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- 12 Mar 2023: A new version of the Optimization-Based Control (OBC) supplement is now complete and posted
- 16 Nov 2024: Python figure sources updated for python-control v0.10.1
- 24 Jul 2020: Copyedited version of FBS2e now available for download
- 28 Aug 2021: Links to first edition supplemental information added to chapter pages
- 30 Oct 2020: Notes on Linear Systems Theory updated (release 0.2.2)
- Admin
- Architecture and System Design
- Bibliography
- Bicycle.py
- Bicycle dynamics
- Biomolecular Feedback Systems
- Congctrl.py
- Congestion control
- Cruise.py
- Cruise control
- Domitilla Del Vecchio
- Dynamic Behavior
- Errata
- Errata: 'a' in equation (14.13) should be 's'
- Errata: C matrix in Example 8.7 (vectored thrust aircraft) is incorrect
- Errata: Example 8.10 missing factor of v, a1 and a2 flipped
- Errata: feedforward term in control law for Example 7.5 is missing Le term
- Errata: sign errors in Example 5.18 (noise cancellation)
- Examples
- Exercise: Exploring the dynamics of a rolling mill
- Exercise: Popular articles about control
- FBS
- FBS release 3.1.5
- Fbs.py
- Feedback Principles
- Feedback Systems: An Introduction for Scientists and Engineers
- Figure 1.11: A feedback system for controlling the velocity of a vehicle
- Figure 1.18: Air–fuel controller based on selectors
- Figure 2.11: Response to a step change in the reference signal for a system with a PI controller having two degrees of freedom
- Figure 2.12: Responses of a static nonlinear system
- Figure 2.14: Responses of the systems with integral feedback
- Figure 2.19: System with positive feedback and saturation
- Figure 2.8: Step responses for a first-order, closed loop system with proportional and PI control
- Figure 2.9: Responses to a unit step change in the reference signal for different values of the design parameters
- Figure 3.11: Simulation of the forced spring–mass system with different simulation time constants
- Figure 3.12: Frequency response computed by measuring the response of individual sinusoids
- Figure 3.22: Queuing dynamics
- Figure 3.24: Consensus protocols for sensor networks
- Figure 3.26: The repressilator genetic regulatory network
- Figure 3.28: Response of a neuron to a current input
- Figure 3.2: Illustration of a state model
- Figure 3.4: Input/output response of a linear system
- Figure 3.8: Discrete-time simulation of the predator–prey model
- Figure 4.12: Internet congestion control
- Figure 4.13: Internet congestion control for N identical sources across a single link
- Figure 4.20: Simulation of the predator-prey system
- Figure 4.2: Torque curves for typical car engine
- Figure 4.3: Car with cruise control encountering a sloping road
- Figure 5.10: Phase portraits for a congestion control protocol running with N = 60 identical source computers
- Figure 5.11: Comparison between phase portraits for a nonlinear system and its linearization
- Figure 5.12: Stability analysis for a tanker
- Figure 5.13: Solution curves for a stable limit cycle
- Figure 5.15: Stability of a genetic switch
- Figure 5.16: Dynamics of a genetic switch
- Figure 5.17: Stabilized inverted pendulum
- Figure 5.18: Bifurcation analysis of the predator–prey system
- Figure 5.19: Stability plots for a bicycle moving at constant velocity
- Figure 5.1: Response of a damped oscillator
- Figure 5.21: Simulation of noise cancellation
- Figure 5.3: Phase portraits
- Figure 5.4: Equilibrium points for an inverted pendulum
- Figure 5.5: Phase portrait and time domain simulation for a system with a limit cycle
- Figure 5.6: Illustration of Lyapunov’s concept of a stable solution
- Figure 5.7: Phase portrait and time domain simulation for a system with a single stable equilibrium point
- Figure 5.8: Phase portrait and time domain simulation for a system with a single asymptotically stable equilibrium point
- Figure 5.9: Phase portrait and time domain simulation for a system with a single unstable equilibrium point
- Figure 6.10: Response of a compartment model to a constant drug infusion
- Figure 6.12: Active band-pass filter
- Figure 6.13: AFM frequency response
- Figure 6.14: Linear versus nonlinear response for a vehicle with PI cruise control
- Figure 6.1: Superposition of homogeneous and particular solutions
- Figure 6.5: Modes for a second-order system with real eigenvalues
- Figure 7.6: State feedback control of a steering system
- Figure 8.13: Vehicle steering using gain scheduling
- Frequency Domain Analysis
- Frequency Domain Design
- Fundamental Limits
- Introduction
- Karl J. Åström
- LST
- LST release 0.2.2
- LTS release 0.2.2
- Lecture: Introduction to Feedback and Control (Caltech, Fall 2008)
- Lecture: Introduction to Feedback and Control (Caltech, Spring 2024)
- Lectures
- Linear Systems
- Main Page
- NCS
- OBC
- OBC: Archived news
- Output Feedback
- PID Control
- Predator-prey dynamics
- Predprey.py
- Preface
- Question: Can a control system include a human operator as a component?
- Question: How are stability, performance and robustness different?
- Question: How can I go from a continuous time linear ODE to a discrete time representation?
- Question: How can we tell from the phase plots if the system is oscillating
- Question: How can we tell from the phase plots if the system is oscillating?
- Question: How do you know when your model is sufficiently complex
- Question: How do you know when your model is sufficiently complex?
- Question: In the predator prey example, where is the fox birth rate term
- Question: In the predator prey example, where is the fox birth rate term?
- Question: What is "closed form"
- Question: What is "closed form"?
- Question: What is a state
- Question: What is a state? How does one determine what is a state and what is not?
- Question: What is a stochastic system
- Question: What is a stochastic system?
- Question: What is the advantage of having a model
- Question: What is the advantage of having a model?
- Question: What is the definition of a system
- Question: What is the definition of a system?
- Question: Why does the effective service rate f(x) go to zero when x = 0 in the example on queuing systems
- Question: Why does the effective service rate f(x) go to zero when x = 0 in the example on queuing systems?
- Question: Why isn't there a term for the rabbit death rate besides being killed by the foxes
- Question: Why isn't there a term for the rabbit death rate besides being killed by the foxes?
- Robust Performance
- Software
- Spring-mass system
- Springmass.py
- State Feedback
- Supplement: Linear Systems Theory
- Supplement: Networked Control Systems
- Supplement: Optimization-Based Control
- System Modeling
- Transfer Functions