Solution_to_problem_11.6

# Solution_to_problem_11.6 - Solution to problem 11.6 One of...

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11.6 – 1 Solution to problem 11.6 One of the limitations of proportional-only control is that a steady-state error (or offset ) occurs after a set-point change or a sustained disturbance. Section 11.3.1 in Seborg et al. 2004 demonstrates that this offset will occur for any value of the controller gain c K , and quantifies the offset. The offset is defined as the difference between the desired steady state value (the set point) and the actual steady state achieved under control: ( ) sp offset y y = - In this problem we need to check the value of the offset when proportional control is used with integrating processes, given a) a step change of the setpoint, and b) a step change of the disturbance. The steady state after these changes can be found by applying the Final Value Theorem: 0 ( ) lim ( ) lim ( ) t s y y t s Y s →∞ ∞ = = Therefore we need to find ( ) Y s . For a closed loop system such as the one in Figure 11.8, the equations relating ( ) Y s to set point changes (

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## This note was uploaded on 11/20/2009 for the course CHME DTU-abroad taught by Professor Rafiqulgani during the Spring '09 term at Rensselaer Polytechnic Institute.

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Solution_to_problem_11.6 - Solution to problem 11.6 One of...

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