© ApICS ® LLC 2000

This study describes the first principal equations used to prescribe a simulation of a "Modular, Autonomous Heavy Ordnance Handling Systems". The study was commisioned by Orbital Research INC (OH). Sets of results that reflect the expected system performance are provided. Included is a brief description of the simulation sub-systems. The simulation description is meant to provide the user with the information required to perform "what-if" scenarios using the simulation.

The scope of this document is limited to describing the first principal equations describing the system, and to providing an overview of the simulation and the control structure sub-systems.

Sets of results that provide insight into the expected behavior of the system with varying system plant and controller parameters are included.

For each presented result, a set of plots including, Handler Position error [cm], Speeds v₀, v₁, v₂, [m/s], K1, K2, Damper Forces [N] F1, F2, Motor Forces [N] (see Figure 1.) are reported. The investigations include: the effect of damper stiffness, the effect of tuning, the effect of a height disturbance, and the effect of wave motion, on the dynamics of the positioning system tracking response.

The study concludes with some pertinent observations, and conclusions/recommendations.

OBSERVATIONS

The use of a linear motor, and a drive that is capable of obtaining 40 – 50 [r/s] bandwidth on the speed loop, and 20 – 30 [r/s] bandwidth on the position regulators, along with speed and momentum compensation feed-forward signals, will provide adequate positioning performance in the positioning loops, over the range of modeled disturbances. One distinct advantage to using a linear motor is the removal of backlash from the drive train. Backlash and torsional wind-up are the factors that most typically limit speed loop bandwidths in large (over 50 [kg] reflected mass) systems.

The modeled stiction force disturbances, as a function of a change in rail separation distance, misalignment of upper and lower tracks, and a change in normal loading as a result of ocean wave motion, were probably more severe than can be expected in the physical application. Based on this observation I am fairly confident that the system should perform adequately in terms of positioning the carriages. The positioning of the handler, which is attached to the carriages by the carriage dampers, is a separate issue, and discussed below.

It should be noted that the effects of motion in the other two degrees of freedom (i.e. side-to-side, and torsional loading forces) and their effect on the stiction force in the rails have not been investigated. Overload conditions may occur in the drive under extreme conditions. In the one degree of freedom model, a total of 300 – 400 [N] of losses per motor were possible as a result of stiction forces with a +/- 1 [cm] deviation in height, a +/- 21^o angular shift in the translational direction, and a misalignment of 1^o between the railings. If these stiction force estimations are correct, and given that the motors to be used are rated at 660 [N], not much headroom is left to accelerate the mass, and compensate for other stiction forces, in a high duty-cycle operational mode. Based on these observations, overloading may prove problematic when the system is implemented on board a ship. Again, this will depend on the amount of stiction in the system under expected ocean-going operating conditions.

The simulations performed to demonstrate the effect of wave motion on the handler momentum showed that the error in the handler position is a function of the ship angle from horizontal. At 20^o - 25^o (worst-case) the deviation with a 100 [N/mm] spring constant was approximately 4 [mm]. This error is directly proportional to the stiffness of the dampers. If dampers with 1000 [N/mm] spring constants were used, the deviation would only be 0.4 [mm]. Depending on the alignment requirements for both the grabber and the mechanism that loads the projectile into the firing chamber, the stiffness of the damper used may have to be re-evaluated based on the expected worst-case ocean going conditions. At the time of this writing, no information was made available with respect to the physical characteristics of the dampers.

Another consideration that must be made with respect to the dampers, is the ability of the dampers to absorb a load shock from a near hit. They cannot be excessively stiff, as this will negate their load shock absorption capabilities. These two conflicting requirements will involve some trade-offs in the choice of the stiffness of the dampers and the expected alignment error in heavy seas. The alignment requirements for the handler should be the starting point for making the trade-off decisions.

Variation in system natural frequencies due to variation in the damper spring constant should not be problematic. Closed loop stability issues as a result of system natural frequency deviations are usually not problematic in positioning systems where the position feedback is taken from a stiff member of the system (i.e. the rails). This appears to be especially true in this application.

Another observation from the simulation that directly affects the alignment of the handler is the effect of the height differential Dh on the positioning error of the handler. It is clear that the combination of both a variation in stiction forces and damper spring constant due to this phenomena will impact the ability of the handler to remain aligned during ocean going operations. Based on these observations, the need for some latitude on the docking mechanism is evident.

The tuning of the two speed and position regulators should be as symmetric as possible. It was found through simulation that the two drive systems tend to "fight" each other when the tuning is not symmetric. Several simulations that were performed using a slaved force reference resulted in a larger deviation in the upper and lower track alignment than was observed with a two-regulator system, although it was not significantly worse. The application may reveal that unmodeled dynamics and non-linear loading factors in the physical implementation will produce a lower misalignment with the slaved regulator structure than with the parallel regulator structure. This should be investigated more closely during the system start-up.

The scope of this study does not include sequencing issues, however it should be noted that the safety issues discussed at the meeting on March 22^nd need to be addressed, before the unit is tested.

• The set-up of the drives should be configured for both a slaved, and a parallel regulator configuration. Both configurations should be tested during system start-up.
• The speed loops should be step tested with load attached, for a 40 – 50 [r/s] bandwidth (time to peak of approx. 60 [msec]). Care should be taken to ensure that no saturation occurs in the loops when the step test is performed.
• The position loops should be step tested for a response of 20 – 30 [r/s] bandwidth (time to peak of approx. 120 [msec]). Care should be taken to ensure that no saturation occurs in the loops when the step test is performed.
• The feed-forward speed, and momentum compensation signals should be verified to be scaled correctly by running the system open speed, and position loop, and checking the response with only the feed-forward signals active (It may be that the drive configuration does not permit this)
• Adequate softening of the references (at least 50% "s") should be used to ensure that stiff torque steps do not excite natural frequencies in the structure.
• The sizing of the dampers w.r.t. their force/deflection characteristics should be carefully investigated. The handler alignment errors that result from working the system while experiencing worst case operating conditions should not affect its ability to perform projectile loading and unloading tasks.
• The docking mechanism should be assessed to verify that it satisfies the need for latitude during operation in an environment that includes the disturbances modeled in this study.