Question 22.4: Consider a system with state space description given by (A, ...
Consider a system with state space description given by (A, B, C, 0), where
(22.13.4)
Synthesize a linear quadratic optimal regulator which forces integral action and where the cost function is built with Ψ and Φ, where Ψ = I and Φ = 0.01 ∗ diag(0.1, 1)
We first choose the poles for the plant state observer to be located at −5 and −10.
This leads to
J = (22.13.5)
Then the regulator will feed the plant input with a linear combination of the plant state estimates and the integrator states. We choose to build an optimal regulator yielding closed loop poles located in a disk with center at s = −3 and unit radius (see section §22.8). We thus obtain an optimal feedback gain given by
K (22.13.6)
This design is simulated in a loop with the same structure as in Figure 22.2 on the preceding page (see SIMULINK file cint.mdl). The tracking performance is illustrated in Figure 22.3, where step references have been applied.
