Root locus control

See also slides and Root locus

closed-loop properties of the function of $K_1 G(s)$

## improving transient response

Question

How to calculate K?

• Product of distances from open-loop pole to point in question

Second-order poles for the second-order system.

improving steady state error (SSE)

adding PID (compensator) with an integrator ($\frac{1}{s}$) in feed forward path.

ideal integral compensation

proportional-plus-integral (PI) controller ⇒ causing error to go to zero.

Important

Add zero! on the pole near the origin at $s=-a$

$$\frac{K}{s}(s+a) = K_p + \frac{K_i}{s}$$

where $K_p$ is the proportional gain, and $K_i$ is the integral gain.

Implementation $G_c(s)$

$$G_c(s) = K_p + \frac{K_i}{s} = \frac{K_p(s+\frac{K_i}{K_p})}{s}$$

lag compensation