title

Control Bootcamp: Overview

description

Overview lecture for bootcamp on optimal and modern control. In this lecture, we discuss the various types of control and the benefits of closed-loop feedback control.
These lectures follow Chapter 8 from:
"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz
Amazon: https://www.amazon.com/Data-Driven-Science-Engineering-Learning-Dynamical/dp/1108422098
Book Website: http://databookuw.com
Brunton Website: eigensteve.com
Chapters available at: http://databookuw.com/databook.pdf
These lectures also follow Chapters 1 & 3 from:
Machine learning control, by Duriez, Brunton, & Noack
https://www.amazon.com/Machine-Learning-Control-Turbulence-Applications-ebook/dp/B01MDUPONF/
Chapters available at: http://faculty.washington.edu/sbrunton/mlcbook/

detail

{'title': 'Control Bootcamp: Overview', 'heatmap': [{'end': 892.74, 'start': 840.551, 'weight': 0.765}, {'end': 932.258, 'start': 912.549, 'weight': 0.791}], 'summary': 'Provides a rapid overview of control theory, including system description, controller design, and kalman filter, emphasizing the application of control theory in dynamical systems, feedback control, and the benefits of sensor-based feedback control in improving system performance.', 'chapters': [{'end': 86.949, 'segs': [{'end': 86.949, 'src': 'embed', 'start': 44.802, 'weight': 0, 'content': [{'end': 51.29, 'text': 'And my goal is to, first of all, get you familiar with the major types of optimal and modern control theory.', 'start': 44.802, 'duration': 6.488}, {'end': 56.156, 'text': 'I want to teach you how to use these in MATLAB to actually work with a real system.', 'start': 51.931, 'duration': 4.225}, {'end': 63.699, 'text': "And what I also want to give you a feeling for is what, in control theory, is easy and what's still quite challenging today,", 'start': 56.937, 'duration': 6.762}, {'end': 68.841, 'text': 'so that you can get up to speed on the real pressing needs of control theory today.', 'start': 63.699, 'duration': 5.142}, {'end': 71.462, 'text': 'And again, this is not exhaustive.', 'start': 70.021, 'duration': 1.441}, {'end': 77.864, 'text': 'So if this is really important to you and you like control theory and you want to go more into depth,', 'start': 71.522, 'duration': 6.342}, {'end': 82.946, 'text': "there's deeper treatments both on the math side and on the applied design side.", 'start': 77.864, 'duration': 5.082}, {'end': 86.949, 'text': 'And so I want to give you just a little bit of perspective.', 'start': 84.546, 'duration': 2.403}], 'summary': 'Familiarize with major types of control theory, use in matlab, and understand pressing needs.', 'duration': 42.147, 'max_score': 44.802, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE44802.jpg'}], 'start': 2.981, 'title': 'Boot camp on control theory', 'summary': 'Provides a rapid overview of optimal and modern control theory, including system description, controller design, and kalman filter, aiming to familiarize the audience with major concepts and practical implementation in matlab.', 'chapters': [{'end': 86.949, 'start': 2.981, 'title': 'Boot camp on control theory', 'summary': 'Introduces a rapid overview of optimal and modern control theory, including system description, controller design, and kalman filter, aiming to familiarize the audience with major concepts and practical implementation in matlab.', 'duration': 83.968, 'highlights': ['The lecture covers system description, controller design, and Kalman filter implementation in MATLAB, providing a high-level understanding of optimal and modern control theory.', 'The goal is to familiarize the audience with major types of optimal and modern control theory and to teach practical implementation in MATLAB, enabling individuals to work with real systems.', 'The chapter aims to provide a perspective on the ease and challenges of control theory today, allowing individuals to understand the pressing needs in the field.']}], 'duration': 83.968, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE2981.jpg', 'highlights': ['The lecture covers system description, controller design, and Kalman filter implementation in MATLAB, providing a high-level understanding of optimal and modern control theory.', 'The goal is to familiarize the audience with major types of optimal and modern control theory and to teach practical implementation in MATLAB, enabling individuals to work with real systems.', 'The chapter aims to provide a perspective on the ease and challenges of control theory today, allowing individuals to understand the pressing needs in the field.']