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KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Simulation)-Chapter_12

KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Simulation)-Chapter_12

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1 Chapter 12 Fig. 12.1. Unit-step disturbance responses for the candidate controllers (FOPTD Model: K = 1, θ 4, τ 20). = = Controller Tuning: A Motivational Example
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2 Chapter 12 PID Controller Design, Tuning, and Troubleshooting Performance Criteria For Closed-Loop Systems The function of a feedback control system is to ensure that the closed loop system has desirable dynamic and steady- state response characteristics. Ideally, we would like the closed-loop system to satisfy the following performance criteria: 1. The closed-loop system must be stable. 2. The effects of disturbances are minimized, providing good disturbance rejection . 3. Rapid, smooth responses to set-point changes are obtained, that is, good set-point tracking .
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3 Chapter 12 1. Steady-state error (offset) is eliminated. 2. Excessive control action is avoided. 3. The control system is robust, that is, insensitive to changes in process conditions and to inaccuracies in the process model. 1. Direct Synthesis (DS) method 2. Internal Model Control (IMC) method 3. Controller tuning relations 4. Frequency response techniques 5. Computer simulation 6. On-line tuning after the control system is installed. PID controller settings can be determined by a number of alternative techniques:
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4 Chapter 12 Direct Synthesis Method In the Direct Synthesis (DS) method, the controller design is based on a process model and a desired closed-loop transfer function. The latter is usually specified for set-point changes, but responses to disturbances can also be utilized (Chen and Seborg, 2002). Although these feedback controllers do not always have a PID structure, the DS method does produce PI or PID controllers for common process models. As a starting point for the analysis, consider the block diagram of a feedback control system in Figure 12.2. The closed-loop transfer function for set-point changes was derived in Section 11.2: (12-1) 1 m c v p sp c v p m K G G G Y Y G G G G = +
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5 Chapter 12 Fig. 12.2. Block diagram for a standard feedback control system.
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6 Chapter 12 For simplicity, let and assume that G m = K m . Then Eq. 12-1 reduces to v p m G G G G @ (12-2) 1 c sp c G G Y Y G G = + Rearranging and solving for G c gives an expression for the feedback controller: / 1 (12-3a) 1 / sp c sp Y Y G G Y Y = - Equation 12-3a cannot be used for controller design because the closed-loop transfer function Y / Y sp is not known a priori . Also, it is useful to distinguish between the actual process G and the model, , that provides an approximation of the process behavior. A practical design equation can be derived by replacing the unknown G by , and Y / Y sp by a desired closed-loop transfer function, ( Y / Y sp ) d : G % G %
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7 Chapter 12 ( 29 ( 29 / 1 (12-3b) 1 / sp d c sp d Y Y G G Y Y = - % The specification of ( Y / Y sp ) d is the key design decision and will be considered later in this section.
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