Backstepping Variable Structure Control with L2 Gain for Nonlinear Torpedo Depth System

The nonlinear torpedo model is converted into the combination of input-output and zero dynamic. The input-output dynamic is established using the torpedo depth, climbing rate and attitude angular velocity as the state variables, with rudder control input. The other is stable zero dynamic, including attitude angular and velocity. Considering attitude angular velocity as the virtual controller of torpedo climbing rate, we present a backstepping robust L2 gain control strategy. Variable structure control term is used to eliminate uncertainties in input parameters. In simulation, the torpedo depth can be controlled well in the conditions of uncertainties and various initial states, and other state variables in torpedo model are stabilized.