9.1.3 Feedback Control Technology

9.1.3.1 Feedback Control Practical inertial navigation began to evolve in the 1950s, using technologies that had evolved in the early twentieth century, or were coevolving throughout the mid-twentieth century. These technologies include classical control theory and feedback² control technology. Its mathematical underpinnings included analytic function theory, Laplace transforms and Fourier transforms, and its physical implementations were dominated by analog electronics and electromagnetic transducers.

Feedback Control Servomechanisms Servomechanisms are electronic and/or electromechanical devices for implementing feedback control. The term "servo" is often used as a noun (short for servomechanism), adjective (e.g., "servo control") and verb (meaning to control with a servomechanism).

²A concept discovered by Harold S. Black (1898-1983) in 1927 and applied to the operational amplifier [20]. According to his own account, the idea of negative feedback occurred to Black when he was commuting to his job at the West Street Laboratories of Western Electric in New York (later part of Bell Labs) on the Hudson River Ferry. He wrote it down on the only paper available to him (a copy of the New York Times), dated it and signed it, and had it witnessed and signed by a colleague when he arrived at work. His initial patent application was refused by the U.S. Patent Office on the grounds that it was a "perpetual motion" device.

Transducers These are devices which convert measurable physical quantities to electrical signals, and vice versa. Early servo transducers for INS included analog shaft angle encoders (angle to signal) and torquers (signal to torque) for gimbal bearings, and torquers for controlling the direction of angular momentum in momentum wheel gyroscopes.

9.1.3.2 Gimbal Control In the mid-1930s, Robert H. Goddard used momentum wheel gyroscopes for feedback attitude control of rockets, and gyros and accelerometers were used for missile guidance in Germany during World War II [8]. These technologies (along with many of their developers) were transferred to the United States and the Soviet Union immediately after the war [47, 215].

All feedback control loops are used to null something, usually the difference between some reference signal and a measured signal. Servos are used in gimbaled systems for controlling the gimbals to keep the gyro outputs at specified values (e.g., earthrate), which keeps the ISA in a specified orientation relative to navigation coordinates, independent of host vehicle dynamics.

9.1.3.3 Torque Feedback Gyroscopes These use a servo loop to apply just enough torque on the momentum wheel to keep the spin axis from moving relative to its enclosure, and use the applied torque (or the motor current required to generate it) as a measure of rotation rate. If the feedback torque is delivered in precisely repeatable pulses, then each pulse represents a fixed angular rotation δθ, and the pulse count in a fixed time interval Δt will be proportional to the net angle change Δθ over that time period (plus quantization error). The result is a digital integrating gyroscope.

Pulse Quantization Quantization pulse size determines quantization error, and smaller quantization levels are preferred. The feedback pulse quantization size also has an effect on outer control loops, such as those used for nulling the east gyro output to align a gimbaled IMU in heading. When the east gyro output is close to being nulled and its pulse rate approaches zero, quantization pulse size will determine how long one has to wait for an LSB of the gyro output.

9.1.3.4 Torque Feedback Gyroscopic Accelerometers These use a torque feedback loop to keep the momentum wheel rotation axis in a gyroscopic accelerometer from moving relative to the instrument housing. In the pulse integrating gyroscopic accelerometer (PIGA), the feedback torque is delivered in repeatable pulses. Each pulse then represents a fixed velocity change δν along the input acceleration axis, and the net velocity change during a fixed time interval Δt will be proportional to the pulse count in that period.

Nulling the outputs of the north and east accelerometers of a gimbaled IMU during leveling is affected by pulse quantization the same way that nulling the east gyro outputs is influenced by quantization (see "Pulse Quantization" above).

9.1.3.5 Force Feedback Accelerometers Except for gyroscopic accelerometers, all other practical accelerometers measure (in various ways) the specific force required to make a proof mass follow the motions of the host vehicle.³

Pendulous Accelerometers One of the design challenges for accelerometers is how to support a proof mass rigidly in two dimensions and allow it to be completely free in the third dimension. Pendulous accelerometers use a hinge to support the proof mass in two dimensions, as illustrated in Fig. 9.7a, so that it is free to move only in the input axis direction, normal to the "paddle" surface. This design requires an external supporting force to keep the proof mass from moving in that direction, and the force required to do it will be proportional to the acceleration that would otherwise be disturbing the proof mass.

Electromagnetic Accelerometer (EMA) Electromagnetic accelerometers (EMAs) are pendulous accelerometers using electromagnetic force to keep the paddle from moving. A common design uses a voice coil attached to the paddle, as illustrated in Fig. 9.8. Current through the voice coil provides the force on the proof mass to keep the paddle centered in the instrument enclosure. This is similar to the speaker cone drive in permanent magnet speakers, with the magnetic flux through the coils provided by permanent magnets. The coil current is controlled through a feedback servo loop including a paddle position sensor such as a capacitance pickoff. The current in this feedback loop through the voice coil will be proportional to the disturbing acceleration.

Integrating Accelerometers For pulse-integrating accelerometers, the feedback current is supplied in discrete pulses with very repeatable shapes, so that each pulse is proportional to a fixed change in velocity. An up/down counter keeps

³This approach was turned inside-out around 1960, when satellites designed to measure low levels of atmospheric drag at the outer edges of the atmosphere used a free-floating proof mass inside the satellite, protected from drag forces, and measured the thrust required to make the satellite follow the drag-free proof mass.

track of the net pulse count between samples of the digitized accelerometer output. The pulse feedback electromagnetic accelerometer is an integrating accelerometer, in that each pulse output corresponds to a constant increment in velocity δν. The electromagnetic accelerometer (EMA) illustrated in Fig. 9.8 is another type of integrating accelerometer, similar to the PIGA, as is the beam accelerometer of Fig. 9.7(b) with SAW strain sensor.