Fractional order PD controller design for third order plants ıncluding time delay

Abstract

Due to the lack of integral operator, proportional derivative controllers have difficulties in providing stability and robustness. This difficulty is especially felt in higher order systems. In this publication, analytical design method of fractional proportional derivative controllers is presented to ensure the stability of third order systems with time delay. In this method, it is aimed to achieve the frequency characteristics of a standard control system to ensure stability. It is aimed to provide the desired gain crossover frequency, phase crossover frequency and phase margin properties of the system. In this way, the stability and robustness of the system can be obtained by choosing the appropriate values. The reason for choosing a fractional order controller is that the controller parameters to provide these features can be tuned more accurately. In order for the obtained stability to be robust to unexpected external effects, it is aimed to flatten the system phase. In the literature, phase flattening is performed by setting the phase derivative to zero at a specified frequency value. This can lead to mathematical complexity. In this publication, the phase flattening process is provided graphically by correctly selecting the frequency characteristics given above. Thus, an accurate and reliable controller design method is presented, avoiding mathematical complexity. The effectiveness of the proposed method has been demonstrated on three different models selected from the literature. The positive contribution of the method to the system robustness has been proven by changing the system gain at certain rates.