The paper considers the optimisation of pulse-position pulsewidth-modulated (PPPWM) control of a position servosystem. The optimisation is carried out via an equivalent PPPWM transformation of the linear optimal control law. The technique developed here is applicable to both tracking and regulator problems, and the equivalence assumes the existence of at least one pole at the origin for the plant transfer function, which is normally true for any position servosystems. The control signal is optimised with respect to the discrete quadratic performance index and a closed-loop analytical solution can be obtained. The solution for a second-order system is simple, as shown, and readily applicable to real-time sampled-data position servosystems.