MTE 484 - Digital Control Applications

Info

Final: Dec 16 4PM - 6:30PM

• 6 questions
• 150 minutes (2.5 hours)
• 1 proof question
• 2 control design questions
  • emphasis on SD systems (but can often convert to DT system)
• 1-2 derivation questions
• 1 question on stability analysis/steady-state performance
• Cumulative, focus on SD systems but the big theme in course has been that SD systems can be converted to DT
  • Know how to find discretized plant $G[z]$ from $P(s)$
  • Know how to choose $T$ and justify your choice

Study:

1. Complete all assignments and repeat midterm
2. Check assignment and midterm solutions closely
3. Review lectures, tutorials, and labs

Background

• Linear Time-invariant Systems
• Laplace Transform
• Z-Transform
  • Linearity of Laplace and Z-Transforms

Introductory Content

• Feedback Control
• Discrete-Time Control Systems
• Sampled-Data Control Systems
  • Choosing Sampling Time
• Frequency-Domain Control Systems
• Transfer Function Classification
• Poles and Zeros
• Transfer Function Pole Decomposition
• Impulse Response

Stability

• Stability Criterion
  • Continuous-Time Stability
  • Discrete-Time Stability
• Sample-Data System Stability
• Time-Domain Stability
• BIBO Stability
  • Constant BIBO Stability Proof
• Closed-Loop Stability
  • Characteristic Polynomial Closed-Loop Stability
• Feedback System Performance Specifications
  • Final Value Theorem
  • Steady-State Response with FVT

IOP / SPA

• Input-Output Parameterization
• Simple Pole Approximation
• Specs for Control Design
• IOP with SPA
• Control Design with IOP and SPA
• Choosing Poles for IOP and SPA
• BIBO stable ⇐> Stable
• YALMIP + MOSEK messages
• Infinity Norm

State Space Models

• State Space Models
  • Mass-Spring Damper State Space Model
• State Space Realization
• Phase Portrait
• Nonlinear State Space Models
  • Linearization of Nonlinear State Space Models
• Numerical Integration for Control Systems
• Emulation Control Design
  • Stability of CT-DT Approximation
• Discretized Plant

Sampled-Data Systems

• Sampled-Data System Stability
• Schur Characteristic Polynomials
• Jury Test
• Nyquist Stability
• Performance of Sampled Data Systems

Tutorial/Examples

• Sept 23 Proof Tutorial
• Sept 30 IOP Tutorial

Labs

• MTE 484 Lab 1
• MTE 484 Lab 2
• MTE 484 A6Q3c
• MTE 484 Lab 3