Expert-level control systems engineering covering feedback control, PID design, root locus, frequency domain methods, state-space design, and digital control.
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Transfer function: Laplace domain ratio of output to input for LTI systems. Block diagram: graphical representation of system interconnections. State-space: x-dot = Ax + Bu, y = Cx + Du, more general than transfer function. Linearization: approximate nonlinear system around operating point. System identification: estimate model parameters from input-output data.
PID: proportional integral derivative, most widely used industrial controller. Root locus: graphical method to design gain for desired closed-loop poles. Lead compensator: improves phase margin, speeds up transient response. Lag compensator: improves steady-state error, reduces high frequency gain. Ziegler-Nichols: empirical PID tuning from step response or ultimate gain.
Gain margin: additional gain before instability, read from Bode at phase -180. Phase margin: additional phase lag before instability, read from Bode at 0 dB. Bandwidth: frequency range of effective control, affects disturbance rejection. Sensitivity function: closed-loop sensitivity to disturbances and model errors.
Discretization: convert continuous controller to discrete, Tustin or ZOH method. Sampling rate: choose 10 to 20 times bandwidth for adequate digital control. Quantization: finite word length effects, limit cycles in digital controllers. Computational delay: accounts for processing time, degrades phase margin.
| Pitfall | Fix |
|---|---|
| Insufficient phase margin | Add lead compensation to improve phase margin |
| Integral windup | Implement anti-windup for all integrating controllers |
| Sampling too slow | Sample at minimum 10 times controller bandwidth |
| Ignoring actuator saturation | Include saturation in analysis and add anti-windup |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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