An implementation of fractional-order PID controller with dynamic quantizer considering the memory constraint

Recently, the fractional-order PID (FO-PID) control, which is the generalization of the PID control, has been focused. Even though the FO-PID needs the high-order filter, it is difficult to realize the high-order one due to the memory limitation of the micro-controller unit (MCU). For implementation of the FO-PID, approximation of the fractional integrator and differentiator is required. Short memory principle (SMP) is one of the effective approximation methods. However, there is a disadvantage that the approximated filter by the SMP can´t eliminate the steady-state error. For this disadvantage, we introduce the distributed implementation of integrator and the dynamic quantizer to make the efficient use of available memory. Our objective is to clarify how to implement the accurate FO-PID with little memories. In this paper, we propose the implementation method of the FO-PID with memory constraint using dynamic quantizer. And the trade-off between approximation of fractional elements and quantized data size are examined so as to close to the ideal responses. Using the temperature control system of heat plate, the proposed method is evaluated by experiments.