## Example 3: Robust Control of a fuel injection system

In this exercise, the nominal model of a fuel injection system (at T = 25°C) is given (see Sanchez-Pena/Sznaier, "Robust Systems", Wiley, 1998):

The control must operate correctly for fuel temperatures ranging from T = 0°C to T = 60°C.
The family of plants can be modeled as the nominal plant G25 subject to multiplicative uncertainty Δ with ||WIΔ|| < 1, where .
The plant is stable and non-minimum-phase, with multiplicative uncertainty.

Your job is to design an H controller that robustly stabilizes the plant G=G25(I+Δ) and renders ||WPS|| ≤ 1, where .
Now, you have many degrees of freedom in choosing the weighting functions. To this end, you can enter the numerator and denominator polynomials of the weights for S and T. The syntax is MATLAB standard for polynomials, e.g. for s^2 + 3*s - 7 you enter [1 3 -7] (the brackets can be omitted).

## Control Objectives:

• Bandwidth ωB = 24 [rad/s]
• H-norm of KS ≤2
• Max. steady-state offset of 1 %
• No overshoot
• Robust stability