Advanced Control for Constrained Processes and Systems

GARELLI, F.; MANTZ, R.; DE BATTISTA, H.

IET Institute of Engineering and Technology

Lugar: Londres; Año: 2011 p. 270

978-1849192613

In every real control loop exist physical limits, security bounds or system dynamic behaviors that constrain the reachable closed-loop performance. In particular, physical and/or technological limitations of actuators give rise to plant input constraints, whilst safety operation regions or non-minimum phase characteristics generally affect the evolution of the controlled variables or system outputs. In a multivariable or MIMO (Multiple-Input Multiple-Output) process, the effects of these constraints are worsened because of the presence of directions associated to input/output vectors and, even more important, the crossed coupling or interactions between the system variables. This book deals with some relevant practical problems of constrained process control. To this end, recently proposed control strategies are unified in a generalized framework to deal with either input, internal or output constraints. The resulting control strategy is based on reference conditioning ideas, implemented by means of an auxiliary or supervisory loop which employs a discontinuous action in order to generate the maximum reference signal compatible with the system constraints. Although design simplicity is a book priority, well established variable structure systems theory and sliding mode related concepts are used for theoretical analysis, which give to the proposal a rigorous mathematical support. The book aims at providing solutions which can be added to pre-existent control designs, thus avoiding the necessity of changing the whole control system or even partial retunings. To this end, a two-step design procedure is adopted, which also allows using conventional control tools for the main loop design. The use of switching signals is always confined to the low-power side of the control systems, so that the implementation of the control schemes results extremely easy, both analogously or digitally.The book is outlined as follows. After introducing in Chapter 1 the main book motivations and aims together with a brief description of the problems to be addressed, the first part of the book (Part I: SISO systems) focuses on providing a description as simple as possible of the methodology to deal with systems constraints. It also aims at illustrating through several practical applications the design and implementation of the developed techniques. Firstly, Chapter 2 introduces the basic ideas behind the conditioning scheme for systems involving biproper transfer function descriptions, such as PI or real PID industrial controllers. Then, the methodology analysis and design is extended to deal with strictly-proper systems/controllers. This general analysis is performed independently of the type of constraint, and it is subsequently interpreted in terms of geometric invariance concepts to give the reader some further insight. With the same objective, the chapter also provides some simple examples.Secondly, different case studies of practical interest are presented in detail in Chapter 3 to illustrate the potential of the described methodology. They consist of: (1) the pitch control of wind turbines with both amplitude and rate actuator saturation; (2) a clean-hydrogen production plant in which the electrolyzer specifications impose internal constraints; (3) the chute level delimitation in a sugar crushing station; (4) the tracking speed autoregulation of a 6 degree-of-freedom robot manipulator in order to avoid path deviations; and (5) the regulation of ethanol concentration below a given threshold in the fed-batch fermentation of the industrial strain Saccharomyces cerevisiae for overflow metabolism avoidance. The results achieved in all these applications confirm the effectiveness of the techniques presented in Chapter 2 for a broad range of engineering problems.Part II is devoted to multivariable constrained control problems. The chapter 4 and the beginning of chapters 5 to 7 revise some important tools of multivariable control theory. From this basis, the second halves of chapters 5 to 7 address significant troubles of MIMO processes caused by the crossed coupling or interactions, control directionality and input or output constraints. They are briefly described in the following.  The first MIMO problem to be treated is the dynamic decoupling preservation of multivariable processes in presence of plant input constraints (Chapter 5). In fact, multiple input saturation changes the amplitude and the direction of the control signal that is necessary to achieve dynamic decoupling. Hence, in addition to the known problem of windup, the change of directionality problem appears, bringing about the loss of the decouplingobtained for the ideal unconstrained case. This difficulty is described in Chapter 5, where a recent method to deal with it is also presented. Differing from previous design methods, which  successfully avoid the change of control directionality by conditioning the whole reference vector, the presented approach does not affect those variables whose set-points remain constants, avoiding in this way to generate undesired transients in these channels. Apart from giving design examples on minimum and non-minimum phase systems, the preservation of the mill torque decoupling in a sugar crushing station under saturation of the turbine speed is addressed in detail.As a second multivariable problem of major interest for industrial engineers, the reduction of cross-interactions in multi-loop or decentralized control is considered in Chapter 6. On this architecture is still based the great majority of industrial process control loops for MIMO systems. However, in spite of their practical benefits, single loop controllers are not able to suppress interactions and so each input affects not only its corresponding output but also the other ones. When the process interactions are significant, the pairing problem of choosing which available plant input is to be used to control each of the plant outputs must be firstly properly solved (an illustrative example is given in the chapter to reveal the effects of crossed interactions on multi-loop control). Useful tools for this choice are the interaction measures, which have been subject of much research since therelative gain array (RGA) was introduced. Nonetheless, neither appropriate control structure selection nor controllers tuning are sufficient to guarantee amplitude delimitation of the input-output coupling. An extension of the reference conditioning techniques described in Part I is shown in this chapter as a powerful tool to impose user-defined boundaries for the loop interactions in decentralized control systems, i.e. to robustly respect output constraints. All the chapter content is then applied to a benchmark quadruple tank process with an adjustable multivariable zero which dynamics simply represents the behavior of several chemical and industrial processes.Multi-loop interaction reduction is at last evaluated in a dead-time catalytic reactor with a Smith-predictor. A half-way strategy between the diagonal decoupling and decentralized control is analyzed for non-minimum phase processes in Chapter 7, regarding that for these systems the former strategy spreads right-half plane zeros (thus imposing additional closed-loop performance constraints), while the latter does not generally give satisfactory results for relatively demanding closed-loop requirements. Hence, partial decoupling is considered and studied thorough the chapter. In a partially decoupled control system, non-zero off-diagonal elements in the closed-loop transfer matrix help to relax the bounds on sensitivity functions imposed by the right-half planezeros, and also permit pushing the effects of these zeros to a particular output. However, the off-diagonal elements also give rise to interactions in a structured form, which strongly depend on the right-half plane zero direction. A conditioning algorithm is here propounded, analyzed and designed to bound the remaining interactions in partial decoupled systems, avoiding as much as possible undershoots in the (decoupled) variable of interest. An interesting previous method is also discussed for comparative purposes. The same non-linear quadruple tank process of Chapter 6 is considered as case study, but subjected to much more demanding control specifications.Finally, the Chapter 8 presents an algorithm for the reduction of the undesired effects caused by manualautomatic or controller switching in multivariable process control, which is also applicable to SISO systems as a particular case. The method simply uses a relay and a first-order filter to avoid inconsistencies between the offline controller outputs and the plant inputs. As a consequence, jumps at the plant inputs are prevented (which is known as bumpless transfer) and undesired transients on controlled variables are significantly reduced. Some advantages of this method are its trivial implementation, its robustness properties and that, unlike other bumpless proposals, it does not need a model of the plant.