Simple adaptive control (SAC) is known as a control method that keeps control performance even if plant properties have changed. However, there is a problem such that the vibratory output occurs in the transient response when SAC is applied to a vibration system which includes anti-resonance modes. The reason why the vibratory output occurs is the structure of SAC with the output caused by the vibratory input corresponding to the anti-resonance frequency. In order to overcome the problem, it is shown that designing parallel feedforward compensator (PFC) appropriately is effective. One of the PFC design methods for continuous-time LTI SISO system has been proposed. In the method, the PFC is designed such that the gain of the augmented system is matched to the one of the desired model. Furthermore, the PFC must give the ASPR property the augmented system. These conditions are described using LMI/BMI conditions. The LMI/BMI conditions are solved by the iterative procedure. However, the leading coefficient of the PFC must be given preliminarily to guarantee the ASPR property. Thus, all coefficients of the PFC could not be design parameters in the conventional method. This paper proposes an alternative method to overcome the problem by using the stability theorem of the descriptor system. By this method, the value of the leading coefficient of the PFC is not required in advance. The effectiveness of the proposed method is verified by numerical simulations.
