A simple reference model based PID control for wafer scanner systems

In this work, we propose a new and simple controller design based on internal model principle (IMP) and existing PID, with the implementation on a wafer stage. PID has been well applied to solve control engineering problems owing to its flexibility to handle various control tasks, and the easiness to tune PID gains for a variety of plants. However, PID may fail to achieve satisfactory tracking performance when dealing with a complex control task that is beyond a simple step reference. IMP suggests that a good control response can only be expected when the internal model of the reference is incorporated into the control loop. For a well-tuned PID, however, it is not that straightforward to incorporate the internal model of the reference into the existing PID. In this work, focusing on a real wafer stage, we explore a new control design approach, reference-model (RM)-based PID, to achieve the internal model and meanwhile retain the well-tuned PID. The new controller design for the wafer stage is achieved through several steps. First, the body plots of the experimental setup of wafer stage are acquired and a second-order approximate model is established. Second, a reference model specific in wafer stage is given and its inherent internal model is analyzed. Then, the feedback controller is constructed by concatenating the internal model and an existing PID that has been well tuned. Next, considering the low-frequency characteristic of the reference, the internal model is further modified with a simple high-pass filter such that more of high-frequency components in the tracking error could be suppressed. Finally, in experiments, more accurate tracking performance of the RM-based PID is illustrated by comparing with two classic PIDs with different bandwidths.