Rate estimation by mixing two independent rate signals

A method of providing an angular rate signal for attitude control in a mile flight control system by linearly mixing a derived rate signal generated from the measured attitude angle and a simulated rate signal generated from the measured nozzle angle. The derived rate is generated from the differentiation of missile attitude data and the simulated rate is generated by simulating the missile attitude dynamics based on the actual nozzle angle. The derived rate, which is filtered to remove the effects of quantization and noise is dominant at low frequencies. The simulated rate, which is filtered to block low frequencies, is dominant at higher frequencies.

BACKGROUND OF THE INVENTION 
This invention relates in general to missile directional control systems 
and, in particular, to a method of providing a rate of change of attitude 
signal to a missile directional control system. 
In the typical ballistic missile attitude control system, a signal related 
to the rate of change in the missile's attitude angle is required to 
implement the attitude control loop. Rate signals have in prior systems 
been obtained from a rate gyro or have been developed from the 
differentiation and filtering of resolver signals. 
Both of the prior techniques have inherent disadvantages in attitude 
control systems. Rate gyros do no provide the required reliability unless 
they are used redundantly. The differentiation of resolver signals places 
tight performance requirements on the resolvers. The use of digital 
techniques with the resolvers results in quantization of the rate data 
which increases the slew rate requirements of thrust vector control 
systems and reduces flight control stability margins. 
SUMMARY OF THE INVENTION 
It is therefore an object of the present invention to provide an angular 
rate signal for missile flight control systems without the foregoing 
disadvantages. 
Another object is to provide an angular rate signal without using a rate 
gyro package. 
Another object is to provide an angular rate signal in which gimble noise 
and digitally derived rate can be filtered without reducing vehicle 
stability margins. 
The present invention involves linearly mixing a derived rate signal with a 
simulated rate signal to obtain an overall rate signal. The mixing takes 
advantage of the characteristics of each to achieve a better overall rate 
signal than could be obtained from either signal individually. The derived 
rate signal is generated from the differentiation and filtering of the 
resolver attitude data. The simulated rate involves the integration and 
smoothing of the nozzle position data based on estimated vehicle control 
torques. The measured nozzle position data is input to a simulation of the 
vehicle attitude dynamics. The simulation then computes the missile rate 
based on the actual nozzle angle. In effect, the present invention uses 
integrated vehicle torque to provide high frequency rate estimates and the 
filtered attitude data to provide low frequency estimates. 
The rate estimation by mixing technique has the advantage that noise or 
gimble resolvers can be filtered without reducing vehicle stability 
margins. The performance of the mechanization can be analysed using linear 
analysis techniques. Additionally, the mixing technique provides 
attenuation of body bending modes without reducing the vehicle rigid body 
stability margins.

DESCRIPITION OF THE PREFERRED EMBODINENT 
Referring now to the drawings, FIG. 1 illustrates the missile flight 
parameters discussed in this description. The missile 10 has a direction 
of motion V that is inclined at an angle .theta. with respect to the 
vertical 12. The angle .theta. is the missile attitude angle and the rate 
of change of .theta. is the attitude rate .theta.. The missile 10 points 
at an angle .phi. with respect to the vertical 12 and has an angle of 
attack .alpha. with respect to the direction of motion. The thrust force F 
is applied at an angle .delta. with respect to the centerline 14 of the 
missile. The angle .delta. is the missile thrust angle or nozzle angle. 
FIG. 2 is a block diagram illustrating a control loop mechanization for 
controlling the missile attitude angle .theta. of a ballistic missile 
during the boost phase of flight. The present attitude angle .theta., 
which is obtained from guidance gimble data (or guidance resolvers), is 
applied as negative feedback to the commanded attitude angle .theta.c at 
16 and adjusted by a gain factor K.sub..theta. to provide an attitude 
error signal .theta..sub..epsilon.. An attitude rate signal .theta. 
adjusted by a gain factor K.sub.R, is subtracted from the attitude error 
signal .theta..sub..epsilon. at 18 to provide a resultant signal 
.theta..sub.R. The present invention relates to providing the attitude 
rate signal .theta.. 
