Optimum performance of a control system in terms of its time domain response can be achieved by the use of a bang-bang controller. The binary nature of the control signal together with the inherent complexity of a controller designed to achieve optimum bang-bang control high-order systems, immediately suggests the use of an on-line digital computer. Previous methods of attempting bang-bang control using an line digital computer have encountered two major difficulties, namely excessively long computation time and excessive ripple at the output to sampling. In such methods the amount of computation increases enormously as the order of the process to be controlled increases. This paper describes a new method which bypasses both of these major difficulties. The problem of long computation time is solved by trading computation time for computer storage. The information required for determination of switching times is determined once and for all at leisure an off-line calculation. The information is then permanently retained the store of the on-line computer. The problem of output ripple is solved by means of a dual-mode system. For large state errors the bang-bang algorithm is employed whilst for suitably small-state errors the computer changes the mode of control to a pseudo-linear mode in which process receives an input signal which is still binary in form but which pulse-duration modulated in such a way that the average value of the signal is that which it would receive from a tightly compensated linear controller.The paper includes details of tests of the new method applied to a third-order type-0 process. These are a series of step-response tests on firstly a purely digital simulation and secondly a real-time hybrid simulation in which a digital computer is used on-line to bang-bang control a process simulated on an analogue computer. The results of these tests are compared with those in which the same process is controlled by means a practical three-term controller. The comparison indicates the superiority of the new system.