[Solved] Design noise filter and controller for a system based on reference model

Khai Nguyen Asks: Design noise filter and controller for a system based on reference model
I have a practical system which can be described in the form $ frac{k}{s(Ts+1)} = frac{5}{s(0.03s+1)}$ (1).

My objective is to design a controller for the system to guarantee that the closed-loop looks like $ G = frac{1}{T_ps+1} = frac{1}{0.035s+1}$ (2) the most. I see that the bandwidth of (2) is about 30Hz. The bandwidth of reference signal is 20Hz.

Therefore, I have implemented a PD controller for this and it partially meets the requirements. However, the sensor results in a lot of random noise, which makes the output slightly oscillatory. So, how to design an reasonable filter to guarantee both noise rejection and bandwidth for (2)? How can I improve the controller?

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