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Intermediate Controls

Dynamic systems, systems with behaviors that change over time, are part of our everyday life. For example, glucose levels in our body depend on insulin and glucagon generation from the pancreas; the angular speed of an electric motor depends on its input voltage; the rate of infection of a disease depends on the fraction of the population that develops immunity. How should you engineer the inputs to a dynamic system to achieve a desired behavior? What sensors or estimations do you need to calculate the system inputs or monitor the system state? Computer algorithms (e.g., controllers and estimators) based on differential equations, linear algebra, and first principles provide a modern answer to those questions. In this course, you will learn how to design those algorithms by

  1. Modeling or representing dynamic systems using difference or differential equations.

  2. Identifying model parameters such that your model matches experimental data.

  3. Understanding the role of feedback and feedforward for the control of dynamic systems.

  4. Analyzing the fundamental properties of your dynamic systems, e.g., define if the system is stable, observable, or controllable.

  5. Designing control algorithms for dynamic systems.

  6. Merging information from sensors and models (estimator design) to estimate the system state and mitigate the effects of individual sensor and model inaccuracies.

  7. Implementing control and estimation algorithms in embedded systems using discrete-time versions of controllers and observers.

The main content of this Intermediate Controls course is modeling, identification, estimation, and control.
The main content of this Intermediate Controls course is modeling, identification, estimation, and control in the context of dynamic systems.

Content and link to notes

Lec. Topics Text Reading HW Exam Project Milestones Link to Notes
1 Introduction and the big picture: feedback, feedforward, control, and estimation. 1.1 - 1.9 (FBS)
HW1
E1
Define group
 Link
2 Feedback principles review: feedback to attenuate disturbances, track reference signals, and provide robustness 2.1 - 2.7 (FBS) Link
3 System modeling: modeling concepts and state-space models 3.1 - 3.3 (FBS)
HW2
 Link
4 System modeling: modeling methodology and modeling examples 3.3 - 3.4 (FBS) Link
5 System modeling: dynamics of mechanical and electric systems 2.1 - 2.3 (FCDS)
HW3
M1: select process and a reliable source of input/output data
 Link
6 System modeling: drug administration, population dynamics, and cruise control 4.1, 4.6, 4.7 (FBS) Link
7 System modeling: modeling brushed direct current motors - case study: selecting an adequate motor Papers
HW4
 Link
8 System modeling: permanent magnet synchronous motors (brushless motors with sinusoidal back-emf) Papers Link
9 Linear algebra review: crimes against matrices and least-squares Notes
M2: model and identify parameters of your model based on experimental data (system identification)
 Link
10 Linear algebra review: system identification using least-squares Notes Link
11 Linear algebra review: system identification using least-squares I Notes
HW5
 Link
12 Dynamic behavior: solving differential equations, qualitative analysis, and stability 5.1 - 5.3 (FBS) Link
13 Linear systems: the matrix exponential, input/output response, and linearization 6.1 - 6.5 (FBS)
HW6
 Link
14 Linear systems: the matrix exponential, input/output response, and linearization 6.1 - 6.5 (FBS) Link
15 Linear systems: the matrix exponential, input/output response, and linearization 6.1 - 6.5 (FBS)   Link
16 State Feedback: reachability, state feedback, and design considerations 7.1 - 7.3 (FBS)
HW7
E2
M3: design an observer for your process/plant
 Link
17 State Feedback: integral action and linear quadratic regulators 7.4 - 7.6 (FBS) Link
18 Output Feedback: observability, state estimation, control using estimated state 8.1 - 8.3 (FBS)
HW8
 Link
19 Output Feedback: state-space controller design, the discrete-time Kalman filter 8.5 (FBS), Ch. 2-5 (OSE) Link
20 Output Feedback: state-space controller design, the discrete-time Kalman filter 8.5 (FBS), Ch. 2-5 (OSE)
HW9
 Link
21 Transfer Functions: freq. domain modeling; block diagrams; zero frequency gain, poles, and zeros 9.1 - 9.5 (FBS) Link
22 Transfer Functions: freq. domain modeling; block diagrams; zero frequency gain, poles, and zeros 9.1 - 9.5 (FBS)
M4: create controller for your system
 Link
23 Transfer Functions: The Bode plot, continuous-time and discrete-time filter design 9.6 - 9.7 (FBS) Link
24 Frequency Domain Analysis: the loop transfer function, the Nyquist criterion, and stability margins. 10.1 -10.6 (FBS)
HW10
 Link
25 PID Control: tuning, integral windup, implementation. 11.3 - 11.5 (FBS) Link
26 Summary 12.1 - 12.3 (FBS)   Link
 
Intermediate Controls Conference: final project presentations. Keynote Speaker: Mark Yeatman, Ph.D., Applied Scientist at The Boston Dynamics AI Institute
M5: Final project presentation
 

Acknowledgements

This course was possible thanks to He Li (2022) and Mohsen Alizadeh Noghani (2023 - 2024), students of our Ph.D. program in Aerospace and Mechanical engineering. They served as Teaching Assistants.

The content of this course follows the material from  the book Feedback Systems: An Introduction for Scientists and Engineers. Second edition. Princeton: Princeton University Press, 2021, from Karl Johan Åström and Richard M. Murray. The textbook, Python libraries, and additional supplements are available online in this link.

The linear algebra portion of the class follows the notation and content from the book Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares. 1st ed. Cambridge University Press & Assessment, 2018. from Boyd, Stephen, and Lieven Vandenberghe. The textbook additional materials are available in this link.