2015年自动化学院东南大学过程控制作业四.docVIP

Process Control The Fourth Exercise of Process Control ——Students’Tail Number 23/4/2015  Chapter8-5．Consider the closed-loop response for IMC when the model is not perfect. Show that there is no offset for a setpoint change for the following process model and actual process transfer function. Also, find the minimum value of λ that assure closed-loop stability for this system. g g Solution: The closed-loop transfer function is y then, q we have known that g g ∴y Assume r So, lim We can find that there is no offset for a setpoint change for the following process model and actual process transfer functions. Used the Routh stability criterion, 8λs s3 8 λ s2 s1 s0 10λ-7.5 0 We can get λ0.8869 Chapter8-7. Packed-bed reactors often exhibit “wrong way”(inverse response)behavior. You are responsible for the control-system design for a packed-bed reactor that has the following step response behavior, where a step decrease in steam value position was made at t = 5mintues. You have developed the following process model (the time unit is minutes):g A、What are the units for the process gain? The uint of output/ the uint of input, so the units are ℃ / % . B、Design an IMC for this process. Use the all-pass factorization for the RHP zero, and assume that q(s) is semiproper (numerator order in s is equal to the denominator order in s). Design an IMC for this process: g ∴ q IMC for this process : q C、Assuming a perfect model, plot qualitatively how the temperature will respond to a step setpoint change of 1°C. Assuming a perfect model, so gp ∴y = The transfer function is : G(s) = (-10s+1) Let λ= 2, Matlab code ： tfunc = tf([ -10 1],[20 12 1],inputdelay,12) tfunc = -10 s + 1 exp(-12*s) * ---------------------------- 20 s^2 + 12 s + 1 step(tfunc) D、It is desirable to make certain that the contro