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During the past few years, many non-linear and/or adaptive control algorithms have been developed for industrial processes. Many have been rather complex schemes either requiring or specifically developed for an on line digital computer. As an alternative to such systems, at least on low order plants, the development of a near time optimal, adaptive control algorithm is proposed. This rule must encompass a significantly large group of the systems to be encountered and yet be simple enough for hardware implementation as a single loop controller. The author's attention is confined primarily to systems whose transfer functions may be approximated by K/S2+AS+B, and whose inputs (setpoints) and disturbances are essentially step functions. System parameter variations are considered slow relative to the frequency of disturbance Inputs or set point changes. The desired, or optimal, closed loop response for those systems is assumed to be the fastest possible response to a step input, with no overshoot. This time optimal deadbeat response is unique for a system with given dynamics and fixed accelerating and braking power sources. An algorithm is developed which provides total response time within a few percent of the time optimal deadbeat response on any system within the general classification. Additionally, the algorithm is adaptive and need not be tuned or adjusted in any way at startup or to compensate for system age or drift.