In this research work, the highly challenging problem of novel modelling and nonlinear control of steam dump system of Pressurized Water Reactor (PWR) type Nuclear Power Plant (NPP) is attempted. The Fractional Order Multi- Scheduling Parameters based Multi-Input Single- Output Linear Parameter Varying (FO-MSP-MISO-LPV) model of Steam Dump System (SDS) is estimated with uncertain dynamics under sudden load variation transients. MSP for uncertain dynamics of SDS in FO framework is the most challenging problem and attempted in a novel fashion for the first time in nuclear industry. Scheduling parameters are dynamic in nature that makes the control problem more challenging. The Model is estimated experimentally by least square method using innovative plant operational data of opening positions of different valves as input variables and steam pressure as an output variable and cold leg coolant temperature coefficient of reactivity, hot leg coolant temperature coefficient, steam flow rate and turbine power as dynamic scheduling parameters. A switching controller is designed to address variable conditions of steam pressure for the actuation of dump valves, relief valves and safety valves in SDS. A robust fractional order LPV switching H∞ (RFO-LPV-SWH∞) controllers are formulated and designed for FO-MSP-MISO-LPV model. The design of RFO-LPV-SWH∞ controllers is another significant contribution in switching mode with non-integer and LPV hybrid framework. RFO-LPV-SWH∞ controllers are tested, simulated and validated against benchmark transients as laid down in Final Safety Analysis Report (FSAR) of PWR-type NPP. The input and output variables at first and second vertex of polytope are fast reference tracking under highly nonlinear uncertain dynamics of SDS. Closed loop simulation experiments are conducted and proved that the proposed closed framework is robust in performance under parametric uncertainty.