Trane CNT-APG002-EN, PID Control

Appendix A The math behind PID loops

56 CNT-APG002-EN

Contents

Main Page Page Contents Chapter 1 Overview of PID control. . . . . . . . . . . . . . . . . . . . . . 1 Chapter 2 PID settings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Chapter 3 Programming PID loops. . . . . . . . . . . . . . . . . . . . . 23 Page Chapter 1 Overview of PID control What PID loops do How PID loops work PID calculations Proportional calculation Integral calculation Derivative calculation Page Velocity model Page Chapter 2 PID settings Throttling range Gains Calculating the gains Example Sampling frequency Page Calculating the sampling frequency To calculate the sampling frequency: Page Example Action Direct action Reverse action Determining the action Example 1 Example 2 Error deadband Typical applications Adjusting error deadband for modulating outputs IMPORTANT Adjusting error deadband for staged outputs To adjust the error deadband for staged outputs: Other PID settings Page Chapter 3 Programming PID loops Programming in PCL Follow these steps to program PID loops in PCL: Page Programming in TGP Follow these steps to program PID loops in TGP: Page Chapter 4 Applications Discharge-air temperature control Page Page Building pressure control Page Cascade controlfirst stage Page Page Staging cooling-tower fans Setting up the PID loop Page Page Page Page Determining the staging points To determine the staging points: Example 1: Two-stage fan system Example 2: Three-stage fan system Chapter 5 Troubleshooting Troubleshooting procedure Tips for specific problems Changing the sampling frequency Changing the gains Examples Example 1 Example 2 Page Example 3 Chapter 6 Frequently asked questions Why is the derivative gain usually zero? What is the difference between direct acting and reverse acting? When should I use proportional-only control? Why should I use PID control in staging applications? How can I tell if a PID loop is working well? Whats the best sampling frequency? Do I need to worry about the throttling range? Page Appendix A The math behind PID loops Velocity model formula Proportional control formula Page Glossary Page Page Page Index Numerics A B C E F G H I S T U V W