Question

The closed loop pole of a stable second order system could be

Answer 1

automotive-controls.ieeecss.org

Linear optimal control systems

Huibert Kwakernaak, Raphael Sivan

Wiley-interscience 1, 608, 1972

During the last few years modem linear control theory has advanced rapidly and is now being recognized as a powerful and eminently practical tool for the solution of linear feedback control problems. The main characteristics of modern linear control theory are the state space description of systems, optimization in terms of quadratic performance criteria, and incorporation of Kalman-Bucy optimal state reconstruction theory. The significant advantage of modern linear control theory over the classical theory is its applicability to control problems involving multiinput multioutput systems and time-varying situations; the classical theory is essentially restricted to singleinput single-output time-invariant situations. The use of the term" modem" control theory could suggest a disregard for" classical," or" conventional," control theory, namely, the theory that consists of design methods based upon suitably shaping the transmission and loop gain functions, employing pole-zero techniques. However, we do not share such a disregard; on the contrary, we believe that the classical approach is well-established and proven by practice, and distinguishes itself by a cnllection of sensible and useful goals and problem formulations. This book attempts to reconcile modern linear control theory with classical control theory. One of the major concerns of this text is to present design methods, employing modern techniques, for obtaining control systems that stand up to the requirements that have been so well developed in the classical expositions of control theory. Therefore, among other things, an entire chapter is devoted to a description of the analysis of control systems, mostly following the classical lines of thought. In the later chapters of the book, in which modern synthesis methods are developed, the chapter on analysis is recurrently referred to. Furthermore, special attention is paid to subjects that are standard in classical control theory but are frequently overlooked in modern treatments, such as nonzero set point control systems, tracking systems, and control systems that have to cope with constant disturbances. Also, heavy emphasis is placed upon the stochastic nature of control problems because the stochastic aspects are so essential. vii