}, {'end': 454.21, 'segs': [{'end': 111.701, 'src': 'embed', 'start': 88.511, 'weight': 0, 'content': [{'end': 95.98, 'text': 'I think about the world in terms of dynamical systems, so systems of ordinary differential equations in terms of the state of your system.', 'start': 88.511, 'duration': 7.469}, {'end': 101.516, 'text': 'And this has been an extremely successful viewpoint for modeling real-world phenomenon.', 'start': 97.014, 'duration': 4.502}, {'end': 111.701, 'text': 'So we model the fluid flow over a wing, or the population dynamics in a city, or the spread of a disease, or the stock market,', 'start': 102.076, 'duration': 9.625}], 'summary': 'Dynamical systems model real-world phenomenon successfully.', 'duration': 23.19, 'max_score': 88.511, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE88511.jpg'}, {'end': 161.234, 'src': 'embed', 'start': 135.336, 'weight': 2, 'content': [{'end': 148.267, 'text': 'And so that could be just imposing some control law, just setting inputs into that system in a certain pre-planned way to manipulate it.', 'start': 135.336, 'duration': 12.931}, {'end': 154.711, 'text': "Or you could actually measure that system and make decisions based on how the system is responding to what you're doing.", 'start': 148.948, 'duration': 5.763}, {'end': 161.234, 'text': "And so that's kind of the overarching view in control theory is that you have some dynamical system of interest.", 'start': 155.871, 'duration': 5.363}], 'summary': 'Control theory involves manipulating systems through input or measurement-based decisions.', 'duration': 25.898, 'max_score': 135.336, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE135336.jpg'}, {'end': 223.262, 'src': 'embed', 'start': 200.134, 'weight': 3, 'content': [{'end': 210.117, 'text': 'Okay. so, for example, if you see a large 18-wheeler transport truck going down the highway and it has those streamlined tail sections,', 'start': 200.134, 'duration': 9.983}, {'end': 218.279, 'text': "that's a form of passive control that's passively causing the air around the truck to behave in a favorable way to reduce drag.", 'start': 210.117, 'duration': 8.162}, {'end': 223.262, 'text': "And if you can get away with passive control of your system, that's actually great,", 'start': 219.019, 'duration': 4.243}], 'summary': 'Passive control, like streamlined tail sections, reduces drag for transport trucks.', 'duration': 23.128, 'max_score': 200.134, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE200134.jpg'}, {'end': 268.83, 'src': 'embed', 'start': 241.112, 'weight': 4, 'content': [{'end': 249.696, 'text': "And so active control essentially just means that this is control where we're actually pumping energy into the system to actively manipulate its behavior.", 'start': 241.112, 'duration': 8.584}, {'end': 253.918, 'text': "And there's lots and lots of different types of active control.", 'start': 250.976, 'duration': 2.942}, {'end': 258.519, 'text': "So one that I'm going to tell you about is open loop.", 'start': 254.458, 'duration': 4.061}, {'end': 268.83, 'text': 'This is probably the most common form of active control, where, essentially, you have your system of interest,', 'start': 259.986, 'duration': 8.844}], 'summary': 'Active control manipulates system behavior by pumping energy. open loop is a common form.', 'duration': 27.718, 'max_score': 241.112, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE241112.jpg'}, {'end': 414.019, 'src': 'embed', 'start': 381.852, 'weight': 1, 'content': [{'end': 389.297, 'text': 'Okay? And so the idea is that what we can do is called closed loop feedback control.', 'start': 381.852, 'duration': 7.445}, {'end': 394.041, 'text': 'So closed loop feedback control.', 'start': 389.337, 'duration': 4.704}, {'end': 403.264, 'text': 'And essentially what this means is that we take sensors I think my pen is drying out.', 'start': 396.983, 'duration': 6.281}, {'end': 412.617, 'text': 'We take sensors, sensor measurements of what the system is actually doing, and then somehow we build a controller.', 'start': 404.165, 'duration': 8.452}, {'end': 414.019, 'text': "I'm just going to call this a controller.", 'start': 412.657, 'duration': 1.362}], 'summary': 'Closed loop feedback control uses sensors to measure system data and build a controller.', 'duration': 32.167, 'max_score': 381.852, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE381852.jpg'}], 'start': 88.511, 'title': 