From classical to state-feedback-based controllers

Automatic control teaching can be fragmented, comprising different streams that seem to be disconnected or even competing. The appeal of new theories and concepts may encourage students to forget that the key issue in the discipline is the control design problem. If two or more different approaches provide a good solution to that problem, then a strong connection should exist between them. If such connections can be established, this should help students better understand the underlying concepts in the control design problem. In this article, we consider continuous-time systems and explore the connections between single-input, single-output (SISO) linear classical controllers (i.e., those defined by transfer functions) and the control design approach based on feedback of an estimated system state. The aim of this article is to provide insight for automatic control teaching and control system design.