Adaptive control mechanism for uncertain systems with actuator dynamics
AssigneeUniversity of South Florida
InventorsBenjamin C. Gruenwald, Tansel Yucelen, Kadriye Merve Dogan, Jonathan A. Muse
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Abstract
The present disclosure describes an actuator system comprising an actuator unit that is configured to be positioned next to a structure; and an adaptive controller unit that is configured to receive a command input for the actuator unit and output an actuator command based on a reference model of a physical system that includes the actuator unit and the structure, wherein the actuator command does not alter trajectories of the reference model. In various embodiments, the uncertain dynamical system of the physical system is augmented with the actuator dynamics to provide improved stability.
Claims10
An actuator system for a vehicle, comprising:
- an actuator unit comprising an actuator positioned next to a structure, where the actuator unit receives and reacts to an actuator command for the actuator;
- and
- an adaptive controller comprising computing circuitry that, in response to a command input for the actuator, produces the actuator command based on a reference model of a vehicle that includes the actuator unit and the structure, wherein the computing circuitry outputs the actuator command to the actuator unit which reacts to the actuator command, wherein the reference model is given by:
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- where c(t) is the command input, Br[0nc×np, −Inc×nc]T, xr(t) is a reference state vector, r(t) is a reference actuator output,
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- Ap is a known system matrix, Bp is a known control input matrix, Ep is a selection matrix, Ŵ(t) is an estimate of an unknown weight matrix W, N=[Inp×np, 0np×nc], K is a gain matrix and M represents actuator bandwidth, 0m×nc, 0nc×np, 0np×nc, 0nc×nc, 0m×np are zero matrices, and Inc×nc, Inp×np are an identity matrices, and wherein the actuator command is given by:
- u(t)=−Kx(t)−T(t)Nx(t),
- where x(t) is a system state vector and Ŵ(t) satisfies:
- (t)=γProjm[(t),σ(⋅)PG],
- where γ is a learning rate, σ(⋅)=[Nx(t)exT(t), Nx(t)eT(t)], ex(t)x(t)−xr(t), e(t)(t)−r(t), P is a solution of a matrix inequality, G=[BT, 0m×m]T, and (t) is the actuator output.
A method for adaptive control of an actuator unit comprising:
- positioning the actuator unit comprising an actuator next to a physical structure of a vehicle;
- determining a reference model of the vehicle that includes the actuator unit, wherein the reference model depicts a closed-loop dynamical system performance of the vehicle, wherein the reference model is given by:
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- where c(t) is a command input, Br[0nc×np, −Inc×nc]T, xr(t) is a reference state vector, r(t) is a reference actuator output,
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- Ap is a known system matrix, Bp is a known control input matrix, Ep is a selection matrix, Ŵ(t) is an estimate of an unknown weight matrix W, N=[Inp×np, 0np×nc], K is a gain matrix and M represents actuator bandwidth, 0m×nc, 0nc×np, 0np×nc, 0nc×nc, 0m×np are zero matrices, and Inc×nc, Inp×np are an identity matrices;
- receiving, by controller circuitry, a command input for the actuator unit;
- and
- outputting, by the controller circuitry, an actuator command to the actuator unit which reacts to the actuator command, the actuator command based on the reference model of the vehicle, wherein the actuator command is given by:
- u(t)=−Kx(t)−T(t)Nx(t),
- where x(t) is a system state vector and Ŵ(t) satisfies:
- (t)=γProjm[(t),σ(⋅)PG],
- where γ is a learning rate, σ(⋅)=[Nx(t)exT(t), Nx(t)eT(t)], ex(t)x(t)−xr(t), e(t)(t)−r(t), P is a solution of a matrix inequality, G=[BT, 0m×m]T, and (t) is the actuator output.
Dependencies are inferred from the claim text.