Using classical Lie symmetry theory，boundary control for a class of parabolic distributed parameter systems has been studied，
and the control laws on open loop and closed loop have been designed to control the system reaching the fixed stationary state． By
means of infinitesimal generators and invariance condition，the analytic control conditions on open loop and closed loop are presented after
having the classical Lie symmetry of the system，which is expressed by infinitesimal generators． The control purpose can be satisfied
under the two types of control laws by setting system parameters，initial condition and control purpose ahead． Comparatively，from the
simulation，the convergence of output error under open loop control is slower than that under closed loop control，and however there are
overshoot phenomena nearby the intake under closed loop control． The result proposed in the paper can be applied for controlling a class
of temperature or concentration models with conduction and convention characteristics．