systems
Modern advanced control techniques are model-based in data and look to apply mathematical optimization tools to optimize the performance based on future predictions and conditions. The necessary components and fields for this background are as follows:
A dynamic model.
Estimator that converts measured process variables into estimates of unmeasured states and/or parameters.
An algorithm that computes the optimal control action based on model predictions (multi-objective optimization function or Pareto and constraint set).
Methods that restrict the model to be linear.
Methods that require a very large amount of data to provide any statistical guarantees.
Methods for uncertainty descriptions are not necessarily accurate or related to physical quantities.
Improving system performance in terms of functionality, security, energy efficiency, environmental impacts, and costs.
Virtual sensors in the industry manages to optimize the operational performance, safety, functionality, and reliability of the bioprocess.
Monitoring, diagnosis, and control could be provided more reliably and robustly using physical sensors.
Embedded system is any device that is made up of a programmable computer (microprocessor or microcontroller).
Computer hardware.
Operating system in real time.
Efficiency and quality in manufacturing.
Hyper-competitive manufacturing sector.
Internet of Things (IoT).
Human–machine interface and supervisory control and data acquisition (SCADA).
Basic regulatory control, advanced regulatory control, multivariable, model-based control, constrained economic optimization, multi-unit constrained economic optimization, first principle economic optimization (RTO), steady-state process model, and economic information (e.g., prices and costs) performance Index to be maximized (e.g., profit) or minimized (e.g., cost) [
29
,
30
].
1.2.1 Advantages
Reducing operational costs to secure tribal knowledge.
Easy maintenance as it is not a compact system. In the case of breakdowns, the affected component is easily replaced without completely replacing the entire system.
They have small size, so they easily adapt to any industrial application without requiring a large workspace.
It is adaptable. Any necessary module can be integrated.
They consume minimum energy, which causes the battery life to be extended.
They give high performance in processing data at high speed and in real time.
1.2.2 Disadvantages
They are specific operating systems.
The software of an embedded system presents some restrictions such as small amounts of memory (generally, in the order of kB).
Limited processing capabilities (generally, the speed of the processors does not exceed the order of MHz).
Limits the consumption of instant energy whether in execution state or not.
They may present cybersecurity risks because they feature weak encryption.
Data shared between two devices can be easily intercepted and decrypted.
For example: data acquisition systems and system monitor parameters such as O2, CO2, temperature, flow, humidity, and pH based on the sensors that will collect data and the controllers to correspond to the set points of the variables. The measured data have the potential to practice another improved software tool for the estimation of variables and parameters from process data [31–33].
1.2.3 Why Control and Monitor?
The measurement of variables in processes is a necessary requirement to overcome following concerns:
To know internal behaviors.
Fault diagnosis.
Monitoring.
Visualization of critical variables.
Processing is subject to disturbances.
Nonlinear systems.
Unstability.
Maintain productivity.
Quality standards.
In addition:
Absence of trusted devices.
Time delays.
Errors in the measurement system.
High device costs.
Measurement conditions.
Unavailability of sensors.
Nowadays, process and system control theory can be divided into two areas: classical methods and modern control theory methods. The main differences between these groups focus on the representation, design, and operation of dynamic systems or data management in real time, at-line, offline, online, and in-line. Figure 1.4 briefly summarizes the differences between classical and modern control theory methods [7].
Figure 1.4 Properties’ comparison of classical and modern control methods. Adapted from Jha et al. [34], Drgoňa et al. [35], Holaza et al. [36].
General characteristics of classical control methods: Classical control methods are not able to incorporate constraints logically ascending from industrial control problems and have optimization missing complete performance. The most common example of classical control methods is the proportional integral derivative (PID) controller, which accounts for more than 95% of the control and automation applications today, mainly thanks to its simple implementation with relative efficiency [37]. Main advantage of state–space representation is the preservation of the time-domain attractiveness, where the response of a dynamical system is a function of many inputs, previous system states, and time, presently
Industrial processes often experience nonlinear behaviors that may include output multiplicity, bifurcations, chaos, unstable dynamic response to disturbances, and changes in system parameters; all these phenomena can lead to instability and, ultimately, affect the yield of production. For this reason, the application of traditional linear controllers is limited since they are not able to cope with the high nonlinear behavior of industrial processes. Aside from this, incidental external and internal disturbances in a manufacturing process lead to disappointment and can be a costly and annoying problem for any engineer. Regulatory control is the main strategy for attaining the basic operational requirements in manufacturing processes. The regulatory control has been performed through classical PID feedback controllers by considering the easiness of its practical implementation and satisfactory performance within common industrial practice [38]. Controllers employed range from simple on–off type to proportional (P), integral (I), derivative (D), and PID controls and expert systems. A scheme of typical control is shown in Eq. (1.2).
