I haven't tried dithering a PWM signal, but amplitude dithering was common with analog servo loops and simply consisted of adding a small (usually sinusoidal) signal to the servo valve control signal. The effectiveness depended on how the servo valve was constructed because that affected the response time of the valve to the dithering signal. The end result was a small oscillation of the servo valve flow, adjustable in amplitude to a level just sufficient to overcome stiction in the valve or stiction in the load cylinder (or whatever the hydraulics were moving) without an overall change in load position.
The approach that
@kellys_eye suggested, logically ANDing the PWM pulse train with a pseudo-random low-frequency pulse train (non-coherent with the PWM frequency) might work okay, but I would want to try it out on a breadboard with an oscilloscope to make some measurements before making a large-scale commitment. I do like working with hydraulics, but throwing around several tons of metal requires experience and patience if disaster is to be avoided.
On a side note: my first experience with hydraulic position control was the alt-az gimbaled turret mount for the M61A1 20mm Gatling Gun located in the tail of the B-52H heavy bomber in the 1960s. The gun was controlled by the AN/ASG-21 Defensive Fire Control System, which has since been removed, although both the G and H models of the B-52 are still operational and currently deployed.
This radar-controlled weapon system was a fascinating piece of electrical and mechanical power engineering by Emerson Electric in St. Louis, MO. The gun-turret gimbals were rotated with swash-plate hydraulic motors geared down to move the gimbals, each motor being roughly the size of a large human fist. The hydraulic power supply, mounted behind and below the gun, used a variable-angle swash-plate pump, driven by a 400 Hz three-phase electric motor, to provide a steady 3000 psig hydraulic pressure to the gimbal motors through Moog analog servo valves controlled by magnetic amplifiers. I had never heard of magnetic amplifiers until I encountered these. Essentially saturable-core transformers, with the saturation controlled by current through one control winding, said current being supplied by a pair of sub-miniature vacuum tubes, they were very reliable and virtually indestructible. Mag-amps were also used to control the 400 Hz servo motors driving the alt-az gimbals of the dual Ku-band radar antennas, as well as the gimbals of the control-line platform (see below).
During search mode, the antenna gimbals drove the radiated antenna beam in a raster pattern, controlled by micro-switches that actuated at left/right and up/down limit-stops from Teflon-coated cams. Even with a Teflon coating, wear was extreme from the constant and rapid raster-scan, so a stamped, thin, sheet-metal actuator was mounted on each micro-switch, interposed between the cam surface and the micro-switch button actuator. This sheet metal part sacrificially wore out, sooner rather than later, as the Teflon coating on the cams deteriorated. When it wore completely through, the antenna quit scanning. Replacing it was difficult in the field as it was nearly inaccessible and secured by two long screws through the body of the micro-switch. Getting the micro-switches re-aligned after replacing the actuator was even more difficult, but the alternative was to remove the entire antenna assembly on the flight-line and replace it, usually a considerably longer job. And we didn't have a lot of spare antenna assemblies tested and waiting on the shelf, so us "bag draggers" were "encouraged" to replace the actuators without removing the antenna assemblies... while working ten feet above ground in the open air on a B-5 stand with below-zero wind chill conditions. And three years later they asked me why I didn't want to re-enlist!
The same pump responded quickly to pressure changes caused by changes in hydraulic fluid-flow demand because it also powered a much larger hydraulic motor that turned the gun barrels when the gun was fired. You wouldn't want to break lock on a target you were tracking just because the gun barrels started spewing out several hundred rounds per second. (Some who have been there and done that have said it sounds like God farting when GAU8 "Vengence" 30mm Gatling Gun, the M61A1's big brother, is fired from an A-10 "Warthog" fighter/bomber. The A-10 was literally designed around this gun.
