This module will give students an introduction to basic control theory. We will use a classic example in dynamics and control, the inverted pendulum (or self balancing car), to demonstrate the capabilities and limits of different control solutions. We will also provide an overview of modern control methods, and line up a few guest talks from people using control in different ways for interesting applications.
Class 1 – Apr 4
- Introduction to feedback control systems
- Open-loop and closed-loop system
- Time continuous and time discrete systems
- Linear Time Invariant (LTI) systems
- Modeling of the inverted pendulum
Class 2 – Apr 9
- Laplace Transformation and Z-Transformation
- Impulse response and transfer function
- Definition of stability and relative stability
- Digital to analog conversion
- Analog to digital conversion
- Pole and zero analysis
- Root Locus analysis
- Introduction to PID control
Class 3 – Apr 11
- Design a PID controller for the inverted pendulum using Matlab
- Simulation of the inverted pendulum using Matlab Simulink
Class 4 – Apr 16
- State space representation
- Controllability, oberservability and stability
- Full state feedback control
- Observer based control
Class 5 – Apr 18
- guest lecture by Dimitris Papanikolaou from Harvard GSD
- Title: Governing the Commons of Mobility
- Abstract: Much of the contemporary discourse on intelligent urban environments celebrates how information technology can close the feedback loop of intelligence in a bottom-up fashion. Often however, information transparency, free access to resources, and selfish behavior can cause ecosystems to collapse, suggesting that the problem of intelligent environments is not always about how to provide informed access to resources, but often about how to design rules that can maintain a balanced allocation of them. Who makes decisions, who takes actions, and who evaluates the results? In this presentation, Dimitris will comparatively discuss two radically different models of governing urban resource allocation networks (centralized vs decentralized control), using Boston’s bike sharing system as a case. In the first model, an operator monitors the system and directs enforcing agents to reposition vehicles from full to empty stations. In the second model, a market mechanism incentivizes shelf-interested users to rebalance the system while disincentivizing them from unbalancing it. Dimitris will also discuss simulation (system dynamics and agent-based systems) and experimental (strategic game design) methods for studying the dynamic behavior, equilibrium, and economic sustainability of such systems.
Class 6 – Apr 30
- Designing an observer based controller for the inverted pendulum
- Simulation of the system in Matlab Simulink
Class 7 – May 2
- Guest lecture by Piero Miotto and Louis Breger from Draper Laboratory Defense & Space
Title: Flight Control law design and Adaptive Control law design for an F-18
Class 8 – May 6
- Guest lecture by Leena Singh from Draper Labs Aerospace Guidance and Control.
- Title: Model Predictive Control for Aerospace Applications
- Abstract: This lecture will explore the concepts of and the fundamentals behind the design and utilization of Model Predictive Control. There will be a brief retrospective of Optimal Control methods and how the optimal control problem extrapolates to MPC. A series of examples will be used to show how MPC solves the control synthesis problem, its sensitivities (in performance and stability) to the choice of the design parameters, utilization with constraints. Some popularly used methods to reduce the curse of dimensionality will be investigated (time permitting). Finally, Leena will provide a brief look at some of the domains and problem classes where MPC has been applied.
Class 9 – May 9
- Guest lecture by Matt Evans and Fabrice Matichard from the MIT-CalTech-launched collaboration ‘LIGO
- Title: Advanced LIGO: What we’re looking for and how we plan to find it. Active control of LIGO seismic isolation systems: theory and practical considerations.
- Abstract: This lecture will give an introduction to the world’s frontier gravitational wave detector and the extreme technical feats they accomplished to realize the extraordinary sensitivity they need to detect gravity waves from collapsing binary black holes, etc. The LIGO detectors, one in Washington State and the other in Louisiana, are double-armed, multipath laser interferometers, with each 2.5 mile long arm in an extreme vacuum – these interferometers detect minute deformations of space-time caused by passing gravitational waves. 30 different control systems have been devised to stabilize both the mirrors and the lasers to unprecedented accuracy, and the detectors are going through an upgrade now to extend their sensitivity even further. This lecture will survey the exciting physics that the updated LIGO detectors aim to accomplish as well as overview the control and stabilization strategies that have been designed to pull it off. More about LIGO here: http://www.ligo.caltech.edu/ orhttp://en.wikipedia.org/wiki/LIGO
Class 10 – May 14
- Final project presentation
Demonstrate understanding of pole placement and pole – zero analysis during a in class test.
Tune PID control for the inverted pendulum to meet design requirements. Simulate results using a model developed in Matlab Simulink.
Reading – Harnessing the power of feedback loops
Critical discussion of using feedback to achieve behavioral change with our guest lecturer Dimitris Papanikolaou .
Final project design and implement a PID controller in your project.