On-Line Process Identification Using the Laguerre Series for Automatic Tuning of the Proportional-Integral-Derivative Controller

A new on-line identification method based on the approximation of closed-loop response is proposed to tackle the shortcomings of previous autotuning methods using a proportional controller as a test signal generator. That is, for both the overdamped and the underdamped closed-loop response in the identification step, the proposed method can easily estimate the second-order plus time delay model only with the measurements of the transient. From the orthonormal property of the Laguerre series, the closed-loop response in the identification step is approximated by a simple least-squares technique effectively, and then a high-order process transfer function is estimated from it. Finally, a simple model reduction method is used to reduce the high-order process transfer function to a second-order plus time delay model via the least-squares technique in the frequency domain. The proposed method does not need any numerical technique such as root-finding or iterative optimization. Since it uses all the measurements of transient response instead of several dominant data points such as peak or valley values, the robustness to the measurement noise is greatly enhanced. From simulation results and comparisons with previous works, we can recognize that it provides more accurate models and better control performances for various process dynamics. In experimental study, it can be noted that it is also very effective in identification and control of real processes.