I am modelling a 6DoF linear aircraft model. I have am studying a situation where aerodynamic coefficients vary w.r.t. time. As you konw, state space of aircraft model rely on aerodynamic coefficients. As an example, coefficients change with altitude.
Is it a true approach to change these aerodynamic coefficients of the linear model during the simulation?
Dear Ömer Abdo
A linear control system, with constant coefficients (matrices; A, B, C, and D),
X_dot=AX+BU,
Y=CX+DU,
is termed linear time-invariant (LTI) control system.
If the coefficients are time-varying; A=A(t), B=B(t), C=C(t), D=D(t), then it is called linear time-varying (LTV) control system.
If you want to only simulate the dynamics of the aircraft without control inputs, it is acceptable to consider the time-varying coefficients and use Matlab ODE solver to simulate the dynamic system as X_dot=A(t).X.
But be warned that, if the matrices are time-varying, the control system would be much difficult to be investigated, as it is one of the topics in modern research on adaptive control.
I have not seen this situation yet. But, if the coefficients (A, B, C, and D) vary with time, we can use the nonlinear controller, for example input-output linearization control, to transform into linear model and then we apply PD controller. It is my opinions.
Coefficient matrices consist of state or Jacobean of output with change in state and the only way that this change is when you have a drastic change in the platform geometric parameters. This is possible in case of battle damage or for platform which involves configuration changes during flight.