The , , and are the tuning parameters of the controller that can be adjusted by varying the dynamics of the control loop. Feed rates can also be adjusted based on an optimal objective function derived online or offline. The objective function targets to increase productivity or maximize operating profits [39].
In relation, other feedback controllers have been proposed for improving the dynamic performance of the manufacturing processes: among them, the adaptive controllers can modify some parameters in the control’s structure to maintain a satisfactory process operation [40]. Controllers designed to combat input disturbances and noisy measurements have been presented in the literature for several years within the following frameworks: sliding-mode theory, observer-based I/O linearizing controllers, and optimal controllers [41]. On the other hand, most of the controllers designed for the aforementioned existing outputs are complicated; therefore, they are difficult to perform in real applications. In fact, how to design a simple and physical controller to perform the control problems of complex chaotic systems is also important both in theory and in application. One of the most important drawbacks of the advanced control designs is their complexity for practical applications and the complete understanding by the plant engineers. Thus, alternative control structures must be simple enough to avoid the abovementioned drawback. Alternatively, most of the controllers designed in the aforementioned existing outputs are complicated; therefore, they are difficult to perform in real applications. Therefore, the alternative control structures must be simple enough to avoid the abovementioned drawback [42, 43].
Once the information is in the supervision and monitoring equipment, not only is interaction with the user achieved through graphics, alarm signals, report generation, and global analysis of the plant, but it can also directly influence the dynamic behavior of the system variables through programming of observers, filters, virtual sensors, among other components that are incorporated into the plant [44]. Supervision achieves the reconfiguration of system parameters through the controller, executing a set of actions to bring the process to its normal operation using model-based self-tuning methods or without mathematical knowledge of the process, among others. This constitutes a crucial difference in relation to monitoring that only covers detection and diagnosis and sometimes those systems that undertake only surveillance tasks and have been mistakenly called supervision systems. Finally, the last levels of the pyramid, manufacturing execution system planning, and enterprise resource planning are manufacturing execution systems that organize the resources necessary to execute the plant’s production plan that covers raw materials, order of priorities, change of production instructions, the controllers, and measurement interval of the sensors, among others. Therefore, there is a strong financial inspiration to develop the finest control scheme that would facilitate rapid startup and stabilization of manufacturing processes subject to redundant disturbances. In the control literature, regardless of the considerable progress in APC proposals such as sliding-mode control, model predictive control, and internal model control, PID controllers are still widely employed in industrial control systems because of their structural simplicity, reputation, robust behavior, and easy implementation (see, Figure 1.5). Along with the system’s stability, it also satisfies chief performance such as smooth reference tracking, efficient disturbance rejection, and measurement of noise attenuation criteria [45–47].
Figure 1.5 Classical and modern control theory.
For a process which is operating satisfactorily, the variation of product quality falls within acceptable limits. These limits normally correspond to the minimum and maximum values of a specified property. Normal operating data can be used to compute the mean deviation and the standard deviations of a given process variable from a series of observations. The standard deviation is a measure for how the values of the variable spread around the mean. A large value indicates wide variations in the variable. Assuming the process variable follows a normal probability distribution, then 99.7% of all observations is to lie within an upper limit and a lower limit. This can be used to determine the quality of the control. If all data from a process lie within the limits, then it can be concluded that nothing unusual has happened during the recorded period, the process environment is relatively unchanged, and the product quality lies within specifications. On the other hand, if repeated violations of the limits occur, then the conclusion can be drawn that the process is out of control and that the process environment has changed. Once this has been determined, the process operator can take action to adjust operating conditions to counteract undesired changes that have occurred in the process conditions [48–51].
1.3 Process Modeling in Control Systems Design
Mathematical model of a dynamic System is a set of equations that represent with a certain degree of accuracy the dynamics of the physical system. The model is generally described as an operator between the inputs and outputs of the system, or as a set of differentials (continuous case) and/or difference (discrete case) equations. Generally, when working with dynamic systems that are modeled by a finite number of coupled first-order ordinary differential equations, the state variables represent the “memory” that the dynamic system has of its past. Vector notation is usually used to write these equations compactly; the first-order differential equations can be defined and rewritten as a vector differential equation of dimension [52–55]. A thorough understanding of the time-dependent behavior of the technological processes is required to instrument and control the process. This, in turn, requires an appreciation of how mathematical tools can be employed in the analysis and design of process control systems. There are several mathematical principles that are utilized for automatic control. These are as follows:
Physical, chemical, biological models, and empirical models.
