  We consider the polynomial representation of Double Affine Hecke Algebras
(DAHAs) and construct its submodules as ideals of functions vanishing on the
special collections of affine planes. This generalizes certain results of
Kasatani in types A_n, (C_n^\vee,C_n). We obtain commutative algebras of
difference operators given by the action of invariant combinations of
Cherednik-Dunkl operators in the corresponding quotient modules of the
polynomial representation. This gives known and new generalized
Macdonald-Ruijsenaars systems. Thus in the cases of DAHAs of types A_n and
(C_n^\vee,C_n) we derive Chalykh-Sergeev-Veselov operators and a generalization
of the Koornwinder operator respectively, together with complete sets of
quantum integrals in the explicit form.
