Abstract: As a typical non-minimal phase (NMP) system, the hydropower turbine could hardly keep up with varying loading commands in the first place to contribute its positive part for grid-plant coordination; while on the contrary, the undershoot caused by NMP leads to amercement on a frequent basis. Advanced control strategies introduced with proved functionalities by simulation have their difficulties in carrying out on-site with reasonable cost of deployment, which lights up a much more easier way of analytic models for online control. Simplified as rigid pipe with straight conduit and penstock, a mathematical model for a three-moment definition during the course of load undershoot, includes power inflection moment, power and its integral zero-crossover moment, is proposed and deduced in the analytic way. In light of the analytic expression of these time scales, we can assess their influence on the overall load changing process for a given water starting time and guide vane moving rate, which paves the way of getting optimal control trajectory with minimal undershoot and later overshoot. Polyline consisting of different optimal inflected straight lines is then proposed. Comparison with straight line control, which is the exception of polyline, as well as inner module control tuned PID control, shows the validity and advantage of polylinear positioning law control, and encourages the site application of this approach.