Processing the Sensor Signal in a PI Control System Using an Adaptive Filter Based on Fuzzy Logic

This paper presents an adaptive fuzzy filter applied to processing a signal from a voltage sensor fed to the input of an object in an automatic temperature control system with a PI controller. (1) The research goal was to develop an algorithm for processing the signal from an RMS voltage sensor, measured at the terminals of a heating element in a temperature control system with a PI controller, in a way that ensures good dynamic properties while maintaining an appropriate level of accuracy. (2) The paper presents a method for designing an adaptive fuzzy filter by synthesizing a first-order low-pass infinite impulse response (IIR) filter and a fuzzy model of the dependence of this filter parameter value on the modulus of the derivative of the measured quantity. The application of a model with a symmetric input and output structure and a modified fuzzy model with asymmetry resulting from the uneven distribution of modal values of singleton fuzzy sets at the output was shown. The innovation in the proposed solution is the use of a signal from a PI controller to determine the derivative module of the measured quantity and, using a fuzzy model, linking its instantaneous value with a digital filter parameter in the measurement chain with a sensor monitoring the signal at the input of the controlled object. It is demonstrated that the signal generated by the PI controller can be used in a control system to continuously determine the modulus of the time derivative of the signal measured at the input of the controlled object, also indicating the limitations of this method. The signal from the PI controller can also be used to select filter parameters. In such a situation, it can be treated as a reference signal representing the useful signal. The mean square error (MSE) was adopted as the criterion for matching the signal at the filter output to the reference signal. (3) Based on a comparative analysis of the results of using an adaptive fuzzy filter with a classic first-order IIR filter with an optimal parameter in the MSE sense, it was found that using a fuzzy filter yields better results, regardless of the structure of the fuzzy model used (symmetric or asymmetric). (4) The paper demonstrates that in the tested temperature control system, introducing a simple fuzzy model with one input characterized by three fuzzy sets, relating the modulus of the derivative of the signal developed by the PI controller to the value of the first-order IIR filter parameter, into the voltage sensor signal-processing algorithm gave significantly better results than using a first-order IIR filter with a constant optimal parameter in terms of MSE. The best results were obtained using a fuzzy model in which an intentional asymmetry in the modal values of the output fuzzy sets was introduced.