Издательство Springer, 2007, -497 pp.
Control and automation in its broadest sense plays a fundamental role in process industries. Control assures stability of technologies, disturbance attenuation, safety of equipment and environment as well as optimal process operation from economic point of view. This book intends to present mode automatic control methods and their applications in process control in process industries. The processes studied mainly involve mass and heat transfer processes and chemical reactors.
It is assumed that the reader has already a basic knowledge about controlled processes and about differential and integral calculus as well as about matrix algebra. Automatic control problems involve mathematics more than it is usual in other engineering disciplines. The book treats problems in a similar way as it is in mathematics. The problem is formulated at first, then the theorem is stated. Only necessary conditions are usually proved and sufficiency is left aside as it follows from the physical nature of the problem solved. This helps to follow the engineering character of problems.
The intended audience of this book includes graduate students but can also be of interest to practising engineers or applied scientists.
Organisation of the book follows the requirement of presentation of the process control algorithms that take into account changes of static and dynamic properties of processes. There are several possibilities to capture these changes. As the control objects in process industries are mainly nonlinear and continuous-time, the first possibility is to use nonlinear mathematical models in the form of partial differential equations, or after some simplifications, nonlinear differential equations. Usage of these models in control is computationally very demanding. Therefore, it is suitable to use robust control methods based on linearised models with uncertainties. However, strong nonlinearities can decrease performance of robust control methods and adaptive control algorithms can possibly be used.
The book presents process control using self-tuning (ST) controllers based on linear models. There are several reasons for their use. ST controllers can take into account changes of operating regimes of nonlinear processes as well as changes in physical process parameters. These changes can be caused by ageing or wearing of materials, etc. Finally, ST controllers can eliminate unmeasured disturbances, process noise, and unmodelled dynamic properties of processes.
The last chapter of the book that discusses adaptive control makes use of all previous parts. Here, discrete and continuous-time ST control of singlevariable and multivariable processes is investigated. For its implementation it is necessary to have in disposition an algorithm of recursive identification that provides an up-to-date model of the controlled process. This model is then used in feedback process control based on either explicit or implicit pole placement methods.
A basic requirement for a successful control is to have a suitable model for control. It is known that the process design in process industries involves nonlinear models with states evolving in space and time. This corresponds to models described by partial differential equations. Automatic control based such models is very difficult as it requires additional capacity of control computers and can be used only in some special cases. Self-tuning control requires linear models only described by ordinary differential equations of low order. This is caused by the fact that higher order models can cause singularities in calculation of the control law.
The first chapter of the book explains basic concepts that can be encountered in process control.
The second chapter describes principles of process modelling. Some principal models as a packed absorption column, a distillation column, and a chemical reactor are developed. Mathematical model of a plug-flow reactor serves for explanation of transport time delay that together with dynamic time delay forms a basic phenomenon in continuous-time process models. Description of specific process models is accompanied by assumptions when the models in the form of ordinary differential equations can be valid. Finally, general process models are explained together with the method of linearisation and the notion of systems and processes.
The third chapter explains briefly the use of the Laplace transform in process modelling. State-space process models obtained in the previous chapter are analysed. A concept of state is defined and the Lyapunov stability of continuous-time processes is investigated. The physical interpretation of theoretical facts is explained on a model of a U-tube. Conditions of controllability and observability are applied to a continuously stirred tank reactor. The state-space process models obtained from material and heat balances are transformed into input-output models for the purposes of identification and control design.
The aim of the fourth chapter on dynamic behaviour of processes is to show responses of processes to deterministic and stochastic inputs. Computer simulations explain how Euler and Runge-Kutta methods for integration of differential equations can be used. Examples include MATLAB/Simulink, C, and BASIC implementations. Process examples in this chapter demonstrate differences between original nonlinear and linearised models. The part dealing with stochastic characteristics explains random variables and processes, the definition of the white noise and others needed in state observation and in stochastic control.
Direct digital process control that constitutes a part of discrete-time adaptive control needs discrete-time process models. Therefore, the fifth chapter deals with the Z-transform, conversion between continuous-time and sampleddata processes. Also discussed are stability, controllability, observability, and basic properties of discrete-time systems.
