Aerospace Blockset

Modeling the Homing Guidance Loop

The complete homing guidance loop consists of these two subsystems:

• The Guidance Subsystem generates the normal acceleration demands that are passed to the autopilot.
• The Seeker/Tracker Subsystem returns measurements of the relative motion between the missile and the target.

The autopilot is now part of an inner loop within the overall homing guidance system. Consult Reference [4] for information on different types of guidance systems and on the analysis techniques that are used to quantify guidance loop performance:

Guidance Subsystem

Initially, the Guidance subsystem searches to locate the target's position and then generates demands during closed-loop tracking. A Stateflow model controls the transfer between the different modes of these operations. Stateflow is the ideal tool for rapidly defining all the operational modes, both during normal operation and during unusual situations:

Guidance Processor Statechart.   Mode switching is triggered by events generated in Simulink or in the Stateflow chart. The variable Mode is passed out to Simulink and is used to control the Simulink model's behavior and to determine the response of the Simulink model. For example, the Guidance Processor state chart, which is part of the Guidance subsystem, shows how the system reacts in response to either losing the target lock or failing to acquire the target's position during the target search.

During the target search, this Stateflow state chart controls the tracker directly by sending demands to the seeker gimbals (Sigma_d). Target acquisition is flagged by the tracker once the target lies within the beam width of the seeker (Acquire) and, after a short delay, closed loop guidance begins:

Proportional Navigation Guidance Measurements.   Once the seeker has acquired the target, a Proportional Navigation Guidance (PNG) law guides the missile until impact. This form of guidance law is the most basic, used in guided missiles since the 1950s, and can be applied to radar-, infrared-, or television-guided missiles. The navigation law requires measurements of the closing velocity between the missile and target, which for a radar-guided missile can be obtained with a Doppler tracking device, and an estimate for the rate of change of the inertial sight line angle:

Proportional Navigation Guidance Measurements

The diagram symbols are defined as follows.

	Navigation gain (> 2)
Vc	Closing velocity
b	Body attitude
	Sight line rate
g	Gimbal angle
L	Look angle
d	Dish angle
az_dem = Vc	Demanded normal acceleration

Seeker/Tracker Subsystem

The Seeker/Tracker subsystem controls the seeker gimbals to keep the seeker dish aligned with the target and provides the guidance law with an estimate of the sight line rate:

Tracker and Sightline Rate Estimator.   The Tracker and Sightline Rate Estimator, the most elaborate subsystem of the Seeker/Tracker subsystem because of its complex error modeling, is shown below.

The subsystem contains a number of feedback loops, estimated parameters, and parasitic effects for the homing guidance. The tracker loop time constant tors is set to 0.05 second, a compromise between maximizing speed of response and keeping the noise transmission within acceptable levels. The stabilization loop compensates for body rotation rates, and the gain Ks, which is the loop crossover frequency, is set as high as possible subject to the limitations of the stabilizing rate gyro's bandwidth. The sight line rate estimate is a filtered value of the sum of the rate of change of the dish angle measured by the stabilizing rate gyro and an estimated value for the rate of change of the angular tracking error (e) measured by the receiver. In this demo, the bandwidth of the estimator filter is set to half that of the bandwidth of the autopilot:

Radome Aberration.   Radome aberration is also modeled by the Tracker and Sightline Rate Estimator subsystem.

Radome aberration is a parasitic feedback effect commonly modeled in radar-guided missile designs. It occurs because the shape of the protective covering over the seeker distorts the returning signal, and it gives a false reading of the look angle to the target. The amount of distortion is, in general, a nonlinear function of the current gimbal angle. But a commonly used approximation is to assume a linear relationship between the gimbal angle and the magnitude of the distortion. Often, other parasitic effects, such as sensitivity to normal acceleration in the rate gyros, are also modeled to test the robustness of the target tracker and estimator filters:

Modeling a Classical Three-Loop Autopilot

Simulating the Missile Guidance System