 Academic Year:
| 2012/3 |
| Owning Department/School:
| Department of Mathematical Sciences |
| Credits:
| 6 |
| Level:
| Honours (FHEQ level 6) |
| Period: |
Semester 1
|
| Assessment:
| EX 100% |
| Supplementary Assessment: | MA30046 Mandatory Extra Work (where allowed by programme regulations) |
| Requisites:
| Before taking this unit you must take MA20216 and take MA20218 and take MA20219 and take MA20220 |
| Description:
| Aims:
The course is intended to provide an elementary and accessible introduction to the state-space theory of linear control systems. Main emphasis is on continuous-time autonomous systems, although discrete-time systems will receive some attention through sampling of continuous-time systems. Contact with classical (Laplace-transform based) control theory is made in the context of realization theory.
Learning Outcomes:
To instill basic concepts and results from control theory in a rigorous manner making use of elementary linear algebra and linear ordinary differential equations. Conversance with controllability, observability, stabilizabilty and realization theory in a linear, finite-dimensional context.
Content:
Topics will be chosen from the following: Controlled and observed dynamical systems: definitions and classifications. Controllability and observability: Gramians, rank conditions, Hautus criteria. Controllable and unobservable subspaces. Input-output maps. Transfer functions and state-space realizations. State feedback: stabilizability and pole placement. Observers and output feedback: detectability, asymptotic state estimation, stabilization by dynamic feedback. Discrete-time systems: z-transform. Deadbeat control and observation. Sampling of continuous-time systems: controllability and observability under sampling.
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Programme availability:
|
MA30046 is Optional on the following programmes:
Department of Mathematical Sciences
- USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
- USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
- USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
- USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
- USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
- USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
- USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- TSMA-AFM09 : MSc Mathematical Sciences (Full-time) - Year 1
- TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 1
- TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 2
- TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time) - Year 1
- TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time) - Year 1
Department of Physics
- USXX-AFB03 : BSc (hons) Mathematics and Physics (Full-time) - Year 3
- USXX-AKB04 : BSc (hons) Mathematics and Physics with Placement (Full-time with Thick Sandwich Placement) - Year 4
- USXX-AAB04 : BSc (hons) Mathematics and Physics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 4
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