(Solved): A negative feedback control system is depicted in Figure 2. Suppose that our design objective is to ...

A negative feedback control system is depicted in Figure 2. Suppose that our design objective is to find a controller $Gc(s)$ of minimal complexity such that our closed-loop system can track a unit step input with a steady-state error of zero. (a) As a first try, consider a simple proportional controller $G_c(s)=K$ where $K$ is a fixed gain. Let $K=2$. Using MATLAB, plot the unit step response and determine the steady-state error from the plot. (b) Now consider a more complex controller $G_c(s)=K_0+\frac{K_I}{s}$ where $K_0=2$ and $K_I=20$. This controller is known as a proportional, integral (PI) controller. Using MATLAB, plot the unit step response, and determine the steady-state error from the plot. (b) Compare the results from parts (a) and (b), and discuss the trade-off between controller complexity and steady-state tracking error performance. Figure 2