SC42015 Control theory

 State-space description of multivariable linear dynamic systems, interconnections, block diagrams

• Linearization, equilibria, stability, Lyapunov functions and the Lyapunov equation
• Dynamic response, relation to modes, the matrix exponential and the variation-of-constants formula
• Realization of transfer matrix models by state space descriptions, coordinate changes, normal forms
• Controllability, stabilizability, uncontrollable modes and pole-placement by state-feedback
• LQ regulator, robustness properties, algebraic Riccati equations
• Observability, detectability, unobservable modes, state-estimation observer design
• Output feedback synthesis (one- and two-degrees of freedom) and separation principle
• Disturbance and reference signal modeling, the internal model principle

Study Goals

The student is able to apply the developed tools both to theoretical questions and to simulation-based controller design projects. More specifically, the student must be able to:

• Translate differential equation models into state-space and transfer matrix descriptions
• Linearize a system, determine equilibrium points and analyze local stability
• Describe the effect of pole locations to the dynamic system response in time- and frequency-domain
• Verify controllability, stabilizability, observability, detectability, minimality of realizations
• Sketch the relevance of normal forms and their role for controller design and model reduction
• Describe the procedure and purpose of pole-placement by state-feedback and apply it
• Apply LQ optimal state-feedback control and analyze the controlled system
• Reproduce how to solve Riccati equations and describe the solution properties
• Explain the relevance of state estimation and build converging observers
• Apply the separation principle for systematic 1dof and 2dof output-feedback controller design
• Build disturbance and reference models and apply the internal model principle

Teachers

Last modified: 2023-11-03