Linear Systems
Duration
- One Semester or equivalent
Contact hours
- 48 Hours
On-campus unit delivery combines face-to-face and digital learning.
Aims and objectives
This unit aims to introduce linear system theory including state space representation, the structural properties of linear systems and the synthesis of linear controllers.
1. Develop mathematical state space representations of continuous and discrete linear system (K1, K2, K3, S1))
2. Evaluate the state transition matrix, for linear and time varying systems (K1, K2, K3, S1)
3. Analyse and evaluate the structural properties of linear systems including controllability, observability and stability (K1, K2, K3, S1, S2)
4. Design and synthesize linear controllers using state feedback (K1, K2, K3, K4, S1, S2, S3)
5. Design asymptotic observers and compensators (K1, K2, K3, K4, S1, S2, S3)
6. Design optimum observers and controllers (K1, K2, K3, K4, S1, S2, S3)
Unit Learning Outcomes
Students who successfully complete this unit will be able to:
2. Evaluate the state transition matrix, for linear and time varying systems (K1, K2, K3, S1)
3. Analyse and evaluate the structural properties of linear systems including controllability, observability and stability (K1, K2, K3, S1, S2)
4. Design and synthesize linear controllers using state feedback (K1, K2, K3, K4, S1, S2, S3)
5. Design asymptotic observers and compensators (K1, K2, K3, K4, S1, S2, S3)
6. Design optimum observers and controllers (K1, K2, K3, K4, S1, S2, S3)
Unit information in detail
- Teaching methods, assessment, general skills outcomes and content.
Teaching methods
*Scheduled face to face: Lectures (36 hours), Tutorials (6 hours), Lab work (6 hours)
*Scheduled synchronous online learning events (N/A)
Non-scheduled online learning events and activities (N/A)
Other non-scheduled learning events and activities including independent study (approx.102 hours)
*Scheduled synchronous online learning events (N/A)
Non-scheduled online learning events and activities (N/A)
Other non-scheduled learning events and activities including independent study (approx.102 hours)
Assessment
| Types | Individual or Group task | Weighting | Assesses attainment of these ULOs |
| Lab reports | Individual | 40% | 1,2,3,4,5,6 |
| Examination | Individual | 60% | 1,2,3,4,5,6 |
Minimum requirements to pass this Unit
As the minimum requirements of assessment to pass a unit and meet all Unit Learning Outcomes to a minimum standard, a student must achieve:
(ii) at least 40% in the final exam, and
(iii) at least 40% of the possible marks for the laboratory hurdle.
General skills outcomes
During this unit students will receive feedback on the following key generic skills:
• Problem solving skills
• Analysis skills
• Communication skills
• Ability to tackle unfamiliar problems, and
• Ability to work independently
• Problem solving skills
• Analysis skills
• Communication skills
• Ability to tackle unfamiliar problems, and
• Ability to work independently
Content
• Model classification, State Space models. Realization, controllable canonical forms
• Observable canonical forms, Other realizations, minimal realization Linearization Solution to continuous-time LTI systems, Controllability, Observability,
• Observability, LTI system, duality
• Controllability & observability for DT LTI systems
• Kalman decomposition
• State feedback, direct method
• State feedback, canonical form method
• State feedback, Lyapunov equation method, Stabilizability
• Observer, detectability ,Observer-based control
• Asymptotic Observers, Reduce order Observer
• Continuous-time finite horizon LQR , Continuous-time infinite horizon LQR, Discrete-time LQR
• Observable canonical forms, Other realizations, minimal realization Linearization Solution to continuous-time LTI systems, Controllability, Observability,
• Observability, LTI system, duality
• Controllability & observability for DT LTI systems
• Kalman decomposition
• State feedback, direct method
• State feedback, canonical form method
• State feedback, Lyapunov equation method, Stabilizability
• Observer, detectability ,Observer-based control
• Asymptotic Observers, Reduce order Observer
• Continuous-time finite horizon LQR , Continuous-time infinite horizon LQR, Discrete-time LQR
Study resources
- References.
References
A list of reading materials and/or required texts will be made available in the Unit Outline.