Theory of Automatic Control: Lecture Notes (Repnikova, 2015)
A 319-page classical automatic-control course covering continuous-time modeling, standard dynamic elements, block-diagram reduction, stability and performance criteria, frequency-domain synthesis, and nonlinear phase-plane and describing-function methods. The course is a strong map of the classical territory, but its advertised state-space chapters are absent and its MATLAB material is dated.
Nataliia B. Repnikova's lecture course is the main supplied source for the continuous-time half of the TAU territory. It is organized around the classical SISO workflow: derive a linear model, factor it into recognizable dynamic elements, assemble the loop, establish stability, measure performance, and synthesize compensation. Its lasting value is the way it connects algebraic, time-domain, frequency-domain, and geometric views of the same closed loop.
Actual coverage #
| Part | PDF pages | What it materially teaches |
|---|---|---|
| Foundations and mathematical description | 7–54 | Control principles and classifications; differential equations; operating-point linearization; standard test inputs; Laplace transforms; time and frequency characteristics |
| Standard dynamic elements | 55–93 | Proportional, integrating, differentiating, first-order, second-order, oscillatory, nonminimum-phase, delay, and distributed elements |
| Block diagrams | 94–112 | Series, parallel, and feedback interconnections; equivalent transfer functions; structural transformations |
| Stability | 113–169 | Characteristic equations; Hurwitz and Mikhailov criteria; Nyquist reasoning; logarithmic margins; parameter-space stability regions |
| Performance and accuracy | 170–215 | Transient specifications; frequency, root, and integral quality criteria; steady-state error; system type; disturbance and harmonic response |
| Improving accuracy and synthesis | 216–264 | Gain and integral action; derivative and PID action; invariance/feedforward; desired Bode shape; lead, lag, and lead–lag compensators |
| Nonlinear systems | 265–307 | Static nonlinearities; relay loops; equilibria and phase portraits; Popov absolute stability; describing functions; harmonic balance; limit cycles |
| Appendices and bibliography | 310–318 | Historical MATLAB/Simulink introduction, block-diagram transformations, and references |
The table of contents advertises later chapters on state-space methods and observers, but those chapters do not occur in the file. Pages 308–309 and 319 are blank; page 310 begins the appendices. GTK therefore treats the source as a classical continuous-time course, not as evidence that modern state-space material was covered. The missing territory is supplied independently by the existing modern control theory branch.
What carries weight #
The durable core is the relationship between representation and reasoning. A pole can be read as a term in a characteristic polynomial, a mode in the time response, a break and phase contribution in a Bode plot, a location in the complex plane, or a branch origin in root-locus design. The course repeatedly changes view without changing the underlying closed-loop system. That is the organizing principle retained across the GTK entries.
The following mechanisms remain technically useful when checked against current references:
- linearization about an explicit operating point and the limited domain of the resulting small-signal model;
- standard first- and second-order responses and the causal role of poles, zeros, damping, delay, and relative degree;
- block-diagram reduction and the characteristic equation ;
- complementary stability tests: coefficient criteria, argument-change criteria, and Nyquist encirclements;
- the connection between low-frequency loop gain, system type, and steady-state error;
- the use of lead and lag networks to trade phase margin, crossover, low-frequency accuracy, noise, and control effort;
- phase-plane reasoning for nonlinear equilibria and limit cycles;
- describing functions as an approximation whose predicted oscillation must be verified against the nonlinear model.
Where the source is insufficient #
- Its MATLAB and Simulink material reflects an older interface and block library. GTK uses current documentation for tool behavior and does not preserve historical menu instructions.
- Mikhailov, Goldfarb, and hand-constructed logarithmic criteria are useful conceptual methods but are no longer presented as the default engineering workflow. Numerical pole, frequency-response, sensitivity, and nonlinear simulation checks accompany them.
- The nonlinear treatment emphasizes phase planes, Popov geometry, and first-harmonic approximations. It does not replace modern Lyapunov, invariant-set, robustness, reachability, or computational nonlinear analysis.
- Examples are predominantly ideal LTI or low-order nonlinear models. Saturation, rate limits, sensor noise, computation delay, jitter, finite precision, and model uncertainty require explicit treatment beyond the source.
- Several claims about software and deployed technology are frozen at the publication date and are not carried into GTK.
How it feeds the bank #
The course supplies topic discovery and the classical narrative, while Feedback Systems, 2nd edition, MIT course materials, and current MathWorks documentation supply present-day definitions, limitations, and design practice. The result is deliberately not a chapter-by-chapter translation. Each GTK topic stands alone, derives its main equations, contains a worked line of reasoning, and links to the neighboring view of the same system.
Visual audit #
All 319 pages were rendered and inspected, including the pages with no extractable text. The load-bearing visuals comprise feedback and functional diagrams, standard-element time and frequency plots, pole/zero sketches, Hurwitz–Mikhailov–Nyquist constructions, gain and phase margins, stability regions, desired Bode shapes, compensation networks, nonlinear static characteristics, phase portraits, Popov lines, and describing-function intersections.
No original figure is retained. Many labels are too small at article width, and several diagrams embed source-specific notation or historical software UI. GTK replaces them with independent, theme-aware SVGs that isolate one causal claim at a time: operating-point linearization, pole-to-response mapping, time-domain metrics, stability-test geometry, root-locus motion, lead–lag tradeoffs, phase portraits, and harmonic-balance intersections. Their topology, signs, axes, units, and direction conventions are checked against current sources before use.