'Control theory in dynamical systems', 'summary': 'Explores the application of control theory in dynamical systems, emphasizing its success in modeling real-world phenomena and the significance of manipulating systems to change their behavior. it also discusses passive and active control in systems, focusing on open loop control as a common form of active control, and feedback control in physics, highlighting the advantages of closed-loop feedback control in stabilizing the system with minimal energy input and sensor measurements.', 'chapters': [{'end': 182.766, 'start': 88.511, 'title': 'Control theory in dynamical systems', 'summary': 'Explores the application of control theory in dynamical systems, emphasizing its success in modeling real-world phenomenon and the significance of manipulating systems to change their behavior, with a focus on various types of control.', 'duration': 94.255, 'highlights': ['The success of modeling real-world phenomena using dynamical systems, such as fluid flow over a wing, population dynamics in a city, disease spread, and stock market, is attributed to the framework of ordinary differential equations (ODEs) (Relevance: High)', 'The need to actively manipulate systems by imposing control laws or making decisions based on system responses is emphasized, indicating the broader view in control theory (Relevance: Medium)', 'The application of control theory involves designing control policies to change the behavior of a dynamical system, with the example of making a pendulum or a crane more stable (Relevance: Low)', 'The chapter delves into the various types of control that exist, setting the stage for further exploration of this topic (Relevance: Low)']}, {'end': 300.983, 'start': 183.447, 'title': 'Passive and active control in systems', 'summary': 'Discusses the concepts of passive and active control in systems, highlighting the prevalence and benefits of passive control, and the need for active control to actively manipulate system behavior, with a focus on open loop control as a common form of active control.', 'duration': 117.536, 'highlights': ['Passive control, such as the streamlined tail sections on a truck, passively manipulates the air around the truck to reduce drag, demonstrating the benefits of passive control in minimizing energy expenditure and achieving desired effects.', "Active control involves actively manipulating a system's behavior by pumping energy into the system, with open loop control being a common form that reverse designs the system to determine the perfect input to achieve a desired output.", 'The chapter explains the prevalence and benefits of passive control, emphasizing that if passive control can achieve the desired effect, it is advantageous due to minimal energy expenditure and upfront design requirements.']}, {'end': 454.21, 'start': 300.983, 'title': 'Feedback control in physics', 'summary': 'Discusses the concept of open-loop and closed-loop feedback control in physics, using an inverted pendulum as an example, highlighting the advantages of closed-loop feedback control in stabilizing the system with minimal energy input and sensor measurements.', 'duration': 153.227, 'highlights': ['Closed-loop feedback control allows for stabilizing the system with minimal energy input and sensor measurements, leading to more subtle control and stability with very low energy input and small hand motions.', 'Open-loop control requires constantly putting in energy to the input signal, leading to instability when the energy input is stopped.', "Using closed-loop feedback control, measurements of the system's output can enable much more subtle control and stabilization with lower energy input."]}], 'duration': 365.699, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE88511.jpg', 'highlights': ['The success of modeling real-world phenomena using dynamical systems, such as fluid flow over a wing, population dynamics in a city, disease spread, and stock market, is attributed to the framework of ordinary differential equations (ODEs) (Relevance: High)', 'Closed-loop feedback control allows for stabilizing the system with minimal energy input and sensor measurements, leading to more subtle control and stability with very low energy input and small hand motions (Relevance: High)', 'The need to actively manipulate systems by imposing control laws or making decisions based on system responses is emphasized, indicating the broader view in control theory (Relevance: Medium)', 'Passive control, such as the streamlined