PD&C HW1pB

Problem Statement: 1. Derive the dynamical equations for two gravity drained tanks connected in series with a Proportional-Integral (PI) controller adjusting the flow into the first tank to bring the liquid level in the second tank to a desired set point. Apply the Fundamental Theorem of Calculus on the integral component of the controller and identify it as an intermediate state variable to facilitate the computational simulation. 2. Use scipy.integrate.solve_ivp to solve the set of dynamical equations in Part B1 for two identical tanks with a cross sectional area of 1 m2, drainage hole of 0.1 m2 and where setpoint for the second tank is increased from the initial steady state level when the flow through the tanks was 1 m3/s.