Optimal ITAE Criterion PID Parameters for PTn Plants Found with a Machine Learning Approach

Abstract

Various approaches are known from the literature on how to find optimal parameter sets for PID control from step responses of plants. The methods of Ziegler- Nichols [1] or Chien, Rhones and Reswick [2] are best known. These are heuristic processes which, although they result in stable control systems, have to be further optimized in practice. One of the optimization methods is carried out using the ITAE criterion (integral of time-multiplied absolute value of error). This uses a step response of the closed loop and integrates the timeweighted absolute value of the difference between the setpoint and the actual value. With the current state of technology, optimization is carried out manually or with the aid of a computer, for example with Matlab toolboxes to minimize the ITAE criterion} [9]. The method presented here uses a machine learning approach to automatically find the optimal PID parameters of the minimum ITAE criterion [3]. For general stable systems, the parameters could even be found directly on the system. However, many systems can be described directly with PTn elements by measuring step responses. For these, the paper provides calculated table values of the minimized ITAE criterion with different control signal limitations. These are verified in practice using the example of a thermal system. The table values are already successfully in use in the control theory course for mechanical engineers at Zurich University of Applied Sciences, School of Engineering.