Homework 11 - Closed Loop - Chemical Engineering Department University of Florida ECH 4323 Process Control Theory HOMEWORK No 11 CLOSED-LOOP DYNAMICS

Chemical Engineering Department University of Florida ECH 4323 Process Control Theory HOMEWORK No. 11 — CLOSED-LOOP DYNAMICS 1.0 Consider the standard feedback loop shown in the figure below. a) The closed-loop relationship between the output and the set-point and disturbance variables is given by the equation ′ Y (s) = G srv (s) ¢ R (s) + G reg (s) ¢ D (s) where G srv (s) and G reg (s) are respectively the servo and regulation transfer functions for the loop. Derive an expression for G reg (s) and confirm the result using the rule of thumb discussed in class. b) The closed-loop relationship between the feedback error and the set-point and disturbance variables is given by the equation ′ E (s) = G er (s) ¢ R (s) + G ed (s) ¢ D (s) where G er (s) and G ed (s) are respectively the closed-loop transfer functions ′ E (s)/ ¢ R (s) and ′ E (s)/ ¢ D (s) . Derive an expression for G ed (s) and confirm the result using the rule of thumb discussed in class. R '( s ) E '( s ) U '( s ) P '(s) D '( s ) Y '( s ) Y m '( s ) + + - + Χοντρολλερ Αχτυατορ Τρανσδυχερ Προχεσσ Γ π ( σ 29 Γ μ (