Using a generic PI transfer function and the transfer functions for the process, the control valve and the measuring device as determined in Tutorial 5.

Problem 2.Consider the stirred tank vessel from Problem 1 of Tutorial 5.Up to time 0 the process is at steady state. At time 0 there is a step change in the influent flow rate, i.e. 𝐹𝑖(𝑡)increases by 0.001 m3/s.Using Simulink for the simulations, carry out the following:a)Build in Simulinkthe closed loop block-diagram for the controlled process, using a generic PI transfer function and the transfer functions for the process, the control valve and the measuring device as determined in Tutorial 5. Use “Scope” blocks to visualise and export the profiles of the liquid level, ℎ′(𝑡), the error 𝜀(𝑡), the controller output 𝑐′(𝑡), and the manipulated variable 𝐹𝑜′(𝑡). For the controller, use a generic PID block and define the Form as “Ideal” and the Time domain as “Continuous-time”.b)Simulate and plot the liquid level in the tank ℎ′(𝑡)versus time for the uncontrolled process (i.e. with all the parameters of the PI controller set to 0).c)Using the P control action alone simulate and plot the liquid level in the tankℎ′(𝑡)with𝐾𝑐values in the range 0 −(-1) atm/m. Discuss the results.d)Starting from the closed loop response equation for the process, calculate the offset for the various 𝐾𝑐values considered in c). Compare the calculated values with those predicted by Simulink and discuss trends in relation to theory.e)Using PI control, simulate and plot the liquid level in the tank for 𝐾𝑐=−1atm/m and 𝜏𝛪=20s. Notethat Simulink uses the reciprocal of 𝜏𝛪, 𝐼,called reset rate, therefore in Simulink we have to use 𝐼=0.05s-1.Compare and discuss the response of the PI controller with the one of the P controller