Absolute and relative stability, plus an interactive loop diagram: each sensitivity function with its name, input, meter, exam use and MATLAB command.
Part A: absolute vs relative stability
Absolute stability (estabilidad absoluta) A yes/no question: does the response settle down in the end? Yes, when all closed-loop (lazo cerrado) poles (polos) lie on the left side (Re < 0). Motor: K = 50, 125, 1000 → all yes.
Relative stability (estabilidad relativa) A “how much” question: how far is the system from losing stability? A glass on a table: in the middle and 1 cm from the edge both “stand”, but only one is safe. Motor: K = 1000 is stable, but it oscillates and overshoots by 30%, so it is close to the edge.
Signs of low relative stability you already know: big overshoot (sobreoscilación), long oscillation, poles high up on the root locus (small ζ). Margins (márgenes) and Ms are just rulers that measure this distance with one number. We will do them separately.
Part B: sensitivity functions (funciones de sensibilidad) = where the signal enters and where the meter is
Words in the problem text that point to it
In the exam: where and why
One rule that is enough to write any of them
Numerator = the blocks on the straight path from the input to the meter. Denominator = always 1 + L, because the signal always goes around the same loop. That is why they all have the same poles: if one is stable, they all are (FR-03 p. 7).
MATLAB shortcut: feedback(A, B) = A / (1 + A·B). For A you put the numerator (path to the meter), for B the rest of the loop.
Check yourself: you want to know how much the motor voltage u goes up when you make a step change in the reference position r. Which function do you use?