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Enhanced Single-Loop Control Strategies Chapter 16

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Cascade Control (multi-loop) Distinguishing features: 1.Two FB controllers but only a single control valve (or other -final control element). 2. Output signal of the "master" controller is the set- point for “slave" controller. 3. Two FB control loops are "nested" with the "slave" (or "secondary") control loop inside the "master" (or "primary") control loop. Terminology slave vs. master secondary vs. primary inner vs. outer Chapter 16

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(Eq.16-5)

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Chapter 16

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Time Delay Compensation Model-based feedback controller that improves closed-loop performance when time delays are present Effect of added time delay on PI controller performance for a second order process ( 1 = 3, 2 = 5) shown below

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Chapter 16

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No model error: (sensitive to model errors > +/- 20%) Chapter 16

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Direct Synthesis Approach (Smith Predictor) Assume time delay between set-point change and controlled variable (same as process time delay, ). If then From Block Diagram, Equating... Chapter 16

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SELECTIVE CONTROL SYSTEMS (Overrides) For every controlled variable, there must be at least one manipulated variable. In some applications # of controlled variables # of manipulated variables Low selector: High selector: Chapter 16

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multiple measurements one controller one final control element Chapter 16 Figure Control of a reactor hot spot temperature by using a high selector.

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Override using PI controllers - “old way” (vs. digital logic) 2 measurements, 2 controllers, 1 F.C.E. Chapter 16 Figure A selective control system to handle a sand/water slurry.

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Split Range Control 2 Manipulated Vars.: V 1 and V 2 1 Controlled Var.: Reactor pressure While V 1 opens, V 2 should close Chapter 16

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Chapter 16

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Inferential Control Problem: Controlled variable cannot be measured or has large sampling period. Possible solutions: 1.Control a related variable (e.g., temperature instead of composition). 2.Inferential control: Control is based on an estimate of the controlled variable. The estimate is based on available measurements. –Examples: empirical relation, Kalman filter Modern term: soft sensor

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Chapter 16

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Gain Scheduling Objective: Make the closed-loop system as linear as possible. Basic Idea: Adjust the controller gain based on current measurements of a “scheduling variable”, e.g., u, y, or some other variable. Chapter 16 Note: Requires knowledge about how the process gain changes with this measured variable.

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Chapter 16 Examples of Gain Scheduling Example 1. Once through boiler The open-loop step response are shown in Fig for two different feedwater flow rates. Fig Open-loop responses. Proposed control strategy: Vary controller setting with w, the fraction of full-scale (100%) flow. Example 2. Titration curve for a strong acid-strong base neutralization.

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Chapter 16 Adaptive Control A general control strategy for control problems where the process or operating conditions can change significantly and unpredictably. Example: Catalyst decay, equipment fouling Many different types of adaptive control strategies have been proposed. Self-Tuning Control (STC): – A very well-known strategy and probably the most widely used adaptive control strategy. – Basic idea: STC is a model-based approach. As process conditions change, update the model parameters by using least squares estimation and recent u & y data. Note: For predictable or measurable changes, use gain scheduling instead of adaptive control Reason: Gain scheduling is much easier to implement and less trouble prone.

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Chapter

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Chapter 16 Figure Membership functions for room temperature.

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Chapter 16 Figure Membership functions for the inputs of the PI fuzzy controller (N is negative, P is positive, and Z is zero).

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Chapter 16

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Basic Design Information

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Final Control System – Distillation Train Chapter 16

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