Designing a feedback control system for a robotic arm requires following several steps. Firstly, you need to define the task that you want the robotic arm to perform, such as moving to a specific position or following a trajectory. Secondly, you must model the dynamics of the plant, which describes how the input affects the output. This can be done using mathematical equations, simulations, or experiments. Thirdly, choose the type of controller that suits your task, such as a PID controller, a fuzzy controller, or a neural network controller. You can tune the parameters of the controller using trial and error, optimization, or learning. Fourthly, implement the controller on a hardware or software platform such as Arduino, Raspberry Pi, or MATLAB. You can program the controller using languages and libraries such as C, Python, or Simulink. Lastly, test and evaluate the performance of the feedback control system using metrics and tools such as error, bandwidth, or root locus.