tail sections on a truck, passively manipulates the air around the truck to reduce drag, demonstrating the benefits of passive control in minimizing energy expenditure and achieving desired effects (Relevance: Medium)', "Active control involves actively manipulating a system's behavior by pumping energy into the system, with open loop control being a common form that reverse designs the system to determine the perfect input to achieve a desired output (Relevance: Low)"]}, {'end': 775.871, 'segs': [{'end': 554.486, 'src': 'embed', 'start': 528.202, 'weight': 3, 'content': [{'end': 533.284, 'text': 'Why would you actually want to have the sensors feeding back into your system?', 'start': 528.202, 'duration': 5.082}, {'end': 544.09, 'text': 'Okay, so, one answer that I get most often is maybe my system has some inherent uncertainty.', 'start': 535.205, 'duration': 8.885}, {'end': 554.486, 'text': 'Okay, so if my system is uncertain, so uncertainty is one of the main enemies of open loop control.', 'start': 544.11, 'duration': 10.376}], 'summary': 'Sensors are essential to counteract system uncertainty in open loop control.', 'duration': 26.284, 'max_score': 528.202, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE528202.jpg'}, {'end': 605.143, 'src': 'embed', 'start': 575.973, 'weight': 4, 'content': [{'end': 583.441, 'text': "But if I measure the output and I realize that it's not doing what I want it to do, I can adjust my control law,", 'start': 575.973, 'duration': 7.468}, {'end': 585.663, 'text': "even if I don't have a perfect model of my system.", 'start': 583.441, 'duration': 2.222}, {'end': 587.405, 'text': 'So uncertainty is a big one.', 'start': 586.243, 'duration': 1.162}, {'end': 591.669, 'text': 'Another really important one is instability.', 'start': 588.706, 'duration': 2.963}, {'end': 602.861, 'text': 'So with open loop control, I can never fundamentally change the behavior of the system itself.', 'start': 594.875, 'duration': 7.986}, {'end': 605.143, 'text': 'So, in the pendulum example,', 'start': 603.822, 'duration': 1.321}], 'summary': 'Adjust control law to address uncertainty and prevent instability in open loop control.', 'duration': 29.17, 'max_score': 575.973, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE575973.jpg'}, {'end': 662.479, 'src': 'embed', 'start': 620.914, 'weight': 0, 'content': [{'end': 630.444, 'text': 'But when I have feedback control, I can directly manipulate the actual dynamics of this closed loop system and I can change the dynamic properties.', 'start': 620.914, 'duration': 9.53}, {'end': 633.106, 'text': 'I can change the eigenvalues of this closed loop system.', 'start': 630.484, 'duration': 2.622}, {'end': 637.11, 'text': "Okay? And I'm going to show you that as the last example in this overview.", 'start': 633.126, 'duration': 3.984}, {'end': 646.758, 'text': 'So the third thing that I think is really, really neat is that with feedback control you can also reject disturbances in your system.', 'start': 638.071, 'duration': 8.687}, {'end': 651.642, 'text': "So let's say that I have some external disturbance D that's coming into my system.", 'start': 647.318, 'duration': 4.324}, {'end': 655.905, 'text': 'And this happens all of the time.', 'start': 654.284, 'duration': 1.621}, {'end': 662.479, 'text': "So for example, let's say in my pendulum example, there's a gust of wind.", 'start': 657.915, 'duration': 4.564}], 'summary': 'Feedback control allows direct manipulation of closed loop dynamics, eigenvalues, and disturbance rejection.', 'duration': 41.565, 'max_score': 620.914, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE620914.jpg'}, {'end': 786.599, 'src': 'embed', 'start': 757.699, 'weight': 2, 'content': [{'end': 760.181, 'text': 'and so you almost have to put no energy in to correct it.', 'start': 757.699, 'duration': 2.482}, {'end': 768.586, 'text': 'So effective sensor-based feedback control is also much more efficient, which is really, really important in lots of applications.', 'start': 761.121, 'duration': 7.465}, {'end': 775.871, 'text': "So if you're going to send a rocket somewhere, you better have an efficient controller because you don't want to be wasting fuel.", 'start': 768.626, 'duration': 7.245}, {'end': 786.599, 'text': 'So the last thing I want to show you is just this idea of why you can change the fundamental system dynamics and change the stability with feedback control.', 'start': 777.773, 'duration': 8.826}], 'summary': 'Efficient sensor-based feedback control