IMC Design for Single Board Heater System

Internal Model Controller contains explicit model of plant [1]. The closed loop system can be stabilized with the use of a stable open loop transfer function and a stable controller. The IMC is mainly used for stable plants.

Figure 8.2: IMC feedback configuration

Let the transfer function of the stable plant be denoted by $G_p (z)$ and its model is denoted by $G(z)$. Hence

$$y(n) = G(z)u(n)+\xi(n)$$ (8.1)

where:
y(n) = plant output
u(n) = plant input
$\xi$(n) = noise

For noise rejection with y=0, we require $G_Q=G_p^{-1}$ and $G=G_p$, i.e., for stable $G_Q$ we require an approximate inverse of G. Also, for internal stability, transfer function between any two points in the feedback loop must be stable [1].

Figure 8.3: Feedback configuration