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Dynamic Behavior and Stability of Closed-Loop Control Systems
directly follows Example 4.4. Consider the unsteady-state mass balance for the tank contents: ρρρρ12 3(11-32) dh Aqqq dt =+ − Substituting the flow-head relation, q3 = h/R, and introducing deviation variables gives 12 (11-33) dh h Aqq dt R ′ ′ =+−′′ Thus, we obtain the transfer functions ( ) () 2 (11-34) τ 1 p p Hs K Gs Qs s
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Control of Multiple-Input, Multiple- Output (MIMO) Processes
sites.chemengr.ucsb.edubut not process dynamics. Chapter 18 19. Example of RGA Analysis: 2 x 2 system • Steady-state process model, The RGA, Λ, is defined as: where the relative gain, λ ... Appropriate for nonlinear processes. () 12 12 11 21 21 22 18 85 18 86 P P P P K T K K. 1 2
Chapter 12
sites.chemengr.ucsb.edu• The IMC and DS methods provide satisfactory set-point responses, but very slow disturbance responses, because the value of is very large. • Fortunately, this problem can be solved in three different ways. Method 1: Integrator Approximation τI ()θ/τ 1 * Approximate ( ) by ( ) 1 where * / . Ke s K e s Gs Gs s s KK −θ−θ == τ+ τ
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