PID controller tuning using mathematical programming

Proportional integral derivative (PID) controllers are extensively used in the process industry. As a result a large number of general purpose tuning methodologies are available. These tuning methodologies can offer initial estimates of the parameters of the PID controllers. However, the design objectives used for the development of these tuning methods can be quite different from the performance objectives specific to a process under investigation. As a result, the control engineer often needs customized tuning methods in order to speed up or even eliminate the retuning procedure, and thus, minimize the time and effort needed to design a satisfactory closed loop system. This paper presents a general mathematical programming formulation for the development of customized PID controller tunings. A reformulation of the mathematical formulation is proposed that transforms the initially nonlinear formulation to a linear one that can be solved to global optimality. A number of case studies are presented to clarify the proposed methodology.