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MA30061 Control Theory, 2024–2025
Mark Opmeer
Contents
Introduction
1 First and second order scalar differential equations
1.1 First order scalar differential equations
1.2 Second order scalar differential equations
1.3 Real-world examples*
2 First order systems of differential equations
2.1 Examples
2.2 Cases studies*
2.2.1 Case study: control of a tape drive
2.2.2 Case study: a suspension system
3 Stability
3.1 Examples
3.2 Case study: a suspension system*
3.3 Case study: control of a tape drive*
4 The step response
4.1 Examples
4.2 Figures*
4.3 Real-world examples*
4.4 Case study: diagnosis of lung diseases*
4.5 Case study: muscle energy*
5 The transfer function
5.1 Examples
5.2 Case study: control of a tape drive*
5.3 Case study: a suspension system*
6 The frequency response
6.1 Examples
6.2 Figures*
6.3 Case study: microphones*
6.4 Case study: control of a tape drive*
6.5 Case study: a suspension system*
7 The impulse response
7.1 Examples
7.2 Figures*
7.3 Case study: a suspension system*
8 Output regulation and disturbance rejection: the full information case I
8.1 Examples
9 Output regulation and disturbance rejection: the full information case II
9.1 Examples
9.2 Case study: control of a tape drive*
10 The Rosenbrock matrix and solvability of the regulator equations
10.1 Examples
11 Output regulation and disturbance rejection: the measurement feedback case
11.1 Examples
11.2 Case study: control of a tape drive*
12 Controllability I
12.1 Examples
13 Controllability II
13.1 Examples
13.2 Case study: control of a tape drive*
13.3 Case study: a suspension system*
14 Observability I
14.1 Examples
15 Observability II
15.1 Examples
15.2 Case study: control of a tape drive*
15.3 Case study: a suspension system*
15.4 Case study: a suspension system (optimal fixed structure)*
16 Stabilizability and detectability
16.1 Stabilizability
16.2 Detectability
16.3 Examples
17 Observer-based controllers
18 Linear Quadratic optimal control I
18.1 Examples
19 Linear Quadratic optimal control II
19.1 Examples
20 \(H^2\) control: the state feedback case
20.1 Examples
20.2 Case study: a suspension system*
21 \(H^2\) control: the measurement feedback case
21.1 Examples
A Problem Sheet 1 (Lectures 1–3)
B Problem Sheet 2 (Lectures 4–5)
C Problem Sheet 3 (Lectures 6–7)
D Problem Sheet 4 (Lectures 8–9)
E Problem Sheet 5 (Lectures 10–11)
F Problem Sheet 6 (Lectures 12–13)
G Problem Sheet 7 (Lectures 14–15)
H Problem Sheet 8 (Lectures 16–17)
I Problem Sheet 9 (Lectures 18–19)
J Problem Sheet 10 (Lectures 20–21)
Bibliography
Introduction
This module is a natural follow-on from the second year module MA20220 Ordinary Differential Equations and Control. We will study linear differential equations mainly using matrices. In the first seven chapters we will be explicitly solving some
differential equations, but in the later chapters we will avoid this and only do computations with matrices which guarantee certain properties of the solutions of the differential equations. For this we will use some theorems that we will not prove.
We will illustrate some things with figures, those are not examinable. There are also some sections with “real world examples” which give an indication where differential equations of a certain type arise, these sections are also not examinable.
Furthermore, there are some sections which are “case studies” illustrating the material using actual engineering or bio-medical applications; those sections are also not examinable.