The resultant signal .theta..sub.R is coupled to the thrust vector control 
system (TVC) represented by b1ock 20 which orients the rocket motor nozzle 
to provide a thrust angle .delta.. The attitude angle .theta. is then 
determined by the response of the missile to the thrust. The thrust at 
nozzle angle .delta. acts through moment coefficient M.delta., related to 
the torque on the vehicle per unit nozzle angle, and moment coefficient 
M.alpha., related to the torque on the vehicle per unit angle of attack 
.alpha., and transfer function 22 as shown to produce a missile attitude 
angle .theta.. 
The present invention is directed to an improved method of providing the 
attitude rate signal .theta.. As previously noted in the background 
section of the specification, in the prior art attitude control systems 
the attitude rate .theta. was provided by one of two methods. As 
illustrated in FIG. 3a, one method utilized a separate rate gyro 24 for 
directly measuring the attitude rate for input into the control loop. In 
the second method as illustrated in FIG. 3b, the attitude rate .theta. is 
digitally derived from the attitude angle .theta.. The resolver outputs of 
the attitude gimble system are converted to digital data in an 
analog-to-digital (A/D) converter 30 and the resulting digital data is 
differentiated in a sample and hold circuit 32 to provide quantized 
attitude rates. Because state of the art resolution in the 
analog-to-digital conversion of the attitude angle is limited to around 
0.03 degrees because of additive noise, a representative sampling rate of 
100 Hz results in a minimum measurable rate of 3 degrees per second. This 
digitally derived rate may be filtered to remove the effects of 
quantization and additive gimble noise. However, such filtering adds low 
frequency phase lag which seriously reduces the flight control system 
stability margin. 
FIG. 4 is a block diagram of the missile attitude control loop 
mechanization using the rate mixing technique of the present invention to 
provide the attitude rate signal .theta.. In the rate estimation by mixing 
technique, a total estimated rate signal .theta..sub.T is provided by 
linearly mixing either a derived rate or a gyro generated rate with a 
simulated rate generated by performing computations on the measured nozzle 
angle .delta.. 
As shown in FIG. 4, the derived rate .theta..sub.DR may be obtained from 
the measured attitude angle .theta. through an A/D converter 30 and a 
sample and hold circuit 32. The derived rate is then passed through a low 
pass filter 34 to remove the effects of quantization and additive gimble 
noise. 
Turning now to the generation of the simulated rate, this rate 
.theta..sub.sim is based on the fact that the missile's autopilot has 
knowledge of the control torque being applied to the missile through the 
effects of thrust and nozzle angle .delta.. This applied torque can then 
be divided by vehicle inertia and integrated once to yield an estimate of 
the resulting angular rate. 
Returning to FIG. 4, the measured nozzle angle .delta. is coupled to a 
computational means 36 which contains a simulation of the vehicle dynamics 
and computes a simulated attitude rate .theta..sub.sim. The simulated rate 
.theta..sub.sim is then passed through a band pass filter 38 which 
supplies compensating phase lead. The filtered and .theta..sub.DR and 
.theta..sub.sim are mixed at 40 to provide an overall rate signal 
.theta..sub.T. The overall rate signal .theta..sub.T is modified by gain 
factor K.sub.R and applied to the overall control loop at 18. 
FIG. 5a shows a first order mixing scheme for generating .theta..sub.T. The 
derived rate .theta..sub.DR is passed through a first order filter 34a 
while the simulated rate .theta..sub.sim is blocked at lower frequencies 
by filter 38a and reaches unity gain above the mixing frequency 
(.omega..sub.mixing =1/.tau.). It is noted that if .theta..sub.DR 
=.theta..sub.sim =.theta., the rate loop gain is unity at all frequencies. 
In general, the value of .tau. is selected to provide the best operation 
of the overall attitude control loop. Larger values of .tau. give best 
noise rejection and smoothing of the analog to digital quantization and 
also give more attenuation at the body bending frequencies (the 
attenuation of body bending frequencies will be discussed hereinafter in 
connection with FIGS. 9 and 10). However, larger values of .tau. result in 
higher nozzle angular defections due to wind shears and at second stage 
separations. The selection of .tau. will thus be a tradeoff to satisfy 
competing considerations. 
