Controllers
1.5 Thesis Overview
Chapter 2 provides a necessary mathematical background for the further develop- ments in the thesis. Some definitions and terminologies used in robust control are given and the inferential control problem studied in this thesis is formally introduced.
The section also provides a brief summary of major results for the Structured Singular Value theory, which is the main theoretical basis for the work in this thesis.
The rest of the thesis is roughly divided into two parts: Chapter 3 which is devoted to the topic of measurement selection and Chapters 4-5 that are devoted to inferential control system design.
In Chapter 3, an approach to the problem of measurement selection is outlined.
The approach taken is to eliminate systematically undesirable candidates for which a controller satisfying a given performance specification cannot be designed. Within this framework, the SSV theory is used as a main vehicle to develop a number of measurement screening tools that address the issue of model/plant mismatch as well as other aforementioned issues in a rigorous and general way. Some proposed tools are independent of the design methods while others are tied to specific design methods.
Various previously proposed criteria are discussed in perspective of the new method.
Even though we develop the chapter in the context of measurement selection, the presented method is applicable to the general problem of control structure selection (which involves selection of actuators as well as measurements) without modification.
Two example applications of the new tools are discussed: applications to a binary high-purity distillation column and multi-component distillation column.
Chapter 4 is devoted to the output estimation based approach to inferential control systems design. This approach involves two independent design steps: design of an output estimator which calculates the estimates for the primary variables from the available measurements and that of a controller which computes the manipulated input moves on the basis of the estimates. The strategic positioning of the output estimation based approach before the state estimation based approach (which is the major contribution of this thesis) in this thesis is br;e to the fact that the control system design for the former approach is a special case of the state estimation based design presented in Chapter 5 and is therefore much simpler. By presenting the simper methods first, we hope that readers will acquire background knowledge and familiarity with our notation before moving onto more complex and general cases.
The output estimator design is discussed in two different contexts: the case where a full dynamic model relating manipulated inputs and disturbances to primary and secondary variables is available and the case where only pIant data for primary and secondary variables are available. For the former case, two major design approaches, Kalman filter design and p-Synthesis design, are outlined and their relative merits are compared. For the latter case, various regression techniques in the literature and their suitability for the estimator design are discussed.
For control system design, traditional techniques such as LQG and IMC are dis- cussed and extended. We also present a novel MPC technique which combines the general state estimation of LQG and operational merits of the trandjtional MPC
techniques. It is also shown that LQG and MPC controllers can be equipped with a set of intuitive, simple on-line tuning parameters without introducing additional complexity to the controllers. Their connections to the traditional techniques such as IMC and DMC are clearly drawn and some of the limitations of these traditional techniques are pointed out.
In order to make the discussion complete, we also discuss p-Synthesis, which can directly exploit the given uncertainty model. It is presented as more of a forward- looking research topic and a number of open theoretical/practical issues are pointed out. The chapter concludes with an application of the techniques to a heavy oil fractionator ("Shell Control Problem") [54].
Chapter 5 is devoted to the development of a general inferential control system design method via state estimation. In contrast to the output estimation based approach of Chapter 4, the approach taken in this chapter is to design directly a full inferential controller that computes the input moves from available measurements.
We address the stability/performance issues in the presence of model/plant mismatch as well as various operational issues such as constraint handling and actuator/sensor failure tolerance. First, the traditional LQG design method is presented for a modified state space model to which most process control problems fit in more a natural way.
Constraint-handling strategies and actuator/sensor failure handling schemes for the LQG controllers are discussed. Finally, an augmented form of the LQG controller which eliminates nonintuitive, redundant design parameters and provides for intuitive on-line tuning is introduced. The main purpose of the discussion on the LQG design is not in itself, but to lead into the subsequent development of a Model Predictive Control technique.
One of the main contributions of this thesis is a novel Model Predicitve Control technique that is applicable to the general inferential control problem. State estima- tion techniques for the LQG design method is combined with finite receding horizon
control used by the tranditional MPC techniques and the end result is an inferential control system design method that is capable of dealing with the issue of model uncer- tainty as well as various operational issues. A drawback of the method is that it does not exploit the given information on model uncertainty in a direct way as p-Synthesis does for example. Designltuning parameters are rather to be selected on the basis of qualitative understandings, and the quantitative performance of the designed control system in the presence of possible mismatches have to be tested through the SSV analysis. Chapter 5 concludes with an application of discussed design methods to a binary high-purity distillation column.
In Chapter 6, the contributions of the thesis are summarized and put in perspec- tive. In addition, suggestions for future research work on the topic of measurement seletion and inferential control system design are given.
Appendix A presents an MPC technique that is analogous to the state-space MPC technique presented in Chapter 4 and uses step response models. Main contributions of this work is that it extends the applicability of the step response model based MPC techniques to integrating systems and to systems with "slow" disturbances and that it provides for intuitive tuning parameters that has direct relationships with closed-loop response time.
Appendix B presents a case study of a high-purity distillation column in which some of the techniques developed in the thesis are brought together and applied to a practical control problem.