Consider a linear system of the form dx dt where u is a scalar and d is a disturbance that enters the system through a disturbance vector FER". In this problem, we will explore how integral feedback compensates for a constant disturbance by giving zero steady- state output error even when d 0. = Ar + Bu + Fd, y = Cx, (a) First, apply basic state feedback u = - Kafr to the system. With an appropriate choice of Ksf, the closed loop system will stabilize and approach a steady state equilibrium, xe,sf. Je, sf- Solve for this equilibrium point to show that, for a nonzero disturbance d, this system will have a nonzero steady state error. (b) Next, we will set up the system to do integral control: Augment the state space description of this system to include a state z that inte- grates the output of the system. In other words, let the augmented system be: 40-40 + Bu + Fd, and find A, B, and F. You are welcome to write these as block matrices. d dt (c) Apply integral control (with r = 0, since our aim is to reject dis- turbances): u = -Kic-kiz to the augmented system from part b. With an appropriate choice of gains Kic and k, the system will again stabilize and approach a stable equilibrium point Te,ic, Zeic Ye,ic. Solve for this equilibrium point. Under what conditions on F does this controller enable the system to reach zero steady-state error on the state, Te,ic = 0?