(Created 2009-08-11.)

MULTIVARIABLE CONTROL | FRTN10 |

**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.