MA30046: Linear control theory
[Page last updated: 05 August 2021]
Academic Year: | 2021/2 |
Owning Department/School: | Department of Mathematical Sciences |
Credits: | 6 [equivalent to 12 CATS credits] |
Notional Study Hours: | 120 |
Level: | Honours (FHEQ level 6) |
Period: |
- Semester 1
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Assessment Summary: | EX 100% |
Assessment Detail: | |
Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
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Requisites: |
Before taking this module you must take MA20216 AND take MA20218 AND take MA20220
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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 (Year 3)
- USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
- USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
- USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
- USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
- USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
- USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
- USMA-AFB05 : BSc(Hons) Statistics (Year 3)
- USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
- USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
- USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
Department of Physics
- USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 3)
- USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
- USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)
- USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 4)
- USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 5)
- USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 5)
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Notes: - This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22.
- Programmes and units are subject to change in accordance with normal University procedures.
- Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
- Find out more about these and other important University terms and conditions here.
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