Abstract
This paper presents the mathematical modeling, guidance and robust control synthesis of a highly maneuverable submersible vehicle (or underwater vehicle) when performing a specific mission at shallow submergence conditions. First, the vertical plane motions (heave and pitch) of the vehicle are modeled by a set of maneuvering equations. After model simplification, a state-space model is compactly obtained. Then a state-feedback controller is proposed for the accurate depth-keeping and pitch motion controls of the vehicle. The control actions to the generalized plant can be provided by the mixedH 2/H ∞ optimal synthesis as well as closed-loop pole constraint with LMIs. The feasibility of the guidance and control approach is verified with direct numerical simulations. The proposed approach ensures reasonable depth-keeping and minimal pitch motions, even under a given uncertainty condition.
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Abbreviations
- I n 0 n×m :
-
n×n identity matrix, n×m null matrix
- R + :
-
set of positive real numbers in [0, ∞] with real fieldR
- A, B :
-
system matrix, (control or disturbance) input matrix
- C, D :
-
output matrix, (control or disturbance) input matrix
- \(J_{\bar y} \) :
-
pitch moment of inertia about\(\bar y - body\) axis
- U :
-
surge rate (forward speed) along with the axis\(\bar x\)
- ω:
-
heave rate (vertical speed) along with the axis\(\bar z\)
- θ,q :
-
pitch angle, pitch angular velocity
- y :
-
measured output vector
- \((\bar x_B ,\bar z_B )\) :
-
coordinates of the center of buoyancy in the body frame
- \((\bar x_G ,\bar z_G )\) :
-
coordinates of the c. g. in the body frame
- m v ,W B ,W W :
-
vehicle mass, buoyancy, weight
- ρ:
-
fluid density
- Z ∞,Z 2 :
-
vectors of performance outputs of interest
- A>0(A<0):
-
positive-definite (negative-definite) matrix
-
: -
state-space realization of the transfer matrixC(s(I−A) −1 B=D
- \(\bar \omega \) :
-
angular frequency
- \(\left\| w \right\|_2 = (\int_0^\infty {w^T wdt} )^{1/2}< \infty \) :
-
theL 2 (energy) norm of the vector of signalsw (t)
- \(\left\| {A(s)} \right\|_\infty = \mathop {\sup }\limits_{0< \varpi< \infty } \bar \sigma [A(j\bar \omega )]\) :
-
H∞ norm of the stable transfer function matrixA (s)
- \(\left\| {A(s)} \right\|_2 = \{ (1/2 \pi ) \int_{ - \infty }^\infty {{\rm T}race} [A^ * (j\bar \omega ) A (j\bar \omega ) d\bar \omega ]\} ^{1/2} \) :
-
H 2 norm of the matrixA(s)
- \(\sigma (A)\) :
-
largest (or maximum) singular value ofA
- \((\tilde \circ )\) :
-
normalized version of variable (o)
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You, SS., Chai, YH. Diving autopilot design for underwater vehicles using multi-objective control synthesis. KSME International Journal 12, 1116–1125 (1998). https://doi.org/10.1007/BF02942585
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DOI: https://doi.org/10.1007/BF02942585