saves energy, vital for applications like rocket propulsion.', 'duration': 28.9, 'max_score': 757.699, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE757699.jpg'}], 'start': 454.21, 'title': 'Feedback control in systems', 'summary': 'Explains the importance of sensor-based feedback control in improving system performance, including addressing uncertainty and instability, and the advantages over open loop control in achieving optimal system behavior. it also highlights the benefits of feedback control, such as manipulating closed-loop system dynamics, rejecting disturbances, handling uncertainty, changing system stability, and improving energy efficiency.', 'chapters': [{'end': 620.033, 'start': 454.21, 'title': 'Feedback control basics', 'summary': 'Explains the importance of sensor-based feedback control in improving system performance, including addressing uncertainty and instability, and the advantages over open loop control in achieving optimal system behavior.', 'duration': 165.823, 'highlights': ['Sensor-based feedback control is crucial for improving system performance and addressing uncertainty and instability.', 'Uncertainty is a key factor favoring feedback control over open loop control.', 'Instability is another critical factor favoring feedback control over open loop control.']}, {'end': 775.871, 'start': 620.914, 'title': 'Benefits of feedback control in systems', 'summary': 'Highlights the advantages of feedback control including the ability to manipulate closed-loop system dynamics, reject disturbances, handle uncertainty, change system stability, and improve energy efficiency.', 'duration': 154.957, 'highlights': ['Feedback control can manipulate the dynamics of a closed-loop system and change eigenvalues.', 'Feedback control enables the rejection of external disturbances in the system.', 'Feedback control can handle uncertainties and disturbances, improving system stability.', 'Efficient sensor-based feedback control reduces energy consumption and is crucial for various applications.']}], 'duration': 321.661, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE454210.jpg', 'highlights': ['Feedback control can manipulate the dynamics of a closed-loop system and change eigenvalues.', 'Feedback control enables the rejection of external disturbances in the system.', 'Efficient sensor-based feedback control reduces energy consumption and is crucial for various applications.', 'Sensor-based feedback control is crucial for improving system performance and addressing uncertainty and instability.', 'Uncertainty is a key factor favoring feedback control over open loop control.', 'Instability is another critical factor favoring feedback control over open loop control.']}, {'end': 1168.193, 'segs': [{'end': 892.74, 'src': 'heatmap', 'start': 802.473, 'weight': 0, 'content': [{'end': 807.335, 'text': 'x is a vector that describes all of the quantities of interest in my system.', 'start': 802.473, 'duration': 4.862}, {'end': 811.576, 'text': 'So for example, in my pendulum, it could be the angle and angular velocity.', 'start': 807.395, 'duration': 4.181}, {'end': 812.496, 'text': 'It could be two states.', 'start': 811.596, 'duration': 0.9}, {'end': 817.158, 'text': 'If I have you know, an airplane going through the sky.', 'start': 813.537, 'duration': 3.621}, {'end': 826.485, 'text': 'It could be the three, the position vector x, y, and z, and also its rotation angles and their derivatives.', 'start': 817.178, 'duration': 9.307}, {'end': 834.891, 'text': 'Okay, so it could be like a six degree of freedom or 12 state, 12 component vector x.', 'start': 826.705, 'duration': 8.186}, {'end': 840.29, 'text': "And so what we're going to look at is the system x dot equals ax.", 'start': 834.891, 'duration': 5.399}, {'end': 846.156, 'text': "So we're going to start with linear systems of equations that describe how those states interact with each other.", 'start': 840.551, 'duration': 5.605}, {'end': 853.742, 'text': "Okay, and so I'm going to assume that we're all pretty comfortable with this linear systems of ODEs.", 'start': 846.176, 'duration': 7.566}, {'end': 864.884, 'text': 'So for example, we know that the solution of this is x of t equals e to the matrix A t times x at time 0.', 'start': 853.823, 'duration': 11.061}, {'end': 868.046, 'text': 'So we know how the system behaves.', 'start': 864.884, 'duration': 3.162}, {'end': 874.849, 'text': 'We know that if A has any eigenvalues with a positive real part, then the system will be unstable.', 'start': 