Automatic tuning of PID controllers using relay feedback experiments has received attention on and off since it was first proposed and industrially implemented in a control system in the 1980s. While optimal experiment design and modern system identification easily outperform the original automatic tuner, they rely on computational resources that are not always available in industrial control systems. Here we present a combination of experiment and subsequent output-error identification of continuous-time first-order time-delayed (FOTD) system models, that requires very little in terms of computations and memory. The method has been extensively evaluated in simulation, and a prototype has been implemented for the ABB AC 800M controller family.

This paper demonstrates how second-order time-delayed models adequate for PID controller synthesis can be identified from significantly shorter relay experiments, than used in previous publications to obtain first-order time-delayed models. Apart from having good noise robustness properties, the proposed method explicitly addresses non-stationary initial states of the dynamics to be identified, and handles constant load disturbances.

A novel autotuning procedure is presented through application to an industrial in-line pH control system. The procedure has three advantages over classical relay auto-tuners: experiment duration is very short (no need for limit-cycle convergence); all data is used for identification (instead of only peaks and switch instances); a parameter uncertainty model is identified and utilized for robust controller synthesis.

In absence of covariance data, Kalman filters are usually initialized by guessing the initial state. Making the variance of the initial state estimate large makes sure that the estimate converges quickly and that the influence of the initial guess soon will be negligible. If, however, only very few measurements are available during the estimation process and an estimate is wanted as soon as possible, this might not be enough. This paper presents a method to initialize the Kalman filter without any knowledge about the distribution of the initial state and without making any guesses.