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For a particular yspt we can solve for yt using the

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Unformatted text preview: ;$ ! mol $ ! kg $ ! mol $ Cdes # 3 & C# 3& #s& e [V ] p [ mA] "m % "% " m % ! GC GA GP GS ! + ! reactor valve GS C !V # m "$ UV cell Class activity Solve for Y(s) (output) in terms of Ysp(s) (input): Solve for Y(s): This is the closed ­loop transfer function. For a particular ysp(t), we can solve for y(t) using the Laplace transform method (assuming Gp and Gc are known). We can construct more complicated closed ­loop block diagrams and transfer functions, with additional dynamic blocks due to sensors and actuators (e.g. valve dynamics), multiple inputs including disturbance inputs. However, we can still solve for all Y(s)’s in terms of all inputs, using the same approach. Only algebra is required when we work in the Laplace domain. Example: (or additional class activity) • Add a sensor block to the lower loop Gm(s). Rederive the closed loop transfer function Y(s)/Ysp(s). • Then add a disturbance between the controller and the plant. Then calculate Y(s)/D(s). Our new closed loop system can be classified just as we did in Chapters 5 and 6. • System order: 1st, 2nd, higher • 2nd order: underdamped, overdamped • Time delay? • Zeros Then we can predict the response to various inputs (setpoint changes) • Step, ramp, sinusoid, impulse, pulse,… Classify stability based on poles (or eigenvalues) in RHP. We design a controller to give us a desired closed ­loop behavior of the system (Chapter 11 +)....
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