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MSc Advanced Control and Systems Engineering with Extended Research / Course details

Year of entry: 2020

Course unit details:
State-Space and Multivariable Control

Unit code EEEN60109
Credit rating 15
Unit level FHEQ level 7 – master's degree or fourth year of an integrated master's degree
Teaching period(s) Semester 1
Offered by Department of Electrical & Electronic Engineering
Available as a free choice unit? No

Overview

Brief Description of the Unit:

  • Introduction to state variables, order and state equations
  • State space modelling of dynamical systems - applications and examples
  • Controllable canonical form and observer canonical form
  • State space realisation of transfer functions
  • State transition matrix, matrix exponential and time response of state space models
  • Laplace transform of state equations and matrix transfer functions for MIMO systems
  • Use of eigenvalues and eigenvectors to diagonalise a state space model
  • Modal form, modal behaviour and system dynamics
  • Jacobi linearisation on nonlinear systems
  • Controllability and observability and links to modal analysis
  • Minimal representations
  • State feedback control design
  • Observer design
  • Output feedback design and separation principle
  • Discrete-time state-space counterparts to continuous-time
  • State space and transfer function matrix representations of multivariable linear systems
  • Realisation of a MIMO transfer function matrix: minimal representation
  • Multivariable poles and zeros; directionality
  • Closed-loop sensitivities; design tradeoffs
  • Diagonal controllers and decoupling
  • Internal model control structure design for both single variable and multivariable control
  • Inner-outer factorisations
  • Design example
 

Aims

The course unit aims to:·    

  • Give students a sound understanding of control systems analysis and synthesis using state space techniques
  • Introduce multivariable control systems
  • Give students an introduction to internal model control design.

 

Learning outcomes

Students will be able to:

Knowledge and Understanding:

  • Describe dynamical systems in mathematical terms using state space representations;
  • Define terms such as eigenvalue, eigenvector, system state matrix, system observability and controllability
  • Design controllers using state space pole assignment and/or observers
  • Understand design limitations due to uncontrollable and unobservable states
  • Demonstrate knowledge of multivariable control and understand differences between SISO systems and MIMO systems.
  • Understand internal model control (IMC)

Intellectual Skills

  • Assess system stability, time response, controllability and observability from state space models
  • Derive linearisation of nonlinear systems
  • Derive expressions for transfer function from state space representation and state space representation from differential equations and transfer functions
  • Derive canonical forms of the system from the state space representation and vice versa applying basis changes and transformations
  • Derive minimal realizations of a MIMO transfer function.
  • Derive factorizations for IMC

Practical skills

  • Analyse continuous linear system's time response, stability, controllability and observability
  • Design controller and observer in the state space representation
  • Design IMC controller 

Transferable skills and personal qualities

  • Development of a critical attitude in the assessment of analytical results
  • Encouragement of physical interpretation where possible
  • Development of capability in problem solving using mathematical models
  • Understand the relation between computer-aided-design and practical implementation.

Teaching and learning methods

Number of Hours Allocated to:

Lectures

Tutorials

Practical Work/ Laboratory

Private Study

Total

30

3

6

111

150

 

Knowledge and understanding

  • Describe dynamical systems in mathematical terms using state space representations;
  • Define terms such as eigenvalue, eigenvector, system state matrix, system observability and controllability
  • Design controllers using state space pole assignment and/or observers
  • Understand design limitations due to uncontrollable and unobservable states
  • Demonstrate knowledge of multivariable control and understand differences between SISO systems and MIMO systems.
  • Understand internal model control (IMC)

Intellectual skills

  • Assess system stability, time response, controllability and observability from state space models
  • Derive linearisation of nonlinear systems
  • Derive expressions for transfer function from state space representation and state space representation from differential equations and transfer functions
  • Derive canonical forms of the system from the state space representation and vice versa applying basis changes and transformations
  • Derive minimal realizations of a MIMO transfer function.
  • Derive factorizations for IMC

Practical skills

  • Analyse continuous linear system's time response, stability, controllability and observability
  • Design controller and observer in the state space representation
  • Design IMC controller

Transferable skills and personal qualities

  • Development of a critical attitude in the assessment of analytical results
  • Encouragement of physical interpretation where possible
  • Development of capability in problem solving using mathematical models
  • Understand the relation between computer-aided-design and practical implementation.

Assessment methods

Method Weight
Other 80%
Written exam 20%

Written Examination:

Four questions, answer all questions

Length of examination: 3 hours

Calculators are permitted, providing they cannot store text.

The written examination forms 80% of the total unit assessment

Coursework - Laboratories

The number of laboratories attended is 2

  • Lab 1: 3 hours - 10% Short report
  • Lab 2: 3 hours -  10% Short report

Study hours

Scheduled activity hours
Lectures 30
Practical classes & workshops 6
Tutorials 3
Independent study hours
Independent study 111

Teaching staff

Staff member Role
Alexander Lanzon Unit coordinator
Long Zhang Unit coordinator

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