I'm working with a linear system, having given matrices A and B $$A = \left[\begin{array}{cc} 0 & 1 \\ -0.9 & 0 \end{array}\right]$$
$$B = \left[\begin{array}{c} 0 \\ 2 \end{array}\right]$$
assume we have full state and no feedtrough matrix $D$ so $$C = \left[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right]$$ $$D = \left[\begin{array}{c} 0 \\ 0 \end{array}\right]$$
I want to design an LQR feedback controller for this system: the LQR theory states that by increasing the elements on the diagonal of $Q$ I will make the corresponding state errors smaller and by increasing the scalar $R$ I will change the control effort, and this tradeoff will be reflected in the $K$ matrix $$K = lqr(A,B,Q,R)$$ However, my question is the following: is it possible to increase the bandwidth without increasing the control effort? I'd like a more reactive system, but I have saturation limits to be taken into account.
Note: I know that MPC would be probably better but it's more to understand the control efforts / control bandwidth relationship in LQR controllers.