Anyway, back to the B-52H... the gun turret motion was slaved to the motion of a three-axis device called a control-line platform or CLP. The purpose of the CLP was to remove the effects of roll, pitch, and yaw motions of the B-52H aircraft, which presumably would be undergoing some pretty fantastic pilot maneuvers if it were necessary to fire the gun during a combat mission. These maneuvers mainly consisted of rapid roller coaster-like changes in altitude and lateral position, called jinxing, and are rarely seen because they put humongous stress on the aircraft. However, because of the size of the B-52, there is little alternative for survival against an attack by fighter-launched missiles or cannon fire from the rear.
The CLP consisted of two nested gimbals for pitch and roll and an outer gimbal for yaw motions. Mounted to the roll gimbal were three mutually perpendicular precision rate-gyroscopes that measured the rate of change of gimbal motion with respect to the rotation axis of each gyro. During normal flight, the gimbals were oriented with the yaw, pitch, and roll axes of the airplane and the gyros were caged so as not to respond to aircraft yaw, pitch, and roll motions. Once radar target tracking started, the CLP was initially aligned with the tracking radar antenna beam and the gyros were un-caged to allow the fire control problem to be solved by the ballistic computer or BC.
The BC was an electro-mechanical marvel consisting of servo motors, resolvers, and multi-gang potentiometers, all connected with precision anti-backlash gears and placed inside a pressurized cylindrical metal case with external forced-air refrigerated cooling of the heatsinks inside the case. The BC took analog inputs from the radar system representing range, azimuth, and altitude and calculated where to point the Gatling Gun based on a myriad of environmental inputs such as pressure altitude, pitch attitude of the B-52, indicated air speed, the type of ammunition loaded, and (for all I knew about it) maybe the phase of the moon. The end result, all calculated continuously and in real time, was an x-y or azimuth-elevation positioning command to the CLP.
This was also my first encounter with discrete circuits that I later identified as operational amplifiers, although the Air Force and Emerson used a different descriptor. By any name you choose to call them, they were op-amps and they did amazing things inside the BC... well amazing to a twenty year old airman still wet behind the ears and fresh out of tech school. The experience later came in handy after my enlistment was up and I had talked my way into a technician job at UDRI, one month after separating from the Air Force.
One of my first tasks there was to help revive a huge hydraulically-operated dynamic fatigue-testing machine, whose California contractor went bankrupt trying to get it to work. It took us almost a year of effort, but eventually it did work and it met the original design specs. We had to replace the original motor-oil hydraulic system with a real mil-spec 3000 psig hydraulic system, and replace the home-made voice-coil-driven servo valve with a real Moog proportional-flow servo valve. It took quite a bit of hubris to believe a small machine shop could duplicate the performance of a Moog, or that ordinary motor oil was a suitable substitute for high-performance hydraulic fluid. The test stand was capable of exerting over 200,000 Lbf static load, and ±100,000 Lbf dynamic load at 60 Hz. Total ram displacement was limited by the hydraulic cylinder to about twenty-four inches, but the test coupons were quite stiff and only required a few inches of displacement for slow fatigue tests, less for high-frequency (up to 60 Hz) fatigue tests.
The gun turret was freed from its stowed position (usually pointed dead aft) and moved to align its azimuth and elevation axes parallel with the azimuth and elevation axes of the CLP. The CLP roll axis maintained its fixed orientation in space, moving with roll motions of the B-52, but it's actual position was just another input to the ballistic computer that continued to calculate the predicted projectile trajectory. Presumably the guns could accurately fire even if the B-52 "stood on its wing" in flight. AFAIK this was never tested on a real aircraft, and probably not tested in the field either. The system was tested with towed targets and one (probably apocryphal) story alleged that the fire control radar "locked on" to the turnbuckle connecting the target tow cable with a similar cable affixed to the aircraft. According to the story, the gun shot the turnbuckle off of the tow cable.
From a practical point of view, dithering the
amplitude of a DC control signal should be similar to dithering the
duty cycle of a PWM signal. In both cases, the
effective amplitude of the control signal is modulated or dithered.
