1. Consider a model of a simple two tank system given in the following figure: u 3.o. hy-h2 and f2 = kan Figure 1: Two tank system with fi = K Assuming that the flow rate, u(t) is input and flow f2(t) is output, where K1, K2 (valve charac- teristics) and A and A2 are constants: = = = = (a) Find the continuous-time state space representation of the system. Let xi h1, X2 h2. (Hint: f1 = (h h2)/K). (b) Find discrete state space model representation for the following parameters K1 = 2, K2 = 2, Aj = 1, A2 = 0.5, and sampling time At = 0.2. (c) Find the overall transfer function by using Z-transform. (d) Find the zero-input state response X zero input (n). (e) Find the zero-state response Xzero state(n) for the step input. (f) Find the overall system response (n) for the initial conditions z(0) = 1