The reduction of drag force and suppression of vortex shedding on a circular cylinder in electrically poorly-conducting water can be realized by utilizing the Lorentz forces. In order to control the cylinder wake effectively, three kinds of control approach, i.e. open-loop, closed-loop and optimal control methods, are proposed and discussed in the present paper. Constant Lorentz forces are used in the open-loop control process, and Lorentz forces are varied to target the zero total drag or the zero pressure drag coefficients during the control process in two closed-loop control procedures. The purpose of optimal flow control is to determine controls that effectively tailor the flow, and the key element of an optimal flow control is the minimization of a cost functional that provides a quantitative measure of the objective. Numerical simulation of the theoretical models is performed in the exponential–polar coordinates system, from which it has been shown that the above three methods can suppress the vortex shedding successfully; moreover, during the control process, the optimal control needs less energy than the closed-loop control method targeting a zero total drag or pressure drag coefficients.