Both adaptive and non-adaptive control methods are usually based on a mathematical model of a process. The sixth chapter is divided into two parts. In the first one identification of process models is based on their response to the step change on input. The second part deals in more detail with recursive least-squares (RLS) methods. Although primarily developed for discrete-time models, it is shown how to use it also for continuous-time models. The RLS method described in the book has been in use for more than 20 years at the authors place. Here we describe its implementation in MATLAB/Simulink environment as a part of the IDTOOL Toolbox available for free in the Inteet (see the web page of the book). IDTOOL includes both discrete-time and continuous-time process identification.
The aim of the seventh chapter is to show the basic feedback control con- figuration, open and closed-loop issues, steady state behaviour and control performance indices. The second part deals with the mostly used controllers in practise - PID controllers. Several problems solved heuristically with PID controllers are then more rigorously handled in next chapters dealing with optimal and predictive control.
The most important part of the book covers design of feedback controllers from the pole-placement point of view. Optimal control follows from the principle of minimum and from dynamic programming. At first, the problem of pole-placement is investigated in a detail based on state-space process models. The controller is then designed from a combination of a feedback and a state observer. This controller can then also be interpreted from input-output point of view and results in polynomial pole-placement controller design. The Youla- Ku?cera parametrisation is used to find all stabilising controllers for a given process. Also, its dual parametrisation is used to find all processes stabilised by a given controller. The Youla-Ku?cera parametrisation makes it possible to unify control design for both continuous-time and discrete-time systems using the polynomial approach. This is the reason why mostly continuous-time systems are studied. Dynamic programming is explained for both continuous-time and discrete-time systems. The part devoted to the Youla-Ku?cera parametrisation treats also finite time control – dead-beat (DB) that describes a discretetime control of a continuous-time process that cannot be realised using a continuous-time controller. State-space quadratically (Q) optimal control of linear (L) process models, i.e. LQ control with observer and its polynomial equivalent are interpreted as the pole-placement problem. Similarly, LQ control with the Kalman filter (LQG) or H2 control can also be interpreted as the pole-placement control problem. An attention is paid to integral properties of controllers and it is shown that optimal controllers are often of the form of modified PID controllers. The examples in the chapter make a heavy use of the Polynomial Toolbox for MATLAB (http://www.polyx.com).
The chapter nine extends the optimal control design with predictive control approach. It is explained why this approach predetermines discrete-time process control. At the beginning, the basic principles and ingredients of predictive control are explained. The derivation of the predictors and controllers is then shown for both input-output and state-space process models. The chapter also deals with incorporation of constraints on input variables and discusses the issue of stability and stabilisability of predictive closed-loop system.
Finally, the chapter concludes with both singlevariable and multivariable tuning and show examples of applications in process control.
The last chapter combines results of previous chapters in adaptive control. We prefer to use the so-called explicit, or self-tuning approach to adaptive control where process parameters are estimated on-line using recursive leastsquares methods. Then, at each sampling instant, the available model is used in control design.
The book has an ambition to integrate interpretations of continuous-time and discrete-time control, deterministic and stochastic control with incorporation of sets of all stabilising controllers. Notations used in separate parts of the books have been adapted to this aim.
Some of the programs and figures of the examples in the book marked in the margin are freely available at the web page of the book: www http://www.kirp.chtf.stuba.sk/~fikar/books/mic/.
The program sources are for MATLAB with toolboxes Simulink, Control System Toolbox, Polynomial Toolbox (http://www.polyx.cz), Multiparametric Toolbox (MPT, http://control.ee.ethz.ch/~mpt) and, IDTOOL (from the web site). The examples are verified in both simulation and realtime test cases using Real-time MATLAB toolbox and the industrial system SIMATIC STEP7.
Each chapter includes bibliographic references related to the text. Besides the classical material on process dynamics or feedback control, there are some parts of the book that follow from the joual publications of the authors.
Introduction.
Mathematical Modelling of Processes.
Analysis of Process Models.
Dynamical Behaviour of Processes.
Discrete-Time Process Models.
Process Identification.
The Control Problem and Design of Simple Controllers.
Optimal Process Control.
Predictive Control.
