Control Theory




Responsible Instructor: T. Keviczky (Tamas)

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Course Contents:

- 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

Education Method:

Lectures and Exercise Sessions

Computer Use:

The exercises will be partially based on Matlab in order to train the use of modern computational tools for model-based control system design.

Literature and Study Materials:

B. Friedland, Control System Design: An Introduction to State-space Methods. Dover Publications, 2005
K.J. Astrom, R.M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, Princeton and Oxford, 2009


Written mid-term examination (15%) and written final examination (85%). For the resit examination there will be a written examination (100%) for which the mid-term result will not count.


Old Course Code: SC4025


3mE Department Delft Center for Systems and Control
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