Multivariable Control Systems


Prerequisite/Recommended prerequisite for participation in the module

The project module builds on knowledge obtained during the 1st semester

Content, progress and pedagogy of the module

Students who complete the module: must be able to analyze modern control methods for multi input/multi output systems and to apply modeling methods and control synthesis for mechanical or energy conversion systems.

Learning objectives


  • Stability and performance limitations in robust control
  • Additive and multiplicative model uncertainty
  • Robust stability
  • Robust performance
  • Small gain theorem
  • Dynamic programming
  • Riccati equation
  • Elimination of steady state errors in optimal control
  • Use of observer in LQG control
  • Stability properties of optimal controller
  • Stability properties of finite horizon control
  • Solving predictive control with constraints using quadratic programming
  • Dealing with uncertain and nonlinear systems in model predictive control.
  • Mass- and energy balances
  • Fundamental laws of thermodynamics
  • Models with lumped and distributed parameters
  • Model structures for system identification: AR, MA, ARMA, ARMAX, Box-Jenkins
  • System identification methods: Moment method , Least squares method, Prediction error method, Maximum likelihood method, Recursive and adaptive parameter estimation
  • Lagrange and Hamiltonian mechanics
  • Rotation parameters, rotation matrices, quaternion
  • Model representations (differential equations, state space, transfer function, differential-algebraic equations, descriptor form)


  • Formulation of optimal control problems with references and disturbances
  • Soft real time implementation
  • Formulation of the standard robustness problem
  • Theory and solution to the standard robust problem
  • Formulation of control problems using models of constraints, disturbances and references combined with a performance function (Model Predictive Control)
  • Software tools for solving constrained optimization problems
  • Should be able to apply system identification methods


  • Synthesis of robust control systems, model predictive control systems, and of LQG systems
  • Should be able to formulate models of a basic energy conversion systems and mechanical systems.

Type of instruction

As described in the introduction to Chapter 3.



Name of examMultivariable Control Systems
Type of exam
Oral exam based on a project
Assessment7-point grading scale
Type of gradingExternal examination
Criteria of assessmentAs stated in Joint Programme Regulations

Facts about the module

Danish titleFlervariable reguleringssystemer
Module codeESNCAK2P1
Module typeProject
Duration1 semester
Empty-place SchemeYes
Location of the lectureCampus Aalborg
Responsible for the module


Study BoardStudy Board of Electronics and IT
DepartmentDepartment of Electronic Systems
FacultyTechnical Faculty of IT and Design