Time-domain analysis is where control theory stops being abstract Laplace algebra and starts predicting how a real system will actually behave when you poke it. This tutorial walks through the three workhorse MATLAB functions every controls engineer reaches for: impulse(), step(), and lsim(), applied to transfer functions you define directly in the workspace.

The impulse response is the system's fingerprint — once you have it, convolution gives you the response to any input. The step response is what you actually care about in practice: rise time, overshoot, settling time, steady-state error. And lsim() is the underrated one — it lets you simulate the response to arbitrary input signals (ramps, sinusoids, recorded disturbance data), which is how you stress-test a controller before it touches hardware.

For anyone studying control systems coursework, or an engineer who learned the theory but never got fluent with the MATLAB tooling, this fills a practical gap. The other contender here was the same channel's Dr. Ananda Natarajan series on force-voltage analogies, but those are pure chalk-and-talk derivations — this one actually shows the simulation workflow end to end.