Abstract
The object of this paper is to extend the sufficient condition for the stability of feedback systems with backlash by using the Passivity Theorem of Zames. It is assumed that the feedback loop consists of an asymptotically linear, monotone nondecreasing nonlinearity, a linear time-invariant system consisting of an integrator and a strictly stable subsystem characterized by the impulse response, and a transducer with backlash.
The stability criterion for the freedback system is of the form
Re[(α+Z(iω))(H(iω)+1/k)]≥δ>0, 0≤ω<∞
where H(iω) is the frequency response of the linear subsystem, k is the incremental gain of the nonlinearity, α is a nonnegative number, and z(t), the inverse Fourier transform of Z(iω), satisfies the conditions: z(t)≥0, z(t)≤0, z(t)≥0, t≥0.
When the asymptotic linearity restriction on the nonlinearity is removed, he stability criterion is of the form
Re[H(iω)+1/k]≥δ>0, 0≤ω<∞
An example is given to compare these criteria with the well-known criteria.
