Due to the simplicity and generality, design of feedback control systems in the frequency domain is among the most prominent topics in the control systems engineering. The problem of compensation means properly adjusting the loop frequency response at critical frequencies. Considering the point that the traditional methods usually use trial and error procedures for compensation, analytical design of fixed-structure controllers for exactly adjusting such values has great importance. Benefitting from the capability of fractional-order dynamics, the compensation problem is studied from three aspects in this thesis. At first according to the importance of adjusting the system frequency response...