Signals and Linear Systems for Robotics
The mathematics of robot signals and dynamics: signal types, energy and power, system properties and linearization, convolution and impulse response, first- and second-order models of motors and mechanisms, Laplace transforms, transfer functions and poles, block diagrams and feedback, Bode plots and stability margins, Fourier series and the FFT, sampling, aliasing and the zero-order hold, the z-transform and discretization, digital filters for sensors, and state-space models, ending with a capstone measurement design for a geared joint.
ROB-230 Year 2 3 credits 12 lessons · 6 h 17 min
Offered by HSM University · Robotics
What you'll learn
- Classify robot signals as continuous or discrete, analog or digital, periodic or aperiodic, and compute their energy, power and RMS value
- Test systems for linearity, time invariance, causality, memory and BIBO stability, and linearize nonlinear robot models about an operating point
- Compute the output of an LTI system by convolution with its impulse response, and relate impulse and step responses
- Derive differential equations for RC filters, mass-spring-dampers and DC motors, and interpret first- and second-order responses through time constant, natural frequency and damping ratio
- Use the Laplace transform to find transfer functions, poles and zeros, invert transforms by partial fractions and apply the final value theorem
- Reduce block diagrams, derive closed-loop transfer functions and explain how feedback affects steady-state error, disturbance rejection, sensitivity and stability
- Sketch and interpret Bode plots, determine bandwidth and resonance, and evaluate gain and phase margins including the effect of delay
- Compute Fourier series and spectra, and use the FFT with appropriate record length, scaling and windowing to analyze sensor data
- Apply the sampling theorem, predict alias frequencies, specify anti-aliasing filters, and quantify quantization noise and zero-order-hold delay
- Analyze discrete-time systems with difference equations and the z-transform, test stability with the unit circle, and discretize continuous designs by Euler, Tustin and exact methods
- Design and implement moving-average, IIR low-pass, high-pass, notch and differentiating filters for robot sensors, and account for their group delay
- Build state-space models, relate eigenvalues to poles, discretize them exactly, and combine modeling, sampling and filtering into a measurement design for a robot joint
Course content
12 lessons · 6 h 17 min total · final exam
- 1 Signals in robotics 33 min · quiz
- 2 Systems and their properties 33 min · quiz
- 3 Convolution and the impulse response 29 min · quiz
- 4 Differential equations and first- and second-order responses 28 min · quiz
- 5 The Laplace transform and transfer functions 31 min · quiz
- 6 Block diagrams and feedback 31 min · quiz
- 7 Frequency response and Bode plots 31 min · quiz
- 8 Fourier series, the Fourier transform and the FFT 30 min · quiz
- 9 Sampling, aliasing and reconstruction 34 min · quiz
- 10 Discrete-time systems and the z-transform 33 min · quiz
- 11 Digital filters for robot sensors 30 min · quiz
- 12 State-space models and capstone: a motor-driven joint 34 min · quiz
- E Final exam 20 questions
Requirements
Recommended background. You can start any course at any time.
Description
The mathematics of robot signals and dynamics: signal types, energy and power, system properties and linearization, convolution and impulse response, first- and second-order models of motors and mechanisms, Laplace transforms, transfer functions and poles, block diagrams and feedback, Bode plots and stability margins, Fourier series and the FFT, sampling, aliasing and the zero-order hold, the z-transform and discretization, digital filters for sensors, and state-space models, ending with a capstone measurement design for a geared joint.
Part of the Science stream, typically taken in year 2.