SYSTEM TDENTIFICATION DEVELOPING AN APPR0 PR1ATE MOOEL OF A YWAMIC SYSTEM US(NG BSERVED DATA COMBINEO WITH: BASIC MECHANICS AND OYNAMICS PR1OR KNOWLEVGE oF RELATIONSKIPS BETWEEN SIGNALS INPUT/OUTPUT MOOELS

USuALLY WE NOT KNOw THE \ACTUAL SYSTE\ So How WE ESTABLISH IF OUR MODEL Is Goo0? VARIOUS TPES OF TESTS CAN BE PERFORMEO PREDICTION ANO SIMULATIONJ ERRORS FRERUENCY RESPONSE FIT >MAKE SVRE YOU USE O1FFERENT 4TA To

Analysis to date has assumed that the atmosphere is calm and fixed -Rarely true since we must contend with gusts and winds -Need to understand how these air motions impact our modeling of the aircraft. Must modify aircraft equations of motion since the aerodynamic forces and moments are functions of the relative motion between the aircraft and the atmosphere, and not of the inertial velocities

Altitude Controller In linearized form, we know from 1-5 that the change of altitude h can be written as the flight path angle times the velocity, so that

Aircraft Lateral dynamics Using a procedure similar to the longitudinal case, we can develop the equations of motion for the lateral dynamics

Recall from 6-2 that the derivative stability derivative terms zai, and Mi ended up on the lhs as modifications to the normal mass and Inertia terms displaced air is \entrained\and moves with the aircraf rounding These are the apparent mass effects- some of the sur Acceleration derivatives quantify this effect Significant for blimps, less so for aircraft e Main effect: rate of change of the normal velocity w causes a transient

Matrix Diagonalization Suppose a is diagonizable with independent eigenvectors use similarity transformations to diagonalize dynamics matrix

Note can develop good approximation of key aircraft motion(Phugoid) using simple balance between kinetic and potential energies. Consider an aircraft in steady, level flight with speed U and height ho. The motion is perturbed slightly so that

Static stability is all about the initial tendency of a body to return to its equilibrium state after being disturbed To have a statically stable equilibrium point, the vehicle must develop a restoring force/ moment to bring it back to the eq. condition Later on we will also deal with dynamic stability, which is concerned with the time history of the motion after the disturbance

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