KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec37

KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec37

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1 Chapter 14 Control System Design Based on Frequency Response Analysis Frequency response concepts and techniques play an important role in control system design and analysis. Closed-Loop Behavior In general, a feedback control system should satisfy the following design objectives: 1. Closed-loop stability 2. Good disturbance rejection (without excessive control action) 3. Fast set-point tracking (without excessive control action) 1. A satisfactory degree of robustness to process variations and model uncertainty 2. Low sensitivity to measurement noise
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2 Chapter 14 Bode Stability Criterion The Bode stability criterion has two important advantages in comparison with the Routh stability criterion of Chapter 11: 1. It provides exact results for processes with time delays, while the Routh stability criterion provides only approximate results due to the polynomial approximation that must be substituted for the time delay. 1. The Bode stability criterion provides a measure of the relative stability rather than merely a yes or no answer to the question, “Is the closed-loop system stable?”
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3 Chapter 14 Before considering the basis for the Bode stability criterion, it is useful to review the General Stability Criterion of Section 11.1: A feedback control system is stable if and only if all roots of the characteristic equation lie to the left of the imaginary axis in the complex plane. Before stating the Bode stability criterion, we need to introduce two important definitions: 1. A critical frequency is defined to be a value of for which . This frequency is also referred to as a phase crossover frequency. 2. A gain crossover frequency is defined to be a value of for which . ω c ω ( 29 φ ω 180 OL = - o ω g ω ( 29 ω 1 OL AR =
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Chapter 14 For many control problems, there is only a single and a single . But multiple values can occur, as shown in Fig. 14.3 for . ω
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KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec37

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