**2.1.1 Controller structure selection based on zero steady-state error condition**

Consider the feedback control loop in Fig. 1 where G(s) is the plant transfer function. According to the Final Value Theorem, the steady-state error

$$\text{l.e.} (\text{\textbullet}) = \lim\_{s \to 0} sE(s) = \lim\_{s \to 0} s \frac{1}{1 + L(s)}\\\mathcal{W}(s) = q \,\text{l.w.} \lim\_{s \to 0} \frac{s^{\nu - q}}{s^{\nu} + K\_L} \tag{1}$$

is zero if in the open-loop L(s)=G(s)GR(s), the integrator degree L=S+R is greater than the degree q of the reference signal w(t)=wqtq, i.e.

$$
\nu\_L > q \tag{2}
$$

where S and R are integrator degrees of the plant and controller, respectively, KL is openloop gain and wq is a positive constant (Harsányi et al., 1998).
