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System Design for Uncertainty
This text covers the design, construction, and testing of field robotic systems, through team projects with each student responsible for a specific subsystem. Projects focus on electronics, instrumentation, and machine elements. Design for operation in uncertain conditions is a focus point, with ocean waves and marine structures as a central theme. Topics include basic statistics, linear systems, Fourier transforms, random processes, spectra, ethics in engineering practice, and extreme events.
- Author
- Franz S. Hover & Michael S. Triantafyllou
- Publisher
- Massachusetts Institute of Technology
- Source
- LibreTexts
- License
- CC BY-NC-SA
- Language
- EN
Contents· 96 sections
- 01: Introduction
- 1.01: Introduction to Course
- 02: Linear Systems
- 2.01: Definition of a System
- 2.02: Time-Invariant Systems
- 2.03: Linear Systems
- 2.04: The Impulse Response and Convolution
- 2.05: Causal Systems
- 2.06: An Example of Finding the Impulse Response
- 2.07: Complex Numbers
- 2.08: Fourier Transform
- 2.09: The Angle of a Transfer Function
- 2.10: The Laplace Transform
- 03: Probability
- 3.01: Events
- 3.02: Conditional Probability
- 3.03: Bayes' Rule
- 3.04: Random Variables
- 3.05: Continuous Random Variables and the Probability Density Function
- 3.06: The Gaussian PDF
- 3.07: The Cumulative Probability Function
- 3.08: Central Limit Theorem
- 04: Random Processes
- 4.01: Time Averages
- 4.02: Ensemble Averages
- 4.03: Stationarity
- 4.04: The Spectrum- Definition
- 4.05: Wiener-Khinchine Relation
- 4.06: Spectrum Interpretation
- 05: Short-Term Statistics
- 5.01: Introduction to Short-Term Statistics
- 5.02: Central Role of the Gaussian and Rayleigh Distributions
- 5.03: Frequency of Upcrossings
- 5.04: Maxima At and Above a Given Level
- 5.05: 1 N'th Highest Maxima
- 5.06: 1 N'th Average Value
- 5.07: The 100-Year Wave - Estimate from Short-Term Statistics
- 06: Water Waves
- 6.01: Constitutive and Governing Relations
- 6.02: Rotation and Viscous Effects
- 6.03: Velocity Potential
- 6.04: Linear Waves
- 6.05: Deepwater Waves
- 6.06: Wave Loading of Stationary and Moving Bodies
- 6.07: Limits of the Linear Theory
- 6.08: Characteristics of Real Ocean Waves
- 07: Optimization
- 7.01: Introduction to Optimization
- 7.02: Single-Dimension Continuous Optimization
- 7.03: Multi-Dimensional Continuous Optimization
- 7.04: Linear Programming
- 7.05: Integer Linear Programming
- 7.06: Min-Max Optimization for Discrete Choices
- 7.07: Dynamic Programming
- 7.08: Solving Dynamic Programming on a Computer
- 08: Stochastic Simulation
- 8.01: Introduction to Stochastic Simulation
- 8.02: Monte Carlo Simulation
- 8.03: Making Random Numbers
- 8.04: Grid-Based Techniques
- 8.05: Issues of Cost and Accuracy
- 09: Kinematics of Moving Frames
- 9.01: Introduction to Moving-Frame Kinematics
- 9.02: Rotation of Reference Frames
- 9.03: Differential Rotations
- 9.04: Rate of Change of Euler Angles
- 9.05: A Practical Example- Dead Reckoning
- 10: Vehicle Inertial Dynamics
- 10.01: Momentum of a Particle
- 10.02: Linear Momentum in a Moving Frame
- 10.03: Example - Mass on a String
- 10.04: Angular Momentum
- 10.05: Example Spinning Book
- 10.6: Parallel Axis Theorem
- 10.7: Basis for Simulation
- 10.8: What Does an Inertial Measurement Unit Measure?
- 11: Control Fundamentals
- 11.01: New Page
- 11.02: New Page
- 11.03: Stability
- 11.04: Representing Linear Systems
- 11.05: Block Diagrams and Transfer Functions
- 11.06: PID Controllers
- 11.7: Example: PID Control
- 11.8: Heuristic Tuning
- 12: Control Systems Loopshaping
- 12.01: Introduction to Loopshaping
- 12.02: Roots of Stability–Nyquist Criterion
- 12.03: Design for Nominal Performance
- 12.04: Design for Robustness
- 12.05: Robust Performance
- 12.06: Implications of Bode’s Integral
- 12.7: The Recipe for Loopshaping
- 13: Math Facts
- 13.01: Vectors
- 13.02: Matrices