We consider sampled-data relay control of semilinear diffusion PDEs. Several control signals, subject to unknown bounded disturbances, enter the system through shape functions. The only information required for calculating the control signal is the sign of a weighted average of the state. First, for a nonlinearity from an arbitrary sector, we derive LMI-based conditions that determine how many controllers one should use to ensure local convergence to a bounded set. For a fixed domain of initial conditions the size of a limit set is proportional to a sampling period. Then we propose a switching procedure for controllers' gains that ensures convergence from an arbitrary domain to the same limit set.