## Feedforward Control

Feedforward control is a strategy to reject persistent disturbances that cannot adequately be rejected with feedback control. Feedforward control is typically added to feedback control and is not usually implemented alone. In certain situations, the performance of control systems can be enhanced greatly by the application of feedforward control. Two key characteristics are needed:

- An identifiable disturbance is affecting significantly the measured variable, in spite of the attempts of a feedback control system to regulate these effects
- This disturbance can be measured, perhaps with the addition of instrumentation

An ideal feedforward controller is the negative ratio of the disturbance transfer function divided by the process transfer function.

$$G_{ff} = -\frac{G_d}{G_p}$$

#### Exercise

A feedforward controller `G_{ff}` is proposed to improve the control of the disturbance `D` with the following transfer functions.

$$G_p(s)=\frac{0.6e^{-37s}}{39s+1} \quad \quad G_d(s)=\frac{0.25e^{-57s}}{31s+1} \quad \quad G_v(s)=\frac{5}{2s+1}$$

Derive a dynamic `G_{ff}` and static `K_{ff}` feedforward controller that will best reject the disturbance.