FIG. 5b shows a second order mixing scheme for generating .theta..sub.T. In 
this case, a numerator term of 2.tau.s (1+.tau./2 s) must be used to make 
the overall rate gain unity at all frequencies. 
Turning now to the computation of the simulated rate .theta..sub.sim. The 
apparent choice for the simulated rate transfer function is the actual 
transfer function between the missile attitude rate .theta. and the nozzle 
angle (.theta./.delta.=G.sub.I (s)). However, the actual transfer function 
of a ballistic missile has an unstable root which will produce an 
uncontrollable system. The actual transfer function is unstable at the low 
frequency end. This problem can be circumvented if a stable transfer 
function can be found which matches the real missile transfer function 
over the frequency range of interest. 
FIG. 6 shows the fraction of the total rate signal which comes from the 
simulated rate path for a first order mixing scheme. It can be seen that 
the contribution of the simulated rate path is relatively unimportant at 
low frequencies where the derived rate signal path is dominent and 
increases in importance as the frequency increases to eventually become 
the dominent rate path. Therefore the simulated rate transfer function 
only need closely match the ideal transfer function in such a manner to 
make the overa11 rale siginal .theta..sub.T satisfactory. 
Referring now to FIG. 7, curves 50 and 52 show the gain (absolute value) 
and phase, respectively, versus frequency for a simulated rate path 
employing an actual missile transfer function 
##EQU1## 
and a first order filter 
##EQU2## 
Curves 54 and 56 show the gain and phase, respectively, versus frequency 
in the simulated rate path employing a simulated transfer function 
##EQU3## 
where K.sub.1 =7.8 and K.sub.2 =3.14. It can be seen that this G.sub.sim 
(s) provides a good approximation at higher frequencies. Other choices for 
G.sub.sim (s) are possible. Stability analysis of the overall missile loop 
with K.sub.e and .tau..sub.e as parameters is necessary to obtain the best 
simulated rate transfer function. In actuality, M.alpha. and M.delta. 
change with altitude and missile velocity. Therefore, the parameters in 
the missile transfer function are time varying and based on a knowledge of 
M.alpha. and M.delta.. 
FIG. 8 shows overall loop gain and phase for the ideal case as solid lines 
and the combination of derived rate and simulated rate when the first 
order approximation (shown in FIG. 5a) is used as dashed lines. The gain 
and phase error in the total rate signal is less that 1 db and 8 deg phase 
over the complete frequency range and therefore the approximation selected 
produces the desired result of (1) a controllable mechanization and (2) a 
rate loop gain/phase which adequately matches the ideal transfer function. 
A significant attribute of simulated rate is the additional filtering it 
provides in the flexible body rate loop. The effect is present using 
either a rate gyro or derived rate as a source of the low frequency rate 
signal. The first order mixing technique results in placing a lag at the 
mixing frequency in the body bending rate loop thus increasing the 
attenuation at the body bending frequencies. 
FIG. 9 illustrates both rigid body and flexible body for a rate gyro 
mechanization. It is observed that the gain in the body bending loop is 
K.sub.R K.sub.BEND and the rigid body rate loop is 
##EQU4## 
FIG. 10(a) illustrates the same rate loops when simulated rate and mixing 
is used for the high frequency rate signal. 
Using G.sub.I (s) as the simulated rate transfer function, and after some 
block diagram manipulation, the mechanization of FIG. 10(a) is reduced to 
FIG. 10(b). It is noted that the rigid body rate loop gain is identical to 
the case of FIG. 9 where a rate gyro is used; however, the mixing filter 
now appears in the flexible body loop. This adds attenuation of the low 
frequency body bending effects. 
There is always considerable uncertainty in the body bending rate which 
lowers the predictable gain margin. The mixing technique allows much 
greater gain margin because body bending effects are not present in the 
high frequency (.theta..sub.sim) loop.