Linear Control System Theory
This undergraduate-level course focuses on single-input single-output linear time-invariant control systems emphasizing frequency-domain methods. Topics include modeling of feedback control systems, transient and steady-state behavior, Laplace transforms, stability, root locus, frequency response, Bode plots, Nyquist plots, Nichols plots, PID control, and loop shaping.
- Introduction
- Topic 1: Feedback Control Principles
- Advantages and disadvantages of feedback control
- Nonlinear static system example
- Cruise control system example
- Topic 2: System Modeling
- Solving first-order linear time-invariant (LTI) ordinary differential equations (ODEs)
- State-space models
- Solving ODEs with MATLAB
- Topic 3: Solving Ordinary Differential Equations
- Linear properties of LTI systems
- LTI ODE solutions
- Topic 4: Laplace Transforms and Transfer Functions
- Complex numbers and rational functions
- Polynomial and rational functions with MATLAB
- The Laplace transform
- Transfer functions
- Topic 5: Block Diagrams and Signal Flow Graphs
- Block diagrams
- Signal flow graphs and Mason's gain formula
- Parameter sensitivity
- Topic 6: Stability
- Equilibria
- Stability
- Linearization
- Topic 7: Transient and Steady-State System Response
- System response to test input signals
- Impulse response
- Step response
- Exponential response
- Frequency response
- Topic 8: Frequency Response
- Bode plots
- Non-minimum phase systems
- Polar plots
- Magnitude-phase plots
- Topic 9: Root Locus
- Topic 10: Control Design
- Proportional integral derivative (PID) control
- PID tuning and implementation
- Inverted pendulum example
- Lead-lag compensation
- Topic 11: Nyquist Stability
- Principle of the argument
- Nyquist's stability criterion
- Topic 12: Performance Measures
- Stability margins
- Frequency domain performance specifications
- Closed-loop control from open-loop frequency response
