Direct design of PID controllers for stable processes with inverse response

Processes that exhibit inverse response impose difficulties on control system design. This paper presents a novel method for proportional-integral-derivative (PID) controller tuning directly using the unit pulse response data of the process without resorting to a process model for stable processes with inverse response. Two formulations of the loop transfer function of and the corresponding reference model obtained by using direct factorization and all-pass factorization methods are developed. A three-dimensional optimization problem is formulated to determine an appropriate loop transfer function for the controlled process. Simulation studies are provided to illustrate the proposed methods using the more generalized loop transfer functions and a comparison with other model-based or/and data-based PID design methods is made.