KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec16

KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec16

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1 Chapter 5 Standard form: Second-Order Systems ( 29 ( 29 2 2 (5-40) τ 2ζτ 1 Y s K U s s s = + + which has three model parameters: steady-state gain τ "time constant" [=] time ζ damping coefficient (dimensionless) K @ @ @ Equivalent form: 1 natural frequency τ n ϖ = @ ( 29 ( 29 2 2 2 n n n Y s K U s s s ϖ ϖ ϖ = + +
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2 1 + )s ( + s K = G(s) 2 1 2 2 1 τ + τ τ τ 2 1 1 τ τ = τ 1 s 2 s K = G(s) 2 2 + ζτ + τ 1 overdamped ζ 2 1 2 1 2 = τ τ τ + τ ζ 2nd order ODE model (overdamped) Block Notation: Composed of two first order subsystems (G 1 and G 2 ) roots: τ ζ ζ 1 2 - ± - Chapter 5 1 1 underdamped critically damped ζ ζ < =
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3 Chapter 5 The type of behavior that occurs depends on the numerical value of damping coefficient, : ζ It is convenient to consider three types of behavior: Damping Coefficient Type of Response Roots of Charact. Polynomial Overdamped Real and ≠ Critically damped Real and = Underdamped Complex conjugates ζ 1 ζ 1 = 1 < Note: The characteristic polynomial is the denominator of the
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