Design of autopilot for BTT UUV based on H∞ Control theory

Dynamic Cross-Coupling of BTT UUV
β ωy
For the convenient analysis and design of UUV autopilot, we usually do the following simplification and suppose to the dynamic model of projects: the neglect of the influence of negative buoyancy; the suppose of symmetry of external form to vertical plane xoy and horizontal plane xoz ; the suppose of propeller thrust along the vertical axis; the suppose of hydrodynamic parameter meet linear assume; the amount of inertia product J xy , J yx , J xz , J zx , J yz , J zy is small and can be neglected; The attack angle α and the sideslip angle β are small; the weight, moment of inertia and velocity shall all be seemed to be constants. On the basis above, we can figure out the mathematics model of UUV three channels as follows [7]: The roll channel: & 0 1 ϕ ω ωx & x = 0 kω x & δ d 0 0 0 ϕ 0 δd kω ωx + 0 δ dc . x δ 1 τ − 1 τ δd d δd
Design of autopilot for BTT UUV based on H∞ Control theory
ZHANG Yi-chao and ZHOU Xu-chang
Department of Weaponry Engineering Naval University of Engineering Wuhan, China e-mail: 57542702@
0
ωω
δe α e e ′α ′δ ′δ kα kn − kα kn − kn τ δe n y y y y δe α δe α ′y k n ′y kωz − kωz kn ω z δ −1 τ δ e e
It can assure that Fl ( P , K ) ∞ < γ , positive definite matrix P meets the following algebraic Riccati inequality: AT P + PA + C T C + P ( B1 B1T γ 2 −
Abstract—A novel robust control scheme using H∞ theory is proposed for three-channel coupling bank-to-turn (BTT) unmanned underwater vehicles (UUV) autopilot. Considering the coupling among the pitch, the yaw and the roll channels as bounded uncertain disturbance, as a result there is no coupling in the UUV model in the form of H∞ standard state function, and the pitch, the yaw and the roll channels are designed independently. The six-DOF simulation results show that the proposed design method is simple and feasible, and the designed autopilot is efficient for the BTT UUV, because it can restrain the disturbances effectively. Keywords- UUV; BTT ; H∞ control
T B2 ( D T D) B2 )P < 0
′α kα x y kn k ′δ e τ y ω β ny δe x ωω kωzx y + 0 δ ec ω xω y 0 1 τ δe
(7)
(2)
Since ε is a positive constant, the following equality is obviously true: AT P + PA + C T C + P ( B1 B1T γ 2 −
δe α ωz ωx
δd
I. INTRODUCTION It has long been understood that bank-to-turn (BTT) controlled missiles offer increased maneuverability over conventional roll stabilized, skid-to-turn (STT) controlled missiles[1,2]. However, it has not yet been given enough focus in the BTT controlled unmanned underwater vehicles (UUV) and the indifference delayed the development of BTT UUV control system[3-5]. Upon receiving a guidance command, fast response is achieved by a combined roll-pitch maneuver with the roll control system rapidly rotating the missile’s maximum lifting orientation into the desired maneuver direction and the pitch control system simultaneously developing the required magnitude of acceleration in the maximum lift orientation. Yaw control system also reduces lateral accelerations to satisfy the small sideslip constraints, so that the induced moment is minor and the stability and maneuverability is excellent[6,7]. To execute such BTT autopilot strategy, the UUV must have the capability to rapidly change the orientation of acceleration by a considerably large roll rate. However, the attendant high rolling rates produces some problems, and introduces unwanted, nonlinear, strong cross-coupling among the pitch-yaw-roll channels, this makes the UUV control system becomes a complex multi-variables plant. In this paper, a new robust approach based on H ∞ theory was applied to the control of a BTT autopilot system. The dynamic model of BTT UUV was taken from [7] and coupling factor was known as definite bounded disturbances.
T B2 ( D T D) B2 )P + ε I = 0
The yaw channel
β &z kβ n ω & β ′β y = k ω y k nz & δ r 0 ω xα kβ ′β kn ωxα z + kω y 0 δr β r ′zβ − kβ ′δ ′zδr τ δr n kβ kn kn − kn z z ω δr δr β β ω y ′ ′ kωyy kω − k k k nz ω y nz y 0 −1 τ δ r δr ωxωz r ′zβ ′δ kn τ δr kβ kn z ω α x ω x ωz kω y + 0 δ rc ωxωz 1 τ δr 0
(8)
′zβ kβ y kn
ω
(3)
The relative coefficients were taken from [7]. III. H∞ SUBOPTIMAL STATE FEEDBACK CONTROL LAW