Dynamic inversion control works by mapping the pilot commands to desired accelerations and not directly to control surfaces. Dynamic inversion control uses a plant model that is in the standard state-space form.
$$\begin{matrix}
\dot{x}=Ax+Bu \\
c_v=Cx
\end{matrix}$$
where \(x\) are the states, \(u\) are the effectors, \(c_v\) are the control variables, \(A\) is the matrix for the aircraft dynamics, \(B\) is the matrix for the control effectiveness, and \(C\) is the control variable matrix. It can be used for SISO and MIMO systems as long as the control matrix is invertible. The assumption that DI makes is that the plant dynamics can be perfectly modeled. The input to the dynamic inversion equations are the desired system dynamics.
The dynamic inversion control law is implemented with the following equations
$$\begin{matrix}
\dot{c_{vdes}}=\dot{Cx}=CAx+CBu \\
u=(CB)^{-1}(\dot{C_{vdes}}-CAx)
\end{matrix}$$
Dynamic Inversion is not limited to first-order inversions, it can do higher-order inversions as well. If the matrix is noninvertable, then the pseudoinverse can be used instead.
In other models ,the inverse dynamics are not dependent on the control variable matrix C.
The eigenvalues of the closed DI loops are used for model selection. If there is a perfect match, then \(A_i=A_j\) ,\(B_i=B_j\), and \(C_i=C_j\). The poles and zeros of this system cancel out and we get a pure integrator. If the poles and zeros don’t cancel and create a fast instability, the outer control loops might not be able to compensate for it.
When you combine the feed forward control and the stabilizing mode, the transfer functions cancel out to 1.
[[Dynamic Inversion Roll Regulator]] – example system
[[Nonlinear Dynamic Inversion]]
[[Dynamic Inversion Controller Optimal Frequency Response]]
MFA Control Law – uses dynamic inversion
Sources
- [1] D. W. Nixon and L.-M. Aeronautics, “Flight Control Law Development for the F-35 Joint Strike Fighter”.
- [2] RVFCSdesignDynamicInversion
- [3] P. Dr. Hamel, “Advances in Aerodynamic Modeling for Flight Simulation and Control Design,” Jan. 2001.
- [4] _20100033140
Backlinks
Dynamic Inversion Control Law Structure
[[Honeywell Multi-Application Control (MACH)]]
[[MIMO]]
State-Space Model