DESIGN OF A NEW PID AUTO-TUNER BASED ON A CROSS-CORRELATION TECHNIQUE

Abstract

This thesis presents the development of an on-line version of a new auto-tuning algorithm for proportional-integral-derivative (PID) controllers based on a cross-correlation technique. The new algorithm is adapted to tune PIO controllers with a structure based on the refined Ziegler-Nichols tuning formula which gives an improved closed-loop response. In this algorithm, a small pseudo random binary sequence (PRBS) probing signal is super-imposed onto the setpoint or process input The resulting perturbation at the process output is observed and correlated with the PRBS signal to compute the impulse response of the process. The impulse response is then numerically transformed into its frequency response to extract the ultimate gain and period of the process for use in the refined Ziegler-Nichols tuning formula. The cross-correlation based auto-tuning algorithm requires the parameters of the PRBS probing signal to be selected properly for correct tuning. The empirical rules for selecting the parameters of the PRBS probing signal used by this method of auto-tuning are derived and explained. A pre-tune function has also been designed to allow automatic selection of the PRBS parameters. A refined Ziegler-Nichols (RZN) prototype controller was implemented on an IBM AT personal computer installed with an AD/DA interface card. This controller has a PID structure based on the refined Ziegler-Nichols tuning formula and a cross-correlation based auto-tuner. It is used to assess and compare the performance of the cross-correlation based auto-tuner. The accuracy and performance of cross-correlation based auto-tuner have been substantiated by extensive simulations, in particular, the auto-tuner is proven to be robust in the presence of measurement noise and sinusoidal load disturbance. The cross-correlation based auto-tuner was further tested on a pilot plant in which the test results reconfirmed the conclusions obtained in the simulation results. A comparative study has also been made between the cross-correlation based auto-tuner and two commercial PID auto-tuners (SattControl auto-tuner and Foxboro EXACT self-tuning algorithm). The results showed that the tuned transient responses of the RZN controller to setpoint change, static load disturbance and measurement noise have the best performance with respect the ISE performance index. The cross-correlation based auto-tuner re-tunes faster than the Foxboro self-tuning algorithm but was slower than the relay technique used by the SattControl auto-tuner. It is more robust in the presence of process noise than the deterministic approach used by the other two auto-tuners. The cross-correlation based auto-tuning algorithm causes only minor perturbation on normal operation of the process and it needs little a priori information. Therefore, it is useful for checking or assisting in tuning PID controllers on-line or off-line. The algorithm may also be incorporated into standalone single-loop controllers or offered in a DDC package as an option for automatic tuning.