Simulation of dynamic models.
Laplace transforms.
Fitting dynamic models to experimental data [
56
–
58
].
Dynamic system: it is the one that generates data that change with the passage of time, that is, they possess certain dynamics. Dynamic systems are systems whose internal variables (state variables) follow a series of temporal rules (see Figure 1.6). They are called systems because they are described by a set of equations that are time-dependent, either implicitly or explicitly. Dynamic system classes:
Isolated: they do not interact with their environment.
Not insulated: interact with your environment.
Natural: unaffected by human intervention.
Artificial: created by man.
Physics: they involve matter and energy.
Not physical: thoughts.
Figure 1.6 Dynamic system modules. Adapted from López-Pérez et al. [59, 60], Jongeneel and Moulay [61].
Black Box: Black box is a system in terms of inputs and outputs. These models allow a global characterization of the model by disturbing its input to observe the variation or effect of said input on the states and parameters of the system at the output, that is to say: an identification, parametric sensitivity, and confidence interval of operation and parameters. Examples of some tools for the development of black-box models are as follows:
Support vector machines.
Partial least squares.
Artificial neural networks.
Fuzzy inference system.
White Boxes:
Detailed mechanistic models (white box) require:
Large sets of well-identified parameters.
Large uncertainty in parameters.
Internals being completely exposed to the user.
Complexity of the implementation.
Gray Boxes:
These models do not study the source code and can lean on the results obtained by testing the user interface (possibly gathered purely by experimentation).
Knowing the internal structure of the program can create more varied and smarter scenario.
Tests cannot hope to provide a complete coverage of the program.
View allows only partial exposure of the system behavior [
14
].
1.4 Ordinary Differential Equations and Laplace
A general form of an ordinary differential equation (ODE) containing one independent and one dependent variable is , where is an arbitrary function of , here is the independent variable, while is the dependent variable, and . The order of an ODE is the order of the highest derivative appearing in it.
A common class of mathematical models for dynamical systems is ODEs written as.
Here is a vector of real numbers that describes the current state of the system, and Eq. (1.3) describes the rate of change of the state as a function of the state itself. Note that we do not bother to write the vector any differently than a scalar variable. It will generally be clear from the context whether a variable is a vector or scalar quantity.
The state of a system is the minimal set of numbers needed together with the input with in the interval to uniquely determine the behavior of the system in the interval. The number is known as the order of the system. As increases, the state of the system evolves and each of the numbers becomes a time variable. These variables are known as state variables. In vector notation, the set of state variables form the state vector.
The differential equation (1.3) is called an autonomous system because there are no external influences. In many examples, it is useful to model the effects of external disturbances or controlled forces on the system. One way to capture this is to replace Eq. (1.3) by
where represents the effect of external influences. The model (1.4) is called a forced or controlled differential equation. The model implies that the rate of change of the state can be influenced by the input .
A description of systems that are linear and time-invariant (LTI) is observed in Eqs. (1.5) and (1.6), that is, systems described by linear differential equations with constant coefficients [8]. If a system is LTI and described by state variables, input variables, and output variables, Eq. (1.4), then the state equation will have the form:
An important property of the linear state equation description is that all system variables may be represented by a linear combination of the state variables and the system inputs, and the output equation will have the form:
where the coefficients and are constants. If we use vector–matrix expressions, these equations can be written as follows:
State equation
Dynamical relation, output equation
Remarks
Matrices , , , and are called the state matrix, input matrix, output matrix, and direct transmission matrix, respectively.
Vectors , , and are the state vector, input vector, and output vector, respectively.
The elements of the state vector are the state variables.
When the dynamical system does not have any control input, i.e., it runs autonomously, then we refer to it as an autonomous system. Mathematically, this is written as follows:
An important concept in dynamical systems is equilibrium. Roughly, the equilibrium of a dynamical system is the point in the state–space where the states remain constant, i.e., steady state. It is defined mathematically as follows (equilibrium):
Remarks
Systematic analysis and synthesis of higher-order systems without truncation of system dynamics.
Convenient tool for Multiple Input, Multiple Output (MIMO) systems.
Uniform platform for representing time-invariant systems, time-varying systems, linear systems, as well as nonlinear systems.
Can describe the dynamics in almost all systems (mechanical systems, electrical systems, biological systems, economic systems, social systems, etc.)
Laplace Transforms
The Laplace transform is a linear operator that switched a function to .
The technique of Laplace transform (and its inverse) facilitates the solution of ODE.
Transformation is from the time domain to the frequency domain.
Functions are complex, often described in terms of magnitude and phase. Laplace Transform for ODEs:
Equation with initial conditions.
