PID tuning based on loop-shaping H∞ control

Loop-shaping H_∞ controllers are designed for both stable and integrating processes, H_∞ controllers for typical industrial processes have a PID structure interpretation. Further, if the precompensator is carefully chosen, the design indicator will be independent of plant constants. This fact leads to the derivation of a direct relation between the controller parameters and the plant constants, and the results can be viewed as new PID tuning rules for stable and integrating processes. The main contribution of the tuning rules is that the PID parameters can be obtained using one design parameter which reflects the trade-off between stability robustness and time domain performance of the closed-loop system, thus making it convenient to choose PID parameters dependent on the uncertainties of the processes