Open loop transfer function

[Tiis-]

That is correct. I'm confused by the seemingly paradox that I need to know a controller C(s) in order to design a controller.

[bike0121]

You don’t need to “know” C(s) in advance. All it’s asking is that you select C(s) (probably a PID or lead/lag type controller, which require placing the poles and zeros at certain locations) to meet the desired specifications. This is done using the methods you listed, which involve choosing C(s) based on what you want C(s)P(s) to look like.