Linear System Theory

Theory for linear multivariable systems, state space models, discretization, canonical forms and realizations, stability, controllability and observability, state feedback, LQR optimal control, state estimation, the Kalman filter and Extended Kalman Filter, descriptions of stochastic processes and random signals.

Knowledge: Detailed knowledge about state space representation of linear time invariant systems in continuous and discrete time. Knowledge about representation and characterization of random signals in linear systems. Detailed knowledge about fundamental concepts like controllability, observability and stability for linear multivariable systems. Substantial knowledge about methods for construction of multivariable controllers for linear systems, and algorithms and methods for state estimation. Use of state estimation for feedback in linear control systems. Knowledge of linearization of nonlinear systems.

Skills: Being able to formulate specifications and dynamic models as a basis for design of linear control systems and state estimators under influence of noise and disturbances. Being able to transform models between continuous and discrete time, and between state space and transfer function matrix representations. Being able to design and tune parameters of controllers with LQR and pole placement. Being able to design and tune parameters of observers and Kalman filters. Being able to apply linear algebra and Matlab for analysis and design of linear control systems. Being able to apply Simulink for rapid prototyping and experimental testing of control systems.

General competence: Understand strengths and limitations of theoretical analysis versus experimental testing. Good system understanding, i.e. how sub-systems consisting of hardware, software, physical systems and humans interact. Have a solid basis for advanced studies in control engineering.

Lectures, a compulsory laboratory project, compulsory assignments.