Andrea Garulli

The general topic of the present book is control of turbomachinery. In particular, it deals with modeling and control techniques for variable speed centrifugal gas compression systems. The main objective of the study, presented in this book, is to design and implement multivariable controllers that regulate the centrifugal gas compressor and minimize fuel consumption of the gas turbine. In particular, the first aim is to design a multivariable controller that regulates the compressor discharge pressure as faster as possible, while preventing surge, by acting on the rotation speed, the inlet guide vanes and the anti surge valve. A further contribution, is the development of a control system that minimizes fuel consumption of the gas turbine at steady state.

It is well known that a large number of problems relevant to the control ?eld can be formulatedas optimizationproblems. For long time, the classical approachhas been to look for a closed form solution to the speci?c optimizationproblems at hand. The last decade has seen a noticeable shift in the meaning of "closed form" solution. The formidable increase of computationalpower has dramatically changed the fe- ing of theoreticians as well as of practitioners about what is meant by tractable and untractableproblems. A main issue regardsconvexity. From a theoretical viewpoint, there has been a large amount of work in the directions of "convexifying" nonc- vex problems and studying structural features of convex problems. On the other hand, extremely powerful algorithmsfor the solution of convexproblemshave been devised in the last two decades. Clearly, the fact that a wide variety of engine- ing problems can be formulated as convex problems has strongly motivated efforts in this direction. The control ?eld is not an exception in this sense: many pr- lems in robust control, identi?cation and nonlinear control have been recognized as convex problems. Moreover, convex relaxations of nonconvex problems have been intensively investigated, as they provide an effective tool for bounding the optimal solution of the original problem. As far as robust control is concerned, it is known since long time that several classes of problemscan be reducedto testing positivity of suitable polynomials.