868.106, 'duration': 6.743}, {'end': 881.833, 'text': 'And if all of the eigenvalues have negative real part, then these have stable dynamics that go to 0 as time goes to infinity.', 'start': 875.49, 'duration': 6.343}, {'end': 888.997, 'text': "But what we're going to do in control theory is we're going to add plus be U.", 'start': 882.694, 'duration': 6.303}, {'end': 892.74, 'text': "So we're going to add this ability to actuate or manipulate our system.", 'start': 888.997, 'duration': 3.743}], 'summary': 'In control theory, we analyze linear systems of odes to understand system behavior and introduce control input for manipulation.', 'duration': 79.36, 'max_score': 802.473, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE802473.jpg'}, {'end': 938.262, 'src': 'heatmap', 'start': 912.549, 'weight': 0.791, 'content': [{'end': 917.276, 'text': 'and B tells you how this control knob directly affects the time rate of change of my state.', 'start': 912.549, 'duration': 4.727}, {'end': 928.415, 'text': "Okay? And down the road we're going to look at another extension where we're actually going to measure only certain aspects of the state.", 'start': 918.018, 'duration': 10.397}, {'end': 932.258, 'text': "So we're going to measure some linear combination of the state x.", 'start': 928.435, 'duration': 3.823}, {'end': 934.499, 'text': 'And this might actually be a limited set of measurements.', 'start': 932.258, 'duration': 2.241}, {'end': 938.262, 'text': "We might not measure all of this state if it's high dimensional.", 'start': 934.539, 'duration': 3.723}], 'summary': 'Control knob affects time rate of change. will measure limited aspects of state.', 'duration': 25.713, 'max_score': 912.549, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE912549.jpg'}, {'end': 1126.26, 'src': 'embed', 'start': 1100.732, 'weight': 3, 'content': [{'end': 1109.04, 'text': 'so figuring out when the system is controllable and how to design this case so that it is well controlled are going to be the subjects of the next couple of lectures.', 'start': 1100.732, 'duration': 8.308}, {'end': 1114.267, 'text': 'Okay? But really, really important, feedback solves all of these fundamental problems.', 'start': 1109.602, 'duration': 4.665}, {'end': 1120.934, 'text': "If I have an uncertainty in my system, I can compensate for it by measuring what's actually happening and feeding that back.", 'start': 1114.547, 'duration': 6.387}, {'end': 1126.26, 'text': 'If I have an instability in my system, I can actually change the dynamics with this feedback.', 'start': 1121.595, 'duration': 4.665}], 'summary': 'Feedback solves fundamental problems by compensating for uncertainty and changing system dynamics.', 'duration': 25.528, 'max_score': 1100.732, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE1100732.jpg'}, {'end': 1168.193, 'src': 'embed', 'start': 1140.953, 'weight': 4, 'content': [{'end': 1144.215, 'text': 'And finally, feedback control is efficient.', 'start': 1140.953, 'duration': 3.262}, {'end': 1150.981, 'text': "If you're doing effective feedback control to stabilize a system, then the more effective you are, the less energy you have to put in.", 'start': 1144.375, 'duration': 6.606}, {'end': 1154.963, 'text': 'Okay, so this should be a really exciting set of lectures.', 'start': 1151.661, 'duration': 3.302}, {'end': 1161.648, 'text': "I'm really hoping to get you up to speed quickly and with MATLAB examples so that you can control these systems.", 'start': 1155.144, 'duration': 6.504}, {'end': 1166.972, 'text': 'You can design controllers to actually manipulate your system to do what you want it to do.', 'start': 1161.668, 'duration': 5.304}, {'end': 1168.193, 'text': 'Okay, thank you.', 'start': 1167.652, 'duration': 0.541}], 'summary': 'Efficient feedback control saves energy, aims to quickly get up to speed with matlab examples.', 'duration': 27.24, 'max_score': 1140.953, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE1140953.jpg'}], 'start': 777.773, 'title': 'Feedback control and control theory basics', 'summary': "Delves into changing system dynamics through feedback control, emphasizing state-space systems and eigenvalues' impact on stability, and also covers the integration of actuation and feedback measurement in control theory, demonstrating the role of sensor-based feedback in stabilizing and manipulating dynamical systems.", 'chapters': [{'end': 881.833, 'start': 777.773, 'title': 'Feedback control and system dynamics', 'summary': 'Explains the concept