Recently a class of inflationary models satisfying the constant rate of roll constraint, ̈φ+(3+α)H&dotphi;=0, has been studied and compared with the latest cosmological observational data. We consider the broader class of constraints  ̈φ+α1/2&dotphi;+α2 H&dotphi;=0 and find an exact particular solution, without initial singularity, which is an attractor of the dynamics governed by a positive periodic potential V(φ)=E+ F cos (Ω φ )+G cos (2 Ω φ ). The spectral index ns and the tensor to scalar ratio r are consistent with the recent observational data.