# Chemical Process Control a First Course with Matlab

**Topics:**Control theory, Laplace transform, Fourier transform

**Pages:**414 (105027 words)

**Published:**May 14, 2013

Table of Contents Preface 1. Introduction ............................................................ [Number of 10-point single-space pages -->] 3

2. Mathematical Preliminaries .................................................................................................. 35 2.1 A simple differential equation model 2.2 Laplace transform 2.3 Laplace transforms common to control problems 2.4 Initial and final value theorems 2.5 Partial fraction expansion 2.5.1 Case 1: p(s) has distinct, real roots 2.5.2 Case 2: p(s) has complex roots 2.5.3 Case 3: p(s) has repeated roots 2.6 Transfer function, pole, and zero 2.7 Summary of pole characteristics 2.8 Two transient model examples 2.8.1 A Transient Response Example 2.8.2 A stirred tank heater 2.9 Linearization of nonlinear equations 2.10 Block diagram reduction Review Problems 3. Dynamic Response ............................................................................................................. 19 3.1 First order differential equation models 3.1.1 Step response of a first order model 3.1.2 Impulse response of a first order model 3.1.3 Integrating process 3.2 Second order differential equation models 3.2.1 Step response time domain solutions 3.2.2 Time-domain features of underdamped step response 3.3 Processes with dead time 3.4 Higher order processes and approximations 3.4.1 Simple tanks-in-series 3.4.2 Approximation with lower order functions with dead time 3.4.3 Interacting tanks-in-series 3.5 Effect of zeros in time response 3.5.1 Lead-lag element 3.5.2 Transfer functions in parallel Review Problems 4. State Space Representation ................................................................................................... 18 4.1 State space models 4.2 Relation with transfer function models 4.3 Properties of state space models 4.3.1 Time-domain solution 4.3.2 Controllable canonical form 4.3.3 Diagonal canonical form Review Problems 5. Analysis of PID Control Systems ........................................................................................ 22 5.1 PID controllers 5.1.1 Proportional control 5.1.2 Proportional-Integral (PI) control 5.1.3 Proportional-Derivative (PD) control 5.1.4 Proportional-Integral-Derivative (PID) control 5.2 Closed-loop transfer functions

P.C. Chau © 2001

5.2.1 Closed-loop transfer functions and characteristic polynomials 5.2.2 How do we choose the controlled and manipulated variables? 5.2.3 Synthesis of a single-loop feedback system 5.3 Closed-loop system response 5.4 Selection and action of controllers 5.4.1 Brief comments on the choice of controllers Review Problems 6. Design and Tuning of Single-Loop Control Systems ............................................................... 19 6.1 Tuning controllers with empirical relations 6.1.1 6.1.2 6.1.3 Controller settings based on process reaction curve Minimum error integral criteria Ziegler-Nichols ultimate-cycle method Direct synthesis Pole-zero cancellation Internal model control (IMC)

6.2

Direct synthesis and internal model control

6.2.1 6.2.2

6.2.3 Review Problems

7. Stability of Closed-loop Systems .......................................................................................... 17 7.1 Definition of Stability 7.2 The Routh-Hurwitz Criterion 7.3 Direct Substitution Analysis 7.4 Root Locus Analysis 7.5 Root Locus Design 7.6 A final remark on root locus plots Review Problems 8. Frequency Response Analysis ................................................................................................ 29 8.1 Magnitude and Phase Lag 8.1.1 The general analysis Some important properties 8.1.2 8.2 Graphical analysis tools 8.2.1 Magnitude and Phase Plots 8.2.2 Polar Coordinate Plots 8.2.3 Magnitude vs Phase Plot 8.3 Stability Analysis 8.3.1 Nyquist Stability criterion 8.3.2 Gain and Phase Margins 8.4 Controller Design 8.4.1 How do we calculate proportional gain without trial-and-error? 8.4.2 A final word: Can frequency response...

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