# EE4C04 Control system design

Topics: Concepts in systems theory and feedback control design

## Contents>

• State-space description of single-input, single-output linear dynamic systems, interconnections, block diagrams
• Linearization, equilibria, stability, Lyapunov functions and the Lyapunov equation
• Dynamic response, relation to modes, the matrix exponential
• Realization of transfer function models by state space descriptions, coordinate changes, canonical forms
• Controllability, stabilizability, uncontrollable modes and pole-placement by state-feedback
• Application of LQ regulator
• Observability, detectability, unobservable modes, state-estimation observer design
• Output feedback synthesis and separation principle
• Reference signal modeling, integral action for zero steady-state error

## Study Goals

By taking this course, the student
• will be able to master the introduced theoretical concepts in systems theory and feedback control design and
• will be able to practically apply these concepts to design projects and tasks
• will be capable to implement these concepts into model-based controller synthesis procedures through Matlab and Simulink
• and will be able to relate the learned concepts and techniques to other more specialized ones, to potentially integrate them by taking adjacent courses.
More specifically, the student will be able to:
• Translate differential equation models into state-space and transfer function descriptions
• Rationalize differences between state-space and transfer function approaches
• Linearize a system, determine its equilibrium points, analyze directly its local stability, leverage Lyapunov theory to study general stability properties
• Describe the effect of eigenvalue/pole locations to the dynamic system response in time/frequency domain. Contrast step and impulse responses. Analyze transients and steady-state
• Investigate model controllability. Formulate and apply the procedure of pole-placement by state-feedback, as well as LQ optimal state-feedback control
• Derive observability properties. Formulate and apply the procedure of state estimation and build converging observers
• Formulate the separation principle and employ it for the design of output feedback
• Build reference models and achieve zero steady-state error using integral control.