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Unformatted text preview: Spring 2006 Process Dynamics, Operations, and Control 10.450 Lesson 8: Cascade and Feedforward Control Schemes 8.0 context and direction Knowledge of the process is the basis for successful process control. In Lesson 7, we used process knowledge to guide, through tuning correlations, our choice of controller parameters. In this lesson, process knowledge will guide our choice of control structure itself: by making additional process measurements, we will augment the single-loop feedback control scheme to give it greater capability. DYNAMIC SYSTEM BEHAVIOR 8.1 a process with identifiable intermediate variable We begin with a process that has three inputs, two of them disturbances, and one output that we will wish to control. As usual, transfer functions G d1 (s), G d2 (s), and G m (s) may refer to the same assembly of equipment, but specify how the output variable y depends on each particular input. G d2 (s) G m (s) x ' d2 (s) x ' m (s) y' (s) G d1 (s) x ' d1 (s) G d2 (s) G m (s) x ' d2 (s) x ' m (s) y' (s) G d1 (s) x ' d1 (s) The Laplace domain process description is then ) s ( x G ) s ( x G ) s ( x G ) s ( y ' 1 d 1 d ' 2 d 2 d ' m m ' + + = (8.1-1) We imagine a case in which process G m (s) could be divided into two parts, connected by a measurable intermediate variable x i : this could be as simple as two tanks in series, as in Lesson 4. Having specified some of the interior structure of G m , we consider x d2 to be typical of disturbances that affect the process further upstream and x d1 to affect the process downstream, after the intermediate variable. G d2a (s) G m2 (s) x ' d2 (s) x ' m (s) G d1 (s) x ' d1 (s) y' (s) G m1 (s) x' i (s) G d2a (s) G m2 (s) x ' d2 (s) x ' m (s) G d1 (s) x ' d1 (s) y' (s) G m1 (s) x' i (s) The process description becomes revised 2006 Mar 29 1 Spring 2006 Process Dynamics, Operations, and Control 10.450 Lesson 8: Cascade and Feedforward Control Schemes ) s ( x G ) s ( x G G ) s ( x G G ) s ( y ' 1 d 1 d ' 2 d 1 m a 2 d ' m 1 m 2 m ' + + = (8.1-2) Equations (8.1-1) and (8.1-2) describe the same process, so they must be equivalent. Comparing them, we find 1 m 2 m m G G G = (8.1-3) and 1 m a 2 d 2 d G G G = (8.1-4) Also, the intermediate variable is given by ) s ( x G ) s ( x G ) s ( x ' 2 d a 2 d ' m 2 m ' i + = (8.1-5) 8.2 response to disturbances Suppose, for illustration, that we let each of these transfer functions be first order. Then the responses of x i and y to a step in x d2 are shown in Figure 8.2-1. 0.2 0.4 0.6 0.8 1 1.2 1 2 3 4 5 6 7 t/ τ d2 response y x i 0.2 0.4 0.6 0.8 1 1.2 1 2 3 4 5 6 7 t/ τ d2 response y x i Figure 8.2-1. Step response of intermediate and output variables We observe that the intermediate variable responds before the output....
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- Feedforward Control Schemes