A　protocol　is　proposed　to　generate　singlet　states　of　three　logical　qubits　constructed　by　pairs　of　spins.　Single　and　multiple　operations　of　logical　qubits　are　studied　for　the　construction　of　an　effective　Hamiltonian,　with　which　robust　control　fields　are　derived　with　invariant-based　reverse　engineering　and　optimal　control.　Moreover,　systematic　errors　are　further　compensated　by　periodic　modulation　for　better　robustness.　Furthermore,　resistance　to　random　noise　and　decoherence　of　the　protocol　is　also　shown　with　numerical　simulations.　Therefore,　the　protocol　may　provide　useful　perspectives　for　the　generation　of　logical　qubit　entanglement　in　spin　systems.