ECE 411: Control Systems
Computer Aided Tools
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- Can switch between state space system representation and
ODE, transfer function, impulse response
- Can construct state and simulation diagrams (for
implementation)
- Can solve systems of state space equations
- Understand connection between system poles and state matrix
eigenvalues
- Understand basic signals: impulses, steps, sinusoids,
exponentials
- Understand both real and complex valued signals,
particularly exponentials
- Can perform basic signal manipulations: scaling,
translation, reflection, time shift
- Can decompose signals into basic elements (steps,
ramps, etc.)
- Understand basic concepts of Linear Time-Invariant
(LTI) Single-Input-Single-Output (SISO) systems
- Can apply principle of superposition
Pre-requisites:
- ECE312
- Understand basic concepts for SISO LTI systems,
including linearity, time-invariance, memory,
causality, stability
- Can manipulate and solve ordinary differential
equations (ODEs)
- Can compute transfer functions
- Can compute time domain convolution
- Can switch between the above system
representations (ODE, transfer function, and
convolution representation (via impulse response))
- Can analyze signals via Fourier Transform (forward
and inverse using tables) for frequency content
- Understand properties of Fourier Transform, especially
time-domain convolution versus frequency domain
multiplication
- Can analyze causal signals via one-sided Laplace
Transform (forward and inverse tables)
- Understand properties of Laplace Transform,
especially time-domain convolution versus frequency
domain multiplication AND final value theorem for
steady state analysis
Linear Systems
Signals and Systems
State Space Representation
Transform Methods
- Can perform all calculations above by hand (for simple systems)
- Can perform all calculations above in Matlab, including
command-line and GUI based tools (Itiview, sisotool)
- Can write custom m-files for controller analysis and design
- Can develop Simulink models for analysis and simulation
- Can design lag, lead, and lag-lead controllers
- Can design PI, PD, and PID controllers
- Can design controllers using Nyquist/Bode plots and root
locus approaches
- Can design controllers using analytic approach
- Can compute steady state performance for close-loop
systems via final value theorem
- Understand concept and utility of integral action
- Understand concepts of time-constant, damping ratio and
natural frequency
- Can compute transient response parameters (overshoot, rise
time, settle time), impulses, step, and ramp response
- Can compute stability margins via Nyquist/Bode analysis
- Can check stability via Routh test
- Can check for stability via Nyquist/Bode plots
- Can check for stability via root locus plot
- Understand connection between open and closed loop
- Understand connections between Time-Domain,
Frequency Domain, and Pole/Zero Location
Controller Design
Classical Closed-Loop
Analysis
Concepts:
- Open and Closed-Loop Systems
- Performance in both Time and Frequency Domain
- Transient and Steady State Response
- Connections between Time-Domain, Frequency
Domain, and Pole/Zero Location in both Open and
Closed-Loop
- Nyquist Stability Criterion
- Stability Margins (Gain and Phase) and their
relation to Nyquist and Bode Plots
- Pole/Zero Location and the Effects of Feedback (root
locus plots)
- Controller Design via classical methods
- Integral action and PID controllers
- State Space approaches
Applications:
- Stability and performance analysis for open and
closed loop systems
- Feedback controller design
Tools:
- Complex Algebra and Analysis
- Ordinary Differential Equations
- Laplace and Fourier Transforms
- MatLab and Simulink, plus Toolboxes (control,
signal processing, symbolic)
- Graphical Techniques (Bode plots, Nyquist plots,
root locus plots)
IN
OUT
As of 12/9/08