Laplace transform is linear.
Apply derivative formula.
Rearrange.
Take the inverse.
Case Study Research 1
The most important mathematical tools used in this chapter are shown in the following text. We study dynamical systems modeled by a finite number of ODE coupled together in the following compact form:
where
and is the state vector, is the vector of control inputs, and is the term of external disturbances to the system. Also, it is considered that is the output of the system, e.g., physically measurable variables, and stabilization of the output at a desired value is sought.
Case Study Research 2
The following is an example of using the Laplace transform for a convergence test.
In this study, the following equations represent the core of such modeling:
These equations are fundamental in capturing the dynamics of microalgae growth in photobioreactors, as they describe the rate of change of biomass, chlorophyll, and substrate concentrations over time. The parameters within these equations, such as , , , , , , and the exponents, are crucial in defining the specific growth conditions and responses of the microalgae. In the sophisticated domain of microalgae growth modeling, particularly in state–space nonlinear systems, the concept of state variables becomes integral. These variables, denoted as , , and , represent the concentrations of biomass, chlorophyll, and substrate, respectively. To streamline the mathematical representation, these variables are aggregated into a state vector, , defined as follows:
where , , and correspond to the concentrations of biomass, chlorophyll, and substrate at any given time . This vector notation allows for a more compact and efficient description of the system dynamics. The evolution of these state variables over time is governed by a set of differential equations, collectively forming a state–space nonlinear system. This system can be succinctly expressed as follows:
Here, represents the derivative of the state vector with respect to time, indicating the rate of change of the state variables. The function is a nonlinear, smooth vector function that is Lipschitz continuous in and uniformly bounded in , the control input vector. The term signifies the additive modeling error inherent in the system. The output vector comprises the measured states, providing a link between the model and empirical observations. This framework of state–space modeling is pivotal in capturing the complex dynamics of microalgae growth, enabling the prediction and control of the system under varying conditions. It is determined that the system is observable since the rank of is 3.
Case Study Research 3
In the proposed observer design, the system represented by Eq. (1.17) and system (1.16) is expressed as follows:
An auxiliary system, serving as an observer for system (1.14), is defined as follows:
The following conditions are established:
The initial condition implies . 2. The norm is bounded by .
The term in
(1.19)
aims to achieve asymptotic estimation error. By selecting and adequately
, with and .
Considering the error (see
Figure 1.7
).
as .
Figure 1.7 Block diagram for the proposed observer.
Therefore:
Applying the Laplace transformation to inequality (1.20) results in:
Assuming homogeneous initial conditions for inequality (1.21), i.e., and , and rearranging algebraically, we obtain:
or equivalently:
Applying the final value theorem to inequality (1.23) for asymptotic behavior:
which implies:
and
or in the time domain:
1.5 Linear Systems
Linear systems: A system is called linear if the superposition principle is applied. This principle states that the response produced by the simultaneous application of two functions of different inputs is the sum of the two individual responses. Thus, for the linear system, the response to several inputs is calculated by treating one input at a time and adding the results. To map a model to frequency space,
system must be linear – output proportional to input.
Given system – input signals: and – output signals (response): and .
Theorem 1.1
Existence and uniqueness
Let be continuous in sections in satisfying the Lipschitz condition
Then there exists a such that
has only one solution [62].
Definition 1.1
Lie or directional derivative [63]
Let , . The Lie derivative of with respect to along , is given by and is defined by
This is the familiar notion of the derivative of along the trajectory of the autonomous system of the form .
Definition 1.2
Equilibrium point [62]
A point in state–space is an equilibrium point of the system , with , if it has the property that the initial condition of the state , remains at for all time , i.e., is the equilibrium point of the system .
Lemma 1.1
Gronwall–Bellman inequality [62]
Let be continuous nonnegative. If a function satisfies
with within the same interval
in particular, if is a constant, then
if, in addition is a constant, then
Lemma 1.2
Lemma of Barbalat [62]
If is uniformly continuous, such that exists and is finite. So
Corollary: If , in addition , for , so .
Lemma 1.3
Lemma of comparison [62]
Consider the scalar differential equation
where is continuous at and locally Lipschitz at , for all and all . Let ( can be infinite) the maximum interval of the existence of the solution , and assume for all . Let a continuously differentiable function whose derivative on the right-hand side satisfies the differential inequality
with for all . So for all .
1.6 Nonlinear Dynamical Systems
Nonlinear systems: A system is nonlinear if the superposition principle is not applied. Therefore, for a nonlinear system, the response to two inputs cannot be calculated by treating each one at a time and summing the results, represented by the system of nonlinear differential equations
Consider an input–output system whose state trajectory,
