I didn’t use it as a student, but Feedback Systems from Murray and Åstrôm tries to be pretty accessible. If you’re going to forego Fourier analysis, I think you need to have at least taken differential equations, and maybe part of the problem is that CS majors in many places tend not to require that…? Thus to cultural home of control being EE/ME…? In my experience, super smart CS folks are surprisingly often allergic to continuous time.
I think all of the main concepts can be taught in discrete time, but it's going to take time and effort to do the translation. Demonstrating this is on my (ever expanding) long list of quixotic academic quests.
One of the ways I teach feedback to grad CS students with zero background in controls is to think of getting a sufficient grade in the course while putting minimum effort. We had H and P grades, and anyone scoring above 70 gets an H. How do you plan the semester given there are 10 readings and 3 homeworks and 1 project. Has all basic elements of feedback without making it complicated.
Feedback is a slippery concept. For example, the usual definition of open-loop control when u(t) depends only on time t breaks down when we no longer assume that we have reliable clocks. Here's a neat little paper by Steve LaValle and Magnus Egerstedt, where they argue that one should think of "classical" open-loop control as perfect *time-feedback* control -- that is, you treat your clock as another sensor and then act based on the output of this sensor:
I think there are some nice technical overviews on feedback (e.g., https://www3.nd.edu/~pantsakl/Publications/449.pdf), but these are all couched in the standard control theory language. In any case, I look forward to your forthcoming book!
Here's an example of the promise and the pitfall of feedback: suppose I want to keep a beach ball a certain position on a windy day. The open loop approach is to apply zero force (assuming it starts at the right place). However, due to wind, the beach ball will move away from the desired location. After T steps, it can be as much as T distance units away.
The closed loop approach is to apply a force proportional to the current distance from my goal position. As long as my gain is reasonable, the ball will remain within a bounded distance of the goal, regardless of disturbances. But if I am too sensitive, i.e. the gain is too high, the ball will diverge into the distance exponentially in T. I can also run into similar trouble if my method for detecting the ball's position is imperfect (regardless of gain).
To me, feedback is all about reshaping the closed-loop dynamics. In the example above, the ball is marginally unstable. Reasonable values for gain lead to stable closed-loop dynamics, while unreasonable values lead to unstable closed-loop dynamics. Because of this perspective, my instinct has been to teach stability for uncontrolled dynamics before discussing feedback. But maybe that's wrong!
The way I teach this in our first undergraduate controls course is that the only way to stabilize an unstable plant is to use feedback. But the main explanation is via pole-shifting, and that requires Laplace and/or z-transforms.
I guess you could also explain this idea in terms of eigenvalues in a state space formulation? Although this would assume that students are not too put off by linear algebra...
This is where we eventually land toward the end of the semester. The coup de grace is to show that controllable SISO systems are feedback-equivalent to a chain of integrators, which nicely ties together the input-output and the state-space formulations.
But the idea that any transfer function has a minimal realization is nontrivial, and I don’t see how it can be easily brought up in an introductory course.
but Fourier transform is too cool to not learn
From your lips to god's ears...
I didn’t use it as a student, but Feedback Systems from Murray and Åstrôm tries to be pretty accessible. If you’re going to forego Fourier analysis, I think you need to have at least taken differential equations, and maybe part of the problem is that CS majors in many places tend not to require that…? Thus to cultural home of control being EE/ME…? In my experience, super smart CS folks are surprisingly often allergic to continuous time.
I think all of the main concepts can be taught in discrete time, but it's going to take time and effort to do the translation. Demonstrating this is on my (ever expanding) long list of quixotic academic quests.
One of the ways I teach feedback to grad CS students with zero background in controls is to think of getting a sufficient grade in the course while putting minimum effort. We had H and P grades, and anyone scoring above 70 gets an H. How do you plan the semester given there are 10 readings and 3 homeworks and 1 project. Has all basic elements of feedback without making it complicated.
Feedback is a slippery concept. For example, the usual definition of open-loop control when u(t) depends only on time t breaks down when we no longer assume that we have reliable clocks. Here's a neat little paper by Steve LaValle and Magnus Egerstedt, where they argue that one should think of "classical" open-loop control as perfect *time-feedback* control -- that is, you treat your clock as another sensor and then act based on the output of this sensor:
https://lavalle.pl/papers/LavEge07.pdf
They also show what goes wrong when your clock is not accurate, but you assume it is.
I think there are some nice technical overviews on feedback (e.g., https://www3.nd.edu/~pantsakl/Publications/449.pdf), but these are all couched in the standard control theory language. In any case, I look forward to your forthcoming book!
Here's an example of the promise and the pitfall of feedback: suppose I want to keep a beach ball a certain position on a windy day. The open loop approach is to apply zero force (assuming it starts at the right place). However, due to wind, the beach ball will move away from the desired location. After T steps, it can be as much as T distance units away.
The closed loop approach is to apply a force proportional to the current distance from my goal position. As long as my gain is reasonable, the ball will remain within a bounded distance of the goal, regardless of disturbances. But if I am too sensitive, i.e. the gain is too high, the ball will diverge into the distance exponentially in T. I can also run into similar trouble if my method for detecting the ball's position is imperfect (regardless of gain).
To me, feedback is all about reshaping the closed-loop dynamics. In the example above, the ball is marginally unstable. Reasonable values for gain lead to stable closed-loop dynamics, while unreasonable values lead to unstable closed-loop dynamics. Because of this perspective, my instinct has been to teach stability for uncontrolled dynamics before discussing feedback. But maybe that's wrong!
The way I teach this in our first undergraduate controls course is that the only way to stabilize an unstable plant is to use feedback. But the main explanation is via pole-shifting, and that requires Laplace and/or z-transforms.
I guess you could also explain this idea in terms of eigenvalues in a state space formulation? Although this would assume that students are not too put off by linear algebra...
This is where we eventually land toward the end of the semester. The coup de grace is to show that controllable SISO systems are feedback-equivalent to a chain of integrators, which nicely ties together the input-output and the state-space formulations.
But the idea that any transfer function has a minimal realization is nontrivial, and I don’t see how it can be easily brought up in an introductory course.