Adaptive Control.
Control and automation in its broadest sense plays a fundamental role in process industries. Control assures stability of technologies, disturbance attenuation, safety of equipment and environment as well as optimal process operation from economic point of view. This book intends to present mode automatic control methods and their applications in process control in process industries. The processes studied mainly involve mass and heat transfer processes and chemical reactors.
It is assumed that the reader has already a basic knowledge about controlled processes and about differential and integral calculus as well as about matrix algebra. Automatic control problems involve mathematics more than it is usual in other engineering disciplines. The book treats problems in a similar way as it is in mathematics. The problem is formulated at first, then the theorem is stated. Only necessary conditions are usually proved and sufficiency is left aside as it follows from the physical nature of the problem solved. This helps to follow the engineering character of problems.
The intended audience of this book includes graduate students but can also be of interest to practising engineers or applied scientists.
Organisation of the book follows the requirement of presentation of the process control algorithms that take into account changes of static and dynamic properties of processes. There are several possibilities to capture these changes. As the control objects in process industries are mainly nonlinear and continuous-time, the first possibility is to use nonlinear mathematical models in the form of partial differential equations, or after some simplifications, nonlinear differential equations. Usage of these models in control is computationally very demanding. Therefore, it is suitable to use robust control methods based on linearised models with uncertainties. However, strong nonlinearities can decrease performance of robust control methods and adaptive control algorithms can possibly be used.
The book presents process control using self-tuning (ST) controllers based on linear models. There are several reasons for their use. ST controllers can take into account changes of operating regimes of nonlinear processes as well as changes in physical process parameters. These changes can be caused by ageing or wearing of materials, etc. Finally, ST controllers can eliminate unmeasured disturbances, process noise, and unmodelled dynamic properties of processes.
The last chapter of the book that discusses adaptive control makes use of all previous parts. Here, discrete and continuous-time ST control of singlevariable and multivariable processes is investigated. For its implementation it is necessary to have in disposition an algorithm of recursive identification that provides an up-to-date model of the controlled process. This model is then used in feedback process control based on either explicit or implicit pole placement methods.
A basic requirement for a successful control is to have a suitable model for control. It is known that the process design in process industries involves nonlinear models with states evolving in space and time. This corresponds to models described by partial differential equations. Automatic control based such models is very difficult as it requires additional capacity of control computers and can be used only in some special cases. Self-tuning control requires linear models only described by ordinary differential equations of low order. This is caused by the fact that higher order models can cause singularities in calculation of the control law.
The first chapter of the book explains basic concepts that can be encountered in process control.
The second chapter describes principles of process modelling. Some principal models as a packed absorption column, a distillation column, and a chemical reactor are developed. Mathematical model of a plug-flow reactor serves for explanation of transport time delay that together with dynamic time delay forms a basic phenomenon in continuous-time process models. Description of specific process models is accompanied by assumptions when the models in the form of ordinary differential equations can be valid. Finally, general process models are explained together with the method of linearisation and the notion of systems and processes.
The third chapter explains briefly the use of the Laplace transform in process modelling. State-space process models obtained in the previous chapter are analysed. A concept of state is defined and the Lyapunov stability of continuous-time processes is investigated. The physical interpretation of theoretical facts is explained on a model of a U-tube. Conditions of controllability and observability are applied to a continuously stirred tank reactor. The state-space process models obtained from material and heat balances are transformed into input-output models for the purposes of identification and control design.
The aim of the fourth chapter on dynamic behaviour of processes is to show responses of processes to deterministic and stochastic inputs. Computer simulations explain how Euler and Runge-Kutta methods for integration of differential equations can be used. Examples include MATLAB/Simulink, C, and BASIC implementations. Process examples in this chapter demonstrate differences between original nonlinear and linearised models. The part dealing with stochastic characteristics explains random variables and processes, the definition of the white noise and others needed in state observation and in stochastic control.
Direct digital process control that constitutes a part of discrete-time adaptive control needs discrete-time process models. Therefore, the fifth chapter deals with the Z-transform, conversion between continuous-time and sampleddata processes. Also discussed are stability, controllability, observability, and basic properties of discrete-time systems.
