Nonlinear Robust Control Design for a High-speed Supercavitating Vehicle

Open Access
Author:
Mao, Xiaofeng
Graduate Program:
Mechanical Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
October 29, 2010
Committee Members:
  • Qian Wang, Dissertation Advisor
  • Qian Wang, Committee Chair
  • Joseph Francis Horn, Committee Member
  • Christopher Rahn, Committee Member
  • Alok Sinha, Committee Member
Keywords:
  • nonlinear system
  • robust control
  • supercavitating vehicle
  • LPV
Abstract:
Considerable skin friction drag on the hull limits the speed that traditional underwater vehicles are capable of achieving. However, it is possible to design a vehicle such that the front of it, the cavitator, can induce and maintain a single gaseous cavity, referred to as Supercavitation. The cavity can envelop most of the vehicle so that only the cavitator and the partial rear control fins are in contact with the water. And, such a design, can thereby dramatically reduce the skin friction drag acting on the vehicle. Vehicles with this feature are called High-Speed Supercavitating Vehicles (HSSVs) and can achieve high speeds of up to 300 m/s compared with 40 m/s of traditional vehicles in water. One of the biggest challenges for control designs comes from the nonlinearity in the modeling of the planing force, which forms during planing condition that occurs when the vehicle's tail penetrates the cavity. Though planing force can be used to counteract the force of gravity when there are no other actuators such as the cavitator and fins available, it could also cause limit cycle of the vehicle, that is, substantial oscillation of the vehicle can happen. In this dissertation, we consider the supercavitating vehicles that are equipped with cavitator and fins, and the objective of our control designs is to eliminate the undesirable planing force for the purpose of drag reduction, stabilize the vehicle and further achieve satisfactory tracking performance. Besides nonlinearity, another research challenge caused by the planing force comes from its strong memory effect because supercavitation involves complicated physics in the cavity-vehicle interaction. Yet, it is difficult to accurately model the hydrodynamic forces of the control surfaces (cavitator and fins) in supercavitation. Additionally, the planing force exhibits strong memory effect because the computation of the planing force depends on the cavity shape, which is a function of the vehicle’s motion history. In the past few years, many important advances have been made in the modeling and control designs for supercavitating vehicles. However, very few studies have explicitly addressed how to handle the uncertainties in the system parameters, the hydrodynamic coefficients, and the size of the time-delay. In this dissertation, the author focuses on handling these uncertainties by exploring advanced robust control design methodologies. This dissertation considers the pitch-plane motion control of a high-speed supercavitating vehicle. Control designs are based on two major nonlinear approaches: the sliding-model control and the Quasi-Linear-Parameter-Varying control (Quasi-LPV). The sliding-mode controller emphasizes robustness with respect to the uncertainties in the system parameters and the hydrodynamic coefficients. The proposed Quasi-LPV formulation of the nonlinear supercavitating vehicle and the resulting control provide performance optimization and also address the time delay due to the cavity-vehicle iteration. Simulations of different model-controller configurations provide insight into the robustness capabilities of the controllers. In order to better understand the benefits that accrue from including the planing force memory effect into the control design, two delay-dependent Quasi-LPV controllers are compared with a Quasi-LPV controller based on a simplified non-time-delay model. Insight is thereby gained especially by comparing pitch-angle tracking performance using constrained control inputs. Given that only a partial set of state variables are measurable, a high-gain observer is designed to estimate the state variable that is not directly available for feedback. The high-gain observer is selected because it is robust to uncertainties in modeling the nonlinear functions. In addition, each controller is also evaluated in terms of the impact of sensor measurement noise on closed-loop system performance.