Single-Course English 10 ECTS

Linear control design 2

Overall Course Objectives

The course aims at providing analytical tools and methods for the design of linear control systems for MIMO (multi-input multi-ouptut) physical systems, based on the state space framework. The course also presents how the theoretical methods transpose into computer aided techniques for the practical design and implementation of the control systems.

Learning Objectives

  • Identify state variables of a single/multivariable dynamical system and formulate the corresponding nonlinear state space models
  • Compute linear state space models from nonlinear ones and relate their behaviours close to/far away from the point of linearization
  • Assess the system’s static and dynamic properties and discuss their effects on the behaviour of the system’s states and outputs
  • Design full state feedback controllers without/with integral action and compare the respective closed loop performances in relation to the design specifications
  • Design full/reduced order state estimators and appraise the behaviour of the estimation error
  • Synthesize output feedback controllers and evaluate their performance in comparison to full state feedback controllers
  • Explain simple stochastic processes and calculate the effect of noise propagation through a dynamical system
  • Design linear quadratic optimal feedback controllers and state estimators (Kalman filter) and evaluate the advantages/disadvantages of optimal solutions with respect to non-optimal ones
  • Synthesize optimal output feedback controllers and evaluate their performance in comparison to non-optimal output feedback controllers
  • Analyse the closed loop system’s performance and conclude about the level of adherence to the design specifications
  • Use Matlab/Simulink as CAD tool for the analysis, design and simulation of dynamical systems

Course Content

Multivariable (MIMO) continuous and discrete time dynamic systems. State-space formulation. Linearization, Laplace- and Z-transforms for MIMO systems. State transformations and canonical forms. Poles, zeros, eigenvalues, minimal representation. Controllability, observability, gramians. Stability. State feedback, pole placement. Integral control. Optimal control in continuous and discrete time (LQR). Observers in continuous and discrete time. Introduction to stochastic processes and Kalman filters. LQG design.

Recommended prerequisites


Teaching Method

Lectures (2 modules per week), group work exercises (Matlab/Simulink), homeworks.


The course is a relevant optional course for B.Eng.-students.
E-learning is used in the form of on-line voting systems, videos of lectures and digital exam.

See course in the course database.





13 weeks




DTU Lyngby Campus

Course code 34745
Course type Candidate
Semester start Week 35
Semester end Week 48
Days Tues 8-12, Fri 13-17

15.000,00 DKK