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Essentials of Process Control phần 8

Tham khảo tài liệu 'essentials of process control phần 8', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 424 PART THREE Frequency-Domain Dynamics and Control a Sketch Bode and Nyquist plots for this process for a gain K I and a deadtime D 0.5 minutes. b Calculate the ultimate frequency and ultimate gain K analytically for arbitrary values of gain and deadtime and confirm your results using the Bode plot from part a for the specific numerical values given. c Calculate analytically and graphically the value of controller gain that gives a phase margin of 45 . d Use a Nichols chart to determine the maximum closedloop log modulus if the gain calculated in part c is used. e Calculate the TLC settings for a PI controller K . 3.2 T 2.2PJ and generate a Bode plot for when these controller constants are used. f What are the phase margin gain margin and maximum closedloop log modulus when this PI controller is used 11.45. A process has the following openloop transfer function between the controlled variable Y and manipulated variable M y r. - Ki e Ds M - а If a proportional analog controller is used calculate the ultimate gain and ultimate frequency for the numerical values Kp 2 To 10 and D 1. б Sketch Nyquist and Bode plots of Gm m - Calculate the value of controller gain that gives a phase margin of 45 . c Use a Nichols chart to determine the maximum closedloop log modulus if the controller gain is 3.19. 11.46. A process has an openloop transfer function that is a double integrator. 7 a Using a root locus plot show that a proportional feedback controller cannot pro- duce a closedloop stable system. b Using frequency-domain methods show the same result as in a . 11.47. The openloop transfer function for a process is G U s Ko Tos 1 a If a proportional-only controller is used calculate the closedloop servo transfer function expressing the closedloop gain and closedloop time constant in terms of the gain the time constant and the controller gain K . Sketch a closedloop log modulus plot for several values of controller gain. b Repeat part n using a proportional-integral feedback .