The generation of dynamic biochemical signals in a microfluidic control system is of importance for the study of the interaction between biological cells and their niches. However, most of microfluidic control systems are not able to provide dynamic biochemical signals with high precision and stability due to inherent mechanical vibrations caused by the actuators of the programmable pumps. In this paper, we propose a novel microfluidic feedback control system integrating an external feedback control system with a Y-shaped microfluidic chip with a "Christmas tree" inlet. The Proportional Integral Derivative (PID) controller is implemented to reduce the influence of vibrations. In order to regulate the control parameters efficiently, a mathematical model is built to describe the actuator of the programmable pump, in which a fractional-order model is utilized. Both simulation and experimental studies are carried out, confirming that the microfluidic feedback control system can precisely and stably generate desired dynamic biochemical signals.