For the purpose of researching the displacement control system of heave compensation for offshore drilling platform, a set of crane type active and passive combined heave compensation device are designed on the basis of the similarity principle. As it known that platform heaving will be caused by the wind, sea wave and ocean current when conducting the drilling operations on the offshore drilling platform, which then will disturb the drilling operation. Therefore, the compensation device must be adopted to keep the vertical relative motion between the drill string system and the drilling platform to zero during the operation. Meanwhile, to improve the real-time performance of the heave compensation, the control system is optimized by establishing the simulation model of the active-passive combined crane, and LS-SVM(Least Squares Support Vector Machine) is improved by the artificial immune algorithm to predict the motion trend of offshore platforms. Eventually, in order to acquire the best control scheme, the Proportion Integration Differentiation (PID), fuzzy PID, BP neural network PID control method are utilized to carry out the simulation analysis, and the BP neural network PID control is found to be the optimum. Experiments showed that after using the BP neural network PID control algorithm, the displacement compensation rate of hook for active-passive combined crane device is more than 90%, the performance of the heave compensation is better, and the control is in time. INDEX TERMS Heave compensation, least squares support vector machine, BP neural network, PID control. FIGURE 1. Schematic diagram of crane type active-passive combined heave compensation device.