The notions of basic controllability and basic control are defined. A quadratic optimal control of the linearized viscous Moore-Greitzer equation is presented, and it is confirmed that stall is uncontrollable in this model. A basic control is constructed for the nonlinear viscous Moore-Greitzer equation which can control both surge and stall. Some extensions of this construction are discussed. Numerical simulations of the basic control are presented, and its performance is compared to the performance of a backstepping control constructed by Banaszuk, Hauksson, and Mezic [SIAM J. Control Optim., 37 (1999), pp. 1503-1537]. It is shown that the viscous Moore-Greizer equation with throttle control is not basically controllable, but under certain conditions, adding air injection control will make the equation basically controllable.