Question

1. Consider a single tank for flow rate control and water level regulation. A single tank subject to the pump dynamics can be modeled as follows Tank dynamics: h.-le,-4M h, -e-eyh.), Pump dynamics: Q,-1(av,-0) Pump dynamics: Q,--(av,-Q.) Tank dynamics: where the parameters are defined as follows: h :water level c: valve resistance r: time constant S,: water tank area Q,: supplied flow rate a: voltage scaling factor ,: applied control input voltage (all the coefficients are positive) (A). Please apply the linearization to the nonlinear system w.rt to an operation point 2,) o (B). state-space representation (including state equation and output equation). (5%) (C). For the linearized model, find the transfer function Ah. (s)/Av'(s) (5%) (D). Please derive the time domain solution Δ/,(r), where Δν, (r)-β and β Based on (A) and consider that the system output is the water height, please find the system is the step size (10%)

Answer 1