TTIT63

Linear feedback systems, 10,5 ECTS-points /Tema3: Återkopplade linjära system/ Advancement level: C

Aim: To acquire an understanding of control theory and the required mathematical tools. Course organization: See the handbook of studies part 1. Course content: Analysis of controlled dynamical systems described by systems of ordinary differential equations. In the course we are mainly concerned with linear time invariant systems and the corresponding differential equations, which then turn out to be linear with constant coefficients. The solutions, representing signals in the system, are studied either as functions of time or, through the Laplace transform, as functions of a complex frequency. The quotient between the input and output signals in the frequency domain defines the transfer function of the system whose dynamical behavior can be related to the location in the complex plane of the singularities of the transfer function. A central part of the course is devoted to the study of different forms of feedback and how this affects the stability and other dynamical qualities of a system. Concepts such as controllability and observability are also introduced and analyzed with methods from linear algebra. The mathematical tools in use are, apart from basic calculus and introductory linear algebra, the Laplace transform and the resolvent- and exponential matrix and their connection with annihilating polynomials for matrices. Concepts such as null space, rang, eigenvalue and eigenvector are important as well. Computers are used frequently in both symbolic and numerical computations and in simulations of the systems. Course literature: According to literature list.

Course language is swedish.