Pid controller design for process with time delay, Truong Nguyen Luan Vu CONTENTS OVERVIEW ............................................................................................. 9 CHAPTER 1. DESIGN OF ADVANCED PID CONTROLLERS FOR TIME-DELAY PROCESSES ...................... 13 1.1. INTRODUCTION ............................................................................ 13 1.2. GENERALIZED IMC APPROACH FOR PID CONTROLLER DESIGN ............................................................................................ 14 1.3. DESIGN OF PID CONTROLLER CASCADED WITH A LEAD-LAG FILTER........................................................................ 16 1.4. PROPOSED TUNING RULES FOR TYPICAL TIMEDELAY MODELS ........................................................................... 18 1.4.1. First-Order plus Dead Time (FOPDT) Process Model ................. 18 1.4.2. Integrator Plus Time Delay Model ................................................ 18 1.4.3. First-Order Delayed Unstable Process (FODUP) Model .............. 19 1.4.4. First-Order Delayed Integrating Process (FODIP) Model ............. 21 1.5. Second-Order Delayed Unstable Process (SODUP) Model ............. 21 1.5.1. SODUP Model with One Unstable Pole ........................................ 21 1.5.2. SODUP Model with Two Unstable Poles ..................................... 22 1.6. PERFORMANCE AND ROBUSTNESS MEASUREMENTS ....... 22 1.6.1. Integral Absolute Error (IAE) Criteria .......................................... 22 1.6.2. Overshoot ....................................................................................... 22 1.6.3. Maximum Sensitivity (Ms) Criterion ............................................ 22 1.6.4. Total Variation (TV) ...................................................................... 23 1.7. SIMULATION STUDY ................................................................... 23 1.8. DISCUSSION ................................................................................... 43 6 1.8.1. Effect Of On the Tradeoff between Performance and Robustness .................................................................................... 43 1.8.2. Effectiveness of the Proposed Method for the Dead-Time Dominant Process ......................................................................... 45 1.9. CONCLUSIONS .............................................................................. 46 REFERENCES ........................................................................................ 47 CHAPTER 2. IMC-PID CONTROLLER TUNING FOR PROCESS WITH TIME DELAY ........................................................ 49 2.1. INTRODUCTION ............................................................................ 49 2.2. GENERALIZED IMC-PID DESIGN APPROACH ........................ 49 2.3. IMC-PID TUNING RULES FOR TYPICAL PROCESS ................ 52 2.3.1. First-order Plus Dead Time (FOPDT) Process Model .................. 52 2.3.2. Integrator Plus Time Delay (IPTD) Model .................................... 54 2.3.3. First-order Delay Unstable Process (FODUP) Model ................... 55 2.3.4. First-order Delayed Integrating Process (FODIP) Model ............. 58 2.3.5. Second-order Delayed Unstable Process (SODUP) Model ........... 58 2.3.5.1. SODUP Model with One Unstable Pole ..................................... 58 2.3.5.2. SODUP Model with Two Unstable Poles ................................... 60 2.4. ROBUST ANALYSIS ...................................................................... 62 2.5. SIMULATION STUDY ................................................................... 64 2.6. CONCLUSIONS .............................................................................. 80 REFERENCES ........................................................................................ 80 CHAPTER 3. FRACTIONAL-ORDER PROPORTIONALINTEGRAL CONTROLLERS DESIGN FOR TIME-DELAY PROCESSES .......................................................................................... 83 3.1. INTRODUCTION ........................................................................... 83 7 3.2. PRELIMINARIES ............................................................................ 84 3.2.1. Fractional calculus ......................................................................... 84 3.2.2. Integer Order Approximation ........................................................ 85 3.2.3. Fractional linear model .................................................................. 85 3.2.4. FOPI controller .............................................................................. 86 3.3. ANALYTICAL DESIGN OF GENERALIZED FOPI CONTROLLER TUNING RULES .................................................. 87 3.4. PERFORMANCE AND ROBUSTNESS MEASUREMENTS ....... 92 3.4.1. Integral Absolute Error (IAE) Criteria .......................................... 92 3.4.2. Overshoot ....................................................................................... 92 3.4.3. Total variation (TV) ....................................................................... 92 3.4.4. Resonant peak (Mp) criterion ........................................................ 92 3.5. SIMULATION STUDY ................................................................... 93 3.6. DISCUSSION ................................................................................. 103 3.6.1. Effect of Mp Values on the Tuning Parameters and the Closed-Loop Performance .......................................................... 105 3.6.2. Fractional order (λ) guideline for the proposed FOPI parameter tuning ......................................................................... 105 3.7. CONCLUSIONS ............................................................................ 108 REFERENCES ...................................................................................... 108 CHAPTER 4. SMITH PREDICTOR BASED FRACTIONALORDER PI CONTROL FOR TIME-DELAY PROCESSES .......... 111 4.1. INTRODUCTION .......................................................................... 111 4.2. THEORY DEVELOPMENT .......................................................... 112 4.2.1. Fractional Calculus ...................................................................... 112 4.2.2. Design of FOPI Controller in Frequency Domain ....................... 114 4.2.3. SP-FOPI Controller Design Procedure ........................................ 115 8 4.3. SELECTION OF TUNING PARAMETERS ................................. 119 4.4. SIMULATION STUDY ................................................................. 120 4.5. CONCLUSIONS ............................................................................ 134 REFERENCES ...................................................................................... 134 CHAPTER 5. FRACTIONAL-ORDER PI CONTROLLER TUNING RULES FOR CASCADE CONTROL SYSTEM............. 137 5.1. INTRODUCTION .......................................................................... 137 5.2. PRELIMINARIES .......................................................................... 138 5.2.1. Fractional Linear Model .............................................................. 139 5.2.2. Design of FOPI Controller in Frequency Domain ....................... 139 5.3. ANALYTICAL TUNING RULES OF FOPI CONTROLLERS FOR CASCADE CONTROL SYSTEM ...................................... 140 5.3.1. FOPI Controller Design Procedure for General Process Models ........................................................................................ 140 5.3.2. Design of Secondary Controller .................................................. 140 5.3.3. Design of Primary Controller ...................................................... 142 5.4. SIMULATION STUDY ................................................................. 144 5.5. CONCLUSIONS ............................................................................ 146 REFERENCES ...................................................................................... 146 APPENDIX USE OF MATLAB IN PID CONTROL ...................... 148 REFERENCES .................................................................................... 151