Mini Time-Domain Analysis

A collection of from-scratch, zero-dependency C implementations of classical control theory — time-domain analysis. Each module maps to MIT (and other top-tier university) courses, bridging theory and practice by translating textbook equations into runnable C code.

Sub-Modules

Sub-Module	Topics	Key Courses
mini-higher-order-reduction	Balanced truncation, dominant pole analysis, modal truncation, model order reduction	MIT 6.242, ETH 227-0216
mini-impulse-step-response	Convolution integral, discrete-time response, impulse/step response for LTI systems	MIT 6.241J, Nise Ch.4
mini-second-order-systems	Canonical 2nd-order systems, ζ/ωn parameter mapping, analytical & numerical response	MIT 6.241J, Nise Ch.4-5
mini-sensitivity-analysis	Bode sensitivity integral, eigenvalue/parametric/time-domain/transfer-function sensitivity	MIT 6.241J, Skogestad, Caltech CDS 110
mini-stability-routh-hurwitz	Routh-Hurwitz criterion, Jury stability (discrete-time), relative stability margins	MIT 6.241J, Nise Ch.6, Stanford ENGR 105
mini-steady-state-error	Error constants (Kp/Kv/Ka), system type, disturbance rejection, final value theorem	MIT 6.241J, Nise Ch.7, Stanford ENGR 105
mini-time-domain-design	Eigenvalue placement, state-space design, matrix functions, linear algebra operations	MIT 6.241J, Nise Ch.9, Stanford ENGR 105
mini-transient-specs	Rise/settling time, overshoot, 1st/2nd/higher-order transients, ISE/IAE/ITAE metrics	MIT 6.241J, Nise Ch.4, Stanford ENGR 105

Design Philosophy

• Zero external dependencies — pure C (C99/C11), only libc and libm
• Self-contained modules — each directory has its own include/, src/, examples/, tests/
• Theory-to-code mapping — every module includes docs/ with course-alignment notes and textbook references (Nise, Ogata, Franklin)
• Classical control heritage — covers the time-domain pillar of control education: transients, error analysis, stability, and sensitivity

Building

Each module is standalone. Navigate to a module directory and run:

cd mini-transient-specs
make all    # build everything
make test   # run tests

Requires GCC and GNU Make.

Project Structure

mini-time-domain-analysis/
├── mini-higher-order-reduction/   # Balanced truncation, dominant pole, modal model reduction
├── mini-impulse-step-response/    # Convolution integral, impulse/step response, discrete-time response
├── mini-second-order-systems/     # Canonical 2nd-order LTI systems, ζ/ωn parameterization
├── mini-sensitivity-analysis/     # Bode integral, eigenvalue/parametric/time-domain sensitivity
├── mini-stability-routh-hurwitz/  # Routh-Hurwitz, Jury criterion, relative stability margins
├── mini-steady-state-error/       # Error constants, system type, disturbance rejection, FVT
├── mini-time-domain-design/       # Eigenvalue design, state-space methods, matrix functions
└── mini-transient-specs/          # Transient specifications, performance indices (ISE/IAE/ITAE)

License

MIT