In this chapter we propose a framework for PID tuning rules comparison by using dimensional analysis. The proposal establishes the framework in which to perform the analysis for any user-selected indexes. The key point enabling the comparison framework yields in the dimensionless representation of both transfer function models and transfer function controllers.

Chapter Contents:

• 7.1 Introduction
• 7.2 Elements of the comparative framework
• 7.3 Dimensionless comparative framework
• 7.4 Dimensionless elements
• 7.4.1 Loop transfer function
• 7.4.2 Dimensionless closed loop transfer functions
• 7.4.3 Dimensionless integral errors
• 7.4.4 Indexes
• 7.5 Application example
• 7.5.1 PID tuning rules dimensionless characterization
• 7.5.2 Dimensionless sensitivity bandwidth comparison
• 7.5.3 Dimensionless sensitivity peak comparison
• 7.5.4 Dimensionless integral absolute error
• 7.5.5 Dimensionless control action variation
• 7.6 PID tuning rules selection
• References

Inspec keywords: transfer functions; three-term control; control system synthesis

Other keywords: user-selected index; dimensionless representation; transfer function controllers; dimensionless PID tuning rules comparison; dimensional analysis; transfer function models

Subjects: Control system analysis and synthesis methods