Chapter 6. PI and PID Parameters from IMC Designs

Objectives of the Chapter

  • Provide methods for approximating most IMC controllers with I, PI, or PID controllers.

  • Provide methods for approximating all other IMC controllers with PI or PID controllers cascaded with first-order or second-order lags.

Prerequisite Reading

Chapter 3, “One-Degree of Freedom Internal Model Control”

Chapter 4, “Two-Degree of Freedom Internal Model Control”

Appendix A.3, “P, PI, and PID Controller Transfer Functions”


While IMC controller implementations are becoming more popular (see Chapter 5), the standard industrial controllers remain the proportional (P), proportional plus integral (PI), and the proportional plus integral and derivative (PID) controllers. Morari ...

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