Frequency domain properties of scalar and multivariable feedback systems
In this monograph, a multivariable control system design method is presented. The method is the so-called frequency response method, which is the straightforward extension of classical methods developed for scalar system design. In the introductory chapter, Chap. 1, it is stressed that classical techniques which are extremely powerful for the design of scalar systems cannot be extended to multivariable systems as they are. It is the goal of this monograph to extend the classical techniques to multivariable systems if at all possible. In Chap. 2, sensitivity and complementary sensitivity functions are introduced. The classical design methods are nothing but to harmonize tradeoffs. One of the tradeoffs is a constraint between the magnitude of both functions. Chap. 3 treats analytical tradeoffs. The case when the plant has minimum zeros and unstable poles are discussed. In Chap. 4, it is emphasized that an alternative method which substitutes the shaping of gain and phase used in classical techniques is necessary for the design of multivariable control systems. In Chap. 5, it is stated that directionality which is essential for multivariable systems prevents the direct extension of classical techniques. The singular value decomposition of the transfer function matrix plays an important role in multivariable systems. In Chap. 6, the concept of phase is reconsidered from a new point of view. In Chap. 7, the relation between properties of open and closed loop systems is considered, which, over some frequency range, have high gains in only some directions, low gains in different directions, or both high and low gains in different directions. In Chap. 8 through Chap. 11, mathematical tools for studying analytical design tradeoffs in multivariable systems are presented. An analytical function is given in Chap. 8. The complex unit sphere is presented in Chap. 9. Differential equations describing how the singular vectors of a matrix transfer function change with frequency are derived in Chap. 10. Transformation of generalized Cauchy-Riemann equations into the generalization of the scalar gain-phase relation is presented in Chap. 11. An illustrative example is introduced in Chap. 12.
multivariable control system design method
scientific article; zbMATH DE number 193003