The MFA Control Law for VISTA is a dynamic inversion-based algorithm. The DI algorithm with desired characteristics creates a numerical integrator. It performs 5DOF integration in pitch, roll, yaw, fore heave, and aft heave. It converts the state acceleration commands into vehicle rate commands. Some of the control laws were implemented in Simulink, or as a Matlab s-funtion. The Research plant models are either in transfer function or state-space form. They can have a stitched-model format with nonlinear kinematics, and time-varying aerodynamics. The controls are allocated in the cascading general inverse method.
The X-62 VISTA used the canonical state-space form of[^2]
$$\dot{x}(t)=Ax(t)+Bu(t)$$
$$y(t)=Cx(t)$$
The block diagram for the integrator creation is[^2]
The DI controller equations are shown below. The desired dynamic are \(cv\)[^2]
$$\dot{cv}(t)=\dot{y}(t)$$
The dynamic inversion feedback then becomes[^2]
$$\dot{cv}(t)=C[Ax(t)+Bu(t)]$$
$$u(t)=[CB]^{-1}[\dot{cv}(t)-CAx(t)]$$
The feedback algorithm is[^2]
$$u_{cmd(t)}=[C_mB_m]^{-1}[\dot{cv_{des}}(t)-C_mA_mx_{des}(t)]$$
Where \(u_{cmd}\) is the commanded control input, \(m\) is the modeled values, and \(\dot{cv}{des}\) are the desired dynamics, \(x{est}\) is the estimated state vector.[^2] This gives the final equation[^2]
$$\dot{cv}(t)=C[Ax(t)+B([C_mB_m]^{-1}[\dot{cv}{des}(t)C_mA_mx{est}(t)])]$$
Use S-function control laws:
[[General Atomics MQ-20 Avenger]]
XQ-58A Valkyrie
[[VCLAW]]
Use Simulink Laws:
[[UCLAW]]
[[HQ CLAW]]
[[Cascading General Inverse Method]]
Stitched Learjet-25D model– stitched model
MFA Testing – the integral for the MFA law is then tested
Sources
- M. C. Cotting, S. S. Stephens, J. Cole, J. Barricklow, and W. Gray, “X-62 VISTA Capabilities and Architecture,” in AIAA SCITECH 2023 Forum, in AIAA SciTech Forum. , American Institute of Aeronautics and Astronautics, 2023. doi: 10.2514/6.2023-1744.[^1]
- M. C. Cotting et al., “X-62 VISTA Simulation and Autonomy Flight Testing,” in AIAA SCITECH 2023 Forum, in AIAA SciTech Forum. , American Institute of Aeronautics and Astronautics, 2023. doi: 10.2514/6.2023-1928.[^2]
Backlinks
[[5DoF Simulations]
[[Dynamic Inversion Control Law Structure
Eurofighter Control Law Control Surface and Integration Location
[[Lockheed Martin]]
[[Simulink]]
[[Simulink S-Function]]
State-Space Estimators
[[State-Space Model]]
Stitched Learjet-25D model
[[Time-Varying Update Equations for Learjet-25D Model]]
Transfer function of an Integrator
[[Transfer Functions]]
[[X-62 VSS]]
XQ-58A Valkyrie