ESA Document - Emits - ESA

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4.4.5.4 Control laws generation
HMM
Assessment Study
Report: CDF-20(A)
February 2004
page 351 of 422
For the control laws generation a trade-off has been made between two possible alternatives:
Non-Linear Dynamic Inversion and Model-Based Predictive Control.
Non-Linear Dynamic Inversion (NLDI) control techniques uses a model of the plant and the
system dynamics under control. In case of a nonlinear plant, this technique uses a two-controller
level scheme design: a feedback component to linearize the dynamics and a performance
enhancement component of the resulting linear system.
NLDI control technique computes a model of the dynamics of the vehicle during its flight. Then,
it inverts the model to cancel all expected dynamics, and finally it inserts the desired vehicle
response to the resulting plant dynamics.
Model Based Predictive Control (MBPC) involves four control elements that use a linearized
model of the plant under control around a set of well pre-defined trimmed points.
The elements are as follows: a process model (a linearized system model obtained
experimentally off-line), a predictor equation (a forward algorithm which will run for several
steps to predict the behavior of the plant), a known future reference trajectory (previously
obtained by other means and off-line), and a cost function (quadratic cost future process output
error and controls).
For the NLDI solution the controller is able to handle smoothly non-linearities, coupled
aerodynamics effects and other uncertainties like Earth atmospheric and gravity disturbances. By
having a broad model of the plant, NLDI can cover the full flight envelope, eliminating pointper-point
design gain-scheduling. In addition, NLDI can handle a variety of vehicle plants when
design evolves or updates.
On the other hand, for the MBPC solution the controller is able to minimise the number of
constraints when calculating the optimal trajectory and improve the failure forecasting function
in the FDIR (fault detection identification and recovery) subsystem. Assuming a linearized
model of the plant for a pre-defined interval of the flight, the predictor equation is based on the
linearized equations of motion around this steady state flight condition.
The NLDI solution requires an acurate model of the non-linear plan (masses, moments of
inertia,…), and good aerodynamic data bases for all Mach number ranges (extensive wind tunnel
campaigns).
The MBPC solution requires a plant linearization on a wide rage of set points along the nominal
trajectory, and on-line optimisation problem to be solved on-board inside a dedicated processor.
The cost function for the quadratic optimal problem is based on a single criteria (minimum
integral of the heat flux).
The final selection is done for the Non-Linear Dynamic Inversion (NLDI) shown in Figure 4-94.