Classical Control Theory

Classical control theory is aimed at 1 input - 1 output systems. It’s all about the frequency domain (and pain).

Source: https://studyelectrical.com/2023/05/time-domain-analysis-vs-frequency-domain-analysis.html

We use frequency domain analysis because (it is a fundamental truth that) all systems are secretly or not so secretly mass-spring-dampers, and so their behavior in the time domain is described by exponentially damped sinusoids— the math for this as we have to integrate/differentiate gets nasty quickly, but if we flop into the frequency domain, a lot of these operations turn into algebraic ones.

We get between the time domain and frequency domain using:

• Fourier transforms
• Laplace transforms (to S domain)

and their variants.

Generally when we’re analyzing these systems, we’re looking at their impulse responses and describing the system through transfer functions (how they respond)

Source: https://resources.pcb.cadence.com/blog/2021-simplify-rlc-circuit-analysis-with-the-rlc-transfer-function

Bode plots

https://en.wikipedia.org/wiki/Bode_plot

Using these tools, you can start designing controllers. In practice, you set this all up in MATLAB, which is a lot fun.

You can do things like use the root locus method:

Root locus plot of dynamic system - MATLAB rlocus

Anyways, this has not been so much of an overview as just a list of topics. If you want to learn classical control theory, this man will teach you:

Brian Douglas