Analysis and Design of Software-Based Optimal PID Controllers

Abstract: A large process industry can have somewhere between five hundred and five thousand control loops, and PID controllers are used in 90–97% of the cases. It is well-known that only 20–30% of the controllers in the process industry are tuned satisfactorily, but with the methods available today it is considered too time-consuming to optimize each single controller. This thesis presents tools for analysis and design of optimal PID controllers, and suggests when and how to use them efficiently. High performing low-level controllers are also likely to be beneficial for higher-level advanced process control, thus promoting the economy of whole factories. Controller design is often a trade-off between conflicting criteria, such as load disturbance attenuation, robustness, and noise sensitivity. In this thesis, a MATLAB-based software tool is used to solve a constrained optimization problem, with respect to all three requirements. This gives tuning of both the PID parameters and a low-pass filter time constant. A large batch of benchmark models, representative for the process industry, has been used throughout the whole thesis for controller analysis. This includes comparisons between PID controllers derived using either optimization or tuning rules. Trade-off plots are also presented, which explicitly show the relationships between performance, robustness and the PID parameters. A new procedure for software-based optimal PID design is suggested, which leads to a set of PID, PI, and I controllers. The user can then select the best performing controller with an acceptable control signal activity. It is shown that the resulting controllers are optimal or near optimal with respect to the three above mentioned criteria. The same procedure can also be used to analyze the benefit of the derivative part by comparing optimal PI and PID controllers with the same level of noise sensitivity. The efficiency of the procedure is demonstrated on an industrial friction stir welding machine. For a more wide-spread use of the proposed procedure, it is shown that better modeling techniques are needed, and guidelines for such methods are also included.