外乱を考慮した非線形系のモデル追従形制御系の設計

抄録

A model following control system (MFCS) can let output signals follow desired ones. Since MFCS permits general signals as desired ones, its application's range is wide. This paper describes the design of nonlinear MFCS of which the inner states are bounded under disturbances, and the output signals converge to desired signals asymptotically. In a nonlinear MFCS the boundedness of inner states is important. In this paper we set the nonlinear part (f(v(t))) of the controlled object as ||f(v(t))||≤α+β||v(t)||^γ, and show the boundedness of inner states by separating the nonlinear part into two cases, i.e. 0≤γ<1 and γ≥1. There are not strong constraints in such a setting of the nonlinear part. In the case of 0≤γ<1, the fact that characteristic roots of system matrix are stable guarantees the boundedness of inner states. In the case of γ≥1, the conditions that the transfer matrix H(p) from f(v(t)) to v(t) is positive real, and the coefficient tensor of the highest degree of f(v(t)) is negative definite guarantee the boundedness of inner states. We show the availability of this design in a numerical example of which the nonlinear degree is five.