Frequency frame approach on tuning FOPI controller for TOPTD thermal processes

The frequency frame is used to tune fractional order proportional-integral​ controllers for stability, performance and robustness of third order plus time delay plants. Such plants are frequently used in describing thermal processes such as an air heater or a fired boiler. The aim is to tune the controller to meet some frequency domain properties. As robustness is an indispensable issue for thermal processes, main inspiration of the paper comes from flattening the phase curve in the Bode plot to provide improved robustness for the system. In spite of some existing studies, flattening is not realized by equalizing the phase derivative to zero at a given frequency value. Firstly, gain and phase crossover frequency points are enclosed with a rectangular frame. Then, lengths of the edges of this frame are changed to tune phase and gain margins. Curves inside the frame can be flattened by proper tuning of the edges. This will enhance the robustness and also ensure the iso-damping property. Equations to obtain the controller are given with two theorems. Demonstrations are made on two different thermal plants which are a novel electrical air heater and a bagasse fired boiler and the results are given on detailed illustrations. The results proved that preferred gain and phase properties are successfully obtained and improved performance and robustness are provided for related systems.