Entry requirements

Linear algebra.

Ordinary differential equations.

Transform methods or Signals and systems

Learning outcomes

Students who pass the course should be able to

• define basic concepts in automatic control
• determine relations between models of linear dynamic systems in form of differential equations, state space models, transient responses, transfer functions and frequency responses
• analyse linear systems with respect to stability, steady state properties, controllability and observability, and fastness and damping
• evaluate closed loop systems with respect to stability, as well as robustness against and sensitivity for model errors and disturbances
• interpret and apply graphical methods and tools like block diagrams, root locus, Bode and Nyquist diagrams
• understand the function of simple controllers (PID controllers, lead-lag filters, state feedback) and controller structures (feedforward and cascade control)
• design simple controllers from given specifications
• understand and design observers for estimating the states in state space models
• study the stability properties of closed loop systems with linear dynamics and static nonlinearities in the feedback loop

Content

Modelling and mathematical description of dynamic systems in the time and frequency domain:

Impulse response, step response, transfer function, Bode and Nyquist diagrams, state space description. Estimation of states using observers. Methods for stability analysis including the Nyquist criteria and describing functions.

Control strategies:

PID controller, lead-lag design, state space feedback. Robustness of feedback systems. Specification and synthesis of control systems. Non linearities.

Laboratory work:

• Computer aided design, simulation and analysis. Five two-hour sessions using the program package MATLAB.
• Laboratory experiments.

Instruction

Lectures, problem solving sessions and laboratory work.

Assessment

Written examination at the end of the course. Passed laboratory course is also required.