Aim
To teach the basic principles for control of systems with multiple inputs and outputs. The course will provide insight on fundamental limitation and on the use of mathematical optimization as a design tool. The course covers linear continuous-time systems.

Knowledge and understanding
For a passing grade the student must

• be able to define and explain basic concepts for multivariable systems

• be able to translate between, and intelligently select among, different representations for multivariable systems, in particular transient responses, transfer function matrices, and state-space descriptions

• be able to derive properties of interconnected systems from the properties of their subsystems, and to characterize and quantify the role of the different subsystems

• be able to formulate constraints on input signals and output signals of a control system and to relate these to conditions on the matrices that describe the system

• be able to analyse how process characteristics put limitatoins on the control performance that can be achieved

Skills and abilities
For a passing grade the student must

• be able to independently formulate technical specifications based on understanding of the control system should be used and interact with the external environment

• be able to select control design methods and model structures, and translate specifications into mathematical optimization problems

• draw conclusions from numerical calculations about the correctness of models and specifications, and about the consequences for the interaction between the system and the environment

Judgement and approach
For a passing grade the student must

• understand relationships and limitations when simplified models are used to describe a complex and dynamic reality

• show ability to teamwork and group collaboration at laboratories

Contents
The control design process, signal size, gain, stability, sensitivity, robustness, small-gain theorem, transfer function matrix, operators, multivariable zeros, non-minimum phase systems, disturbance models in the time domain and frequency domain, frequency-domain specifications, controller structures, Youla parameterization, convex specifications, linear-quadratic optimization of state feedbacks and Kalman filters, synthesis using Linear Matrix Inequalities (LMI).

Literature
Torkel Glad, Lennart Ljung: Control Theory: Multivariable and Nonlinear Methods, Taylor & Francis, 2000, ISBN 0748408789
Compendium with additional lecture material and exercises sold by the department.