Calculate the number of degrees of freedom for the system and the maximum number ofcontrolled and manipulated variables

EX40HC – Tutorial 9 Degrees of freedom and generation of control loopsProblem 1. Consider the CSTR below, where an exothermic reaction 𝐴𝐴→𝐵𝐵 takes place. The feed containsspecies A at concentration𝐶𝐶𝐴𝐴𝐴𝐴(𝑡𝑡). The aim of the control system is to maintain the conversion ofspecies A 𝐶𝐶𝐴𝐴𝐴𝐴(𝑡𝑡)and the reaction temperature 𝑇𝑇(𝑡𝑡) at the desired setpoints. The disturbances are 𝐶𝐶𝐴𝐴𝐴𝐴(𝑡𝑡),𝑇𝑇𝐴𝐴(𝑡𝑡),𝑇𝑇𝑐𝑐𝑐𝑐(𝑡𝑡). a) Calculate the number of degrees of freedom for the system and the maximum number ofcontrolled and manipulated variables. b) Generate a suitable control loop that controls the maximum number of controllable variables.