Both adaptive and non-adaptive control methods are usually based on a mathematical model of a process. The sixth chapter is divided into two parts. In the first one identification of process models is based on their response to the step change on input. The second part deals in more detail with recursive least-squares (RLS) methods. Although primarily developed for discrete-time models, it is shown how to use it also for continuous-time models. The RLS method described in the book has been in use for more than 20 years at the authors place. Here we describe its implementation in MATLAB/Simulink environment as a part of the IDTOOL Toolbox available for free in the Inteet (see the web page of the book). IDTOOL includes both discrete-time and continuous-time process identification.
The aim of the seventh chapter is to show the basic feedback control con- figuration, open and closed-loop issues, steady state behaviour and control performance indices. The second part deals with the mostly used controllers in practise - PID controllers. Several problems solved heuristically with PID controllers are then more rigorously handled in next chapters dealing with optimal and predictive control.
The most important part of the book covers design of feedback controllers from the pole-placement point of view. Optimal control follows from the principle of minimum and from dynamic programming. At first, the problem of pole-placement is investigated in a detail based on state-space process models. The controller is then designed from a combination of a feedback and a state observer. This controller can then also be interpreted from input-output point of view and results in polynomial pole-placement controller design. The Youla- Ku?cera parametrisation is used to find all stabilising controllers for a given process. Also, its dual parametrisation is used to find all processes stabilised by a given controller. The Youla-Ku?cera parametrisation makes it possible to unify control design for both continuous-time and discrete-time systems using the polynomial approach. This is the reason why mostly continuous-time systems are studied. Dynamic programming is explained for both continuous-time and discrete-time systems. The part devoted to the Youla-Ku?cera parametrisation treats also finite time control – dead-beat (DB) that describes a discretetime control of a continuous-time process that cannot be realised using a continuous-time controller. State-space quadratically (Q) optimal control of linear (L) process models, i.e. LQ control with observer and its polynomial equivalent are interpreted as the pole-placement problem. Similarly, LQ control with the Kalman filter (LQG) or H2 control can also be interpreted as the pole-placement control problem. An attention is paid to integral properties of controllers and it is shown that optimal controllers are often of the form of modified PID controllers. The examples in the chapter make a heavy use of the Polynomial Toolbox for MATLAB (http://www.polyx.com).
The chapter nine extends the optimal control design with predictive control approach. It is explained why this approach predetermines discrete-time process control. At the beginning, the basic principles and ingredients of predictive control are explained. The derivation of the predictors and controllers is then shown for both input-output and state-space process models. The chapter also deals with incorporation of constraints on input variables and discusses the issue of stability and stabilisability of predictive closed-loop system.
Finally, the chapter concludes with both singlevariable and multivariable tuning and show examples of applications in process control.
The last chapter combines results of previous chapters in adaptive control. We prefer to use the so-called explicit, or self-tuning approach to adaptive control where process parameters are estimated on-line using recursive leastsquares methods. Then, at each sampling instant, the available model is used in control design.
The book has an ambition to integrate interpretations of continuous-time and discrete-time control, deterministic and stochastic control with incorporation of sets of all stabilising controllers. Notations used in separate parts of the books have been adapted to this aim.
Some of the programs and figures of the examples in the book marked in the margin are freely available at the web page of the book: www http://www.kirp.chtf.stuba.sk/~fikar/books/mic/.
The program sources are for MATLAB with toolboxes Simulink, Control System Toolbox, Polynomial Toolbox (http://www.polyx.cz), Multiparametric Toolbox (MPT, http://control.ee.ethz.ch/~mpt) and, IDTOOL (from the web site). The examples are verified in both simulation and realtime test cases using Real-time MATLAB toolbox and the industrial system SIMATIC STEP7.
Each chapter includes bibliographic references related to the text. Besides the classical material on process dynamics or feedback control, there are some parts of the book that follow from the joual publications of the authors.
Introduction.
Mathematical Modelling of Processes.
Analysis of Process Models.
Dynamical Behaviour of Processes.
Discrete-Time Process Models.
Process Identification.
The Control Problem and Design of Simple Controllers.
Optimal Process Control.
Predictive Control.
Adaptive Control.