of changing system dynamics and stability using feedback control, focusing on state-space systems of ordinary differential equations, and the implications of eigenvalues on system stability.', 'duration': 104.06, 'highlights': ['The system x dot equals ax describes how the states interact with each other, and the solution x of t equals e to the matrix A t times x at time 0 provides insights into system behavior.', 'The eigenvalues of matrix A determine the stability of the system, with positive real part eigenvalues indicating instability and negative real part eigenvalues indicating stable dynamics that converge to 0 over time.', "The state variable x is a vector that describes the quantities of interest in the system, such as the angle and angular velocity of a pendulum or the position and rotation of an airplane, with implications for the system's degree of freedom and component vector size."]}, {'end': 1168.193, 'start': 882.694, 'title': 'Control theory basics', 'summary': 'Explains the integration of actuation and feedback measurement in control theory, showcasing the impact of feedback in stabilizing and manipulating dynamical systems, with examples of sensor-based feedback and its ability to stabilize an originally unstable system.', 'duration': 285.499, 'highlights': ['The integration of actuation and feedback measurement in control theory', 'The impact of feedback in stabilizing and manipulating dynamical systems', 'Examples of sensor-based feedback and its ability to stabilize an originally unstable system']}], 'duration': 390.42, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/Pi7l8mMjYVE/pics/Pi7l8mMjYVE777773.jpg', 'highlights': ['The eigenvalues of matrix A determine the stability of the system, with positive real part eigenvalues indicating instability and negative real part eigenvalues indicating stable dynamics that converge to 0 over time.', 'The system x dot equals ax describes how the states interact with each other, and the solution x of t equals e to the matrix A t times x at time 0 provides insights into system behavior.', "The state variable x is a vector that describes the quantities of interest in the system, such as the angle and angular velocity of a pendulum or the position and rotation of an airplane, with implications for the system's degree of freedom and component vector size.", 'The integration of actuation and feedback measurement in control theory', 'The impact of feedback in stabilizing and manipulating dynamical systems', 'Examples of sensor-based feedback and its ability to stabilize an originally unstable system']}], 'highlights': ['The success of modeling real-world phenomena using dynamical systems, such as fluid flow over a wing, population dynamics in a city, disease spread, and stock market, is attributed to the framework of ordinary differential equations (ODEs) (Relevance: High)', 'Closed-loop feedback control allows for stabilizing the system with minimal energy input and sensor measurements, leading to more subtle control and stability with very low energy input and small hand motions (Relevance: High)', 'The lecture covers system description, controller design, and Kalman filter implementation in MATLAB, providing a high-level understanding of optimal and modern control theory (Relevance: Medium)', 'The goal is to familiarize the audience with major types of optimal and modern control theory and to teach practical implementation in MATLAB, enabling individuals to work with real systems (Relevance: Medium)', 'Feedback control can manipulate the dynamics of a closed-loop system and change eigenvalues (Relevance: Medium)', 'The need to actively manipulate systems by imposing control laws or making decisions based on system responses is emphasized, indicating the broader view in control theory (Relevance: Medium)', 'Efficient sensor-based feedback control reduces energy consumption and is crucial for various applications (Relevance: Medium)', 'Sensor-based feedback control is crucial for improving system performance and addressing uncertainty and instability (Relevance: Medium)', 'The chapter aims to provide a perspective on the ease and challenges of control theory today, allowing individuals to understand the pressing needs in the field (Relevance: Low)', "Active control involves actively manipulating a system's behavior by pumping energy into the system, with open loop control being a common form that reverse designs the system to determine the perfect input to achieve a desired output (Relevance: Low)"]}