Modelling, analysis and controller design of time-variable flow processes

A systematic theory for analysis and controller design of material transport systems under unsteady flow conditions is developed. It is assumed that the system is linear with respect to material concentrations so that the input-output dynamics can be characterized by a time-varying weighting function. The relation between the residence time distribution function and the weighting function is derived, and it is shown that the two functions become equal, when represented as functions of a new integrated time variable. A considerable complexity reduction is achieved, if, additionally, the weighting function becomes invariant with respect to the new time scale (volumetric scale). It is shown that systems consisting of a series of perfect mixers with possible bypass flows and recycling is invariant with respect to the volumetric scale. A similar result applies to time variable delays, which become constants in the new time scale. Structural properties i.e. stability, controllability and observability are shown to be unchanged in the transformation thus making it possible to use analysis and synthesis methods of classical control theory of linear time-invariant systems. By this way, a time-variable PID controller and LQ controller are derived and tested. As a special result it is shown that a PID-controller with time-variable coefficients can stabilize a system, which would be unstable in the case of varying flow rates, if a controller with constant coefficients were used. The theoretical results and controller performance are tested by simulations and practical tests carried out by a laboratory-scale pilot plant. The results are shown to be in excellent agreement with those predicted in the theory. Preface The thesis was carried out in the Control Engineering Laboratory at Helsinki University of Technology. I wish to express my sincere gratitude to Professor Antti J. Niemi, who introduced me to the topic and was always helpful during long discussions concerning the difficult points in the theory. Professor Heikki Koivo was not involved in this research, but his character, humour and encouragement have had a great role especially in the last period of the work. Discussions with Professor Raimo Ylinen and Dr. Jussi Orava on the theoretical part have been invaluable on many occasions. Several persons helped me during the test phase–especially in the use of the pilot plant and in the preparation of tracer tests by radioactive tracers. The assistance of Dr. during different phases of the tests has been of great help. Mr